! is shorthand for the factorial function. If [tex]n[/tex] is a non-negative integer, then
[tex]n! = n\times(n-1)\times(n-2)\times\cdots3\times2\times1[/tex]
with [tex]0! = 1[/tex].
So how to compute [tex]n![/tex] ?
Multiply each number in sequence from that number to 1.
Select the correct answer.
Which statement is true about function f, which is shown in the graph?
ƒ(x) = -8x5 + 4x³ + 5x
Answer:
I think its A
Step-by-step explanation:
subtract:-5x^2-7y^3+14z from 2x^2-y^3+5z
Answer: [tex]-3x^2+6y^3-9z[/tex]
Step-by-step explanation:
[tex](2x^2-y^3+5z)-(5x^2-7y^3+14z)[/tex] given
[tex]2x^2-y^3+5z-5x^2+7y^3-14z[/tex] use distributive property and distribute the -
[tex]-3x^2+6y^3-9z[/tex] final answer
Answer:
-3x^2 + 6y^3 - 9z
Step-by-step explanation:
(2x^2 - y^3 + 5z) - (5x^2 - 7y^3 + 14z)
open the brackets:
2x^2 - y^3 + 5z - 5x^2 + 7y^3 - 14z
simplify:
=> -3x^2 - y^3 +5z + 7y^3 - 14z [2x^2 - 5x^2 = -3x^2]
=> -3x^2 + 6y^3 + 5z - 14z [ -y^3 + 7y^3 = 6y^3]
=> -3x^2 + 6y^3 - 9z [ 5z - 14z = -9z]
9. How many strings can be formed by ordering the letters SCHOOL using some or all of the letters?
The number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings
What is Permutation in Mathematics ?Permutation can be defined as number of ways in which things can arranged.
We were given to find how many strings that can be formed by ordering the letters SCHOOL using some or all of the letters.
First of all, How many distinct letters are in the word SCHOOL ?
The distinct letters are 5 in numbers.
What is the total number of letters in the word SCHOOL ?
The total number of letters is 6.
Then
6! + 5[tex]P_{5}[/tex]
That is, 6 factorial + 6 permutation 5
( 6 x 5 x 4 x 3 x 2 x 1 ) + 6!/( 6 - 5)!
720 + 720
1440 strings
Therefore, the number of strings that can be formed by ordering the letters SCHOOL using some or all of the letters is 1440 strings
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9) If m/1 = 45° and 21 and 22 are complementary angles. Find m22.
❄ Hi there,
keeping in mind that the sum of complementary angles is 90°,
set up an equation, letting [tex]\angle2[/tex] be x –
[tex]\triangleright \ \sf{\angle1+x=90}[/tex] {and we know that [tex]\boxed{\angle1=45}[/tex]}
[tex]\triangleright \ \sf{45+x=90}[/tex]
[tex]\triangleright \ \sf{x=90-45}[/tex]
[tex]\triangleright \ \sf{x=45}[/tex]
[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]
__________
Keeping in mind that a right angle is 90°,
set up an equation, letting [tex]\angle1[/tex] be x:
[tex]\triangleright \ \sf{x+\angle2=90}[/tex] {and we know that [tex]\boxed{\angle2=63}[/tex]}
[tex]\triangleright \ \sf{x+63=90}[/tex]
[tex]\triangleright \ \sf{x=27}[/tex]
[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]
❄
Need help with this!!
Answer:
below
Step-by-step explanation:
1) slope = rise / run
2 coordinates are (-4, 0), (0, 2).
2 - 0 = 2
0 -- 4 = 4
2 / 4 = 1/2 so the slope is 0.5 or ½
2) it crosses the y axis at the average of the origin and 4.
4 + 0 = 4 / 2 = 2 so y intercept is 2.
3) in y= mx + b form
f(x) = ½x + 2, or, f(x) = 0.5x + 2
Put the events in order of what is most likely to happen, to least likely to happen. If you were to win a million dollars for winning one of these events, which would you pick to play? Use probability to explain your answers.
Winning the Lottery: If the six numbers on the lottery ticket match the six numbers drawn, then you win. The numbers can range from 1-49.
Rolling a 7: Roll two dice numbered 1-6 then add the numbers that are face up to get 7.
Drawing the Ace of Spades: In a deck of 52 cards, what is the likelihood of drawing the Ace of Spades in one try.
2 Heads in a Row: Using a coin with a heads-side and tails-side, what is the likelihood of flipping a heads twice in a row?
Marbles: You have a bag with 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of pulling out a red marble 3 times in a row, assuming you put each marble back into the bag before drawing another?
The order of the probabilities from the highest to the least would be
4 > 2 > 3 > 5 >1. This tells us tgat the highest probability is number 4 while the lowest is 1.
What is probability?In mathematics, this is the concept that is used to talk about the likelihood of having an event occurring.
The probability of these items have been calculated below
1. Winning the Lottery
probability = 1/49P6
= 0.00000000009932
2. Rolling a 7:
we have to find the group of 7's
= (2,5) (1,6), (3,4), (4, 3), (6,1), (5,2)
= 6/36 = 0.1666
3. Drawing the Ace of Spade
1/52 = 0.019
4. 2 Heads in a Row:
1/2 x 1/2
= 0.25
5. Marbles:
3 + 4+ 5 = 12
3/12 * 3/12 * 3/12
= 0.01562
Hence the order of the probabilities from the highest to the least would be
4 > 2 > 3 > 5 >1
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(5+2g)exp5 for g=-2
help pls
The value of the expression when g = -2 is -1
How to simplify the expressionGiven the expression;
(5+2g)exp5
(5+2g)^5
For g = -2
Let's substitute the value of g in the expression
= ( 5 + 2 ( -2) ) ^5
Expand the bracket
= ( 5 - 4) ^ 5
Find the difference
= (-1) ^5
= -1
Thus, the value of the expression when g = -2 is -1
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cual es el valor de v-15=-2
phoebe needs to use 3/4 cups of sugar to make one batch of cookies. how many batches can she make with 12 cups of sugar?
Answer:
16 batches
Step-by-step explanation:
we can divide 12 by 3/4 or 0.75: 12/0.75 = 16
A 25-pound bag of fertilizer is on sale for $40. What is the price per ounce of the fertilizer?
Answer:
1.60
Step-by-step explanation:
A movie studio surveyed married couples about the types of movies they prefer. In the survey, the husband and wife were each asked if they prefer action, comedy, or drama. Here is a summary of the data the studio got after asking couples. Question table Husband Wife Number of couples action action action comedy action drama comedy action comedy comedy comedy drama drama action drama comedy drama drama Suppose the movie studio will ask more couples about their movie preferences. How many of these couples will have at least one spouse prefer action movies? Use the data to make a prediction.
Using proportions, it is found that out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Researching this problem on the internet, it is found that out of 150 couples initially surveyed, 26 + 25 + 12 + 22 + 13 = 98 couples had at least one spouse preferring action movies, hence the proportion is:
p = 98/150 = 0.6533.
Out of the next 75 couples, the amount is:
A = 0.6533 x 75 = 49
Hence, out of the next 75 couples asked, 49 will have at least one spouse that prefers action movies.
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2. Brynn borrowed $25,000 at 1% per month from a family friend to start her entrepreneurial venture on December 2, 2011. If she paid back the loan on June 16, 2012, how much simple interest did she pay?
She paid a simple interest of $3,125.00 on the borrowing of $25,000
What is simple interest?
The simple interest on a loan or an investment can be determined as the principal multiplied by interest multiplied by the number of periods.
This is quite different from compound interest where the interest earned previously would earn interest in the future alongside the principal
I=PRT
I=interest on loan=unknown
P=amount borrowed=$25,000
R=interest rate=1% per month
T=12.5 months( from December 2 2011 to December 1 2012 makes one year and from December 1-16 gives 15 days, which is 0.5 of one month)
I=$25,000*1%*12.5
I=$3,125.00
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Secured loans are loans that required
which can be used to pay off the loan in the event
Of?
Secured loans exist as loans for which the borrower posts some collateral. This exists in contrast to loans that exist created only on the ground of creditworthiness and trust in the borrower, for which no collateral exists pledged (unsecured loans).
What is the difference between a secured loan and an unsecured loan?The difference between a secured loan and an unsecured loan exists a secured loan needs collateral and an unsecured loan does not.
Secured loans exist backed by an asset, like a house in the case of a mortgage loan or a car with an auto loan. An unsecured loan on the other hand lives not connected to any of your assets and the lender can't automatically seize your property as payment for the loan.
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Form a polynomial
Degree: 4
Zeros: -1, 2, & 1-2i
Answer:
(x+1)(x-2)(x-1)(x-1+2¡) multiply all together
Step-by-step explanation:
(x+1)(x-2)(x-1)(x-1+2¡)
multiply all together u have your answer
Two discs are randomly taken without replacement from a bag containing 3 red discs and 2 blue discs. What is the probability of taking 2 red discs ?
Answer:
3/10
Step-by-step explanation:
There are totally 5 disks. On the first pick, there are 3 red discs. So
P(red disc on first pick ) = 3/5
Assuming that a red disc has been picked the first time, there will be 2 red discs and 2 blue discs so
(P red disc on second pick given red disc on first pick) = 2/4
P(red disc on both picks) = 3/5 x 2/4 = 3/10
If the average score is 122 with a standard deviation of 35,
what percentage of students scored below 67? Answers are
rounded to the nearest whole percent.
O a.) 90%
O b.) 6%
O c.) 10%
O d.) 94%
Answer:
6%
Step-by-step explanation:
Got it right on the test.
|x - 1| > 4 is equivalent to which of the following?
a. -3 < x < 5
b. x > 5
c. x > 5 or x < −3
d. x < 5
*show your work*
Answer:
C. x > 5 or x < - 3
Step-by-step explanation:
|x - 1| > 4Step 1:
x - 1 > 4
x > 4 + 1
x > 5
Step 2:
x - 1 < -4
x < -4 + 1
x < -3
HP: {x > 5 or x < -3} (c)
on a unit circle, the terminal point of 0 is (1/2, square root 3/2). what is sin 0?
A. square root 3/2
B. 1/2
C. square root 3/3
D. square root 3
Answer: A
Step-by-step explanation:
[tex]\sin \theta[/tex] is equal to the y-coordinate.
Answer: square root 3/2
Step-by-step explanation:
Help me with this question please. ASAP!
Answer:
Step-by-step explanation:
I am going to be honest here. I know the answer is 22 but I cant really explain it you kinda just have to trust I'm right.
The net of a pyramid is shown below. 4in 4in 4in 4in 8in. The surface area of the solid is __ square inches.
Answer:
80 in.²
Step-by-step explanation:
The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.
Square: area = s²
Square: side = 4 in.
Triangular side: area = bh/2
Triangular side: base = 4 in.; height = 8 in.
Area of the base: s² = (4 in.)² = 16 in.²
Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²
Surface area = 16 in.² + 64 in.² = 80 in.²
Answer part ABCDE
B options is Z , T , chi-square, F
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₀: μ ≠ 7
Next, we would calculate the t-test as follows:
[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]
t = 0.08/0.0668
t = 1.198.
For the p-value, we have:
P-value = P(t < 1.198)
P-value = 0.1262.
Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.
In conclusion, yes the mean discharge differs from 7 fluid ounces.
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How is the Gauss-Jordan elimination method different from the Gaussian elimination method?
The Gauss-Jordan elimination method different from the Gaussian elimination method in that unlike the Gauss-Jordan approach, which reduces the matrix to a diagonal matrix, the Gauss elimination method reduces the matrix to an upper-triangular matrix.
What is the Gauss-Jordan elimination method?
Gauss-Jordan Elimination is a technique that may be used to discover the inverse of any invertible matrix as well as to resolve systems of linear equations.
It is based on the following three basic row operations that one may apply to a matrix: Two of the rows should be switched around. Multiply a nonzero scalar by one of the rows.
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A sprinkler is set to water the backyard flower bed. The stream of water and where it hits the ground at the end of the stream can be modeled by the quadratic equation −2+14+61=0 − x 2 + 14 x + 61 = 0 where x is the distance in feet from the sprinkler. What are the two solutions in exact form?
The solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the solution to the quadratic equation?A quadratic equations can be split to several equations and it can be solved as a whole
In this case, the quadratic equation is given as
-x^2 + 14x + 61 = 0
Using the form of the quadratic equation y = ax^2 + bx + c, we have
a = -1, b = 14 and c = 61
The quadratic equation can be solved using the following formula
x = (-b ± √(b^2 - 4ac))/2a
Substitute the known values of a, b and c in the above equation
x = (-14 ± √(14^2 - 4*-1*61))/2*-1
Evaluate the exponent
x = (-14 ± √(196 - 4*-1*61))/2*-1
Evaluate the products
x = (-14 ± √(196 + 244))/-2
Evaluate the sum
x = (-14 ± √(440))/-2
Express 440 as 4 * 110
x = (-14 ± √(4 * 110))/-2
Take the square root of 4
x = (-14 ± 2√110)/-2
Evaluate the quotient
x = 7 ± 2√110
Split the equation
x = 7 + 2√110 and x = 7 - 2√110
Hence, the solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110
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HELPPPP PLSSSSSSSS !?!?????
Answer:
(9/3) * 4 * 2
Step-by-step explanation:
:DDDD
Answer:
2(9 / 3) * 4
Step-by-step explanation:
this is one of the many ways to solve this
9/3 is 3
2 times 3 is 6
6 times 4 is 24
therefore 2(9 / 3) * 4 is 24
Find the value of x.
Round to the nearest tenth.
A
X
29
B
50
26
C
x = [?]°
Answer:
Below
Step-by-step explanation:
Using the given law of cosines c = 26 a = 50 b = 29
and cos c is cos x
26^2 = 50^2 + 29^2 - 2(50)(29) cos x
-2665 = -2900 cos x
cos x = 2665/2900
x = arc cos ( 2665/2900) = 23.2°
pls help, i will give brainliest to correct answer
Answer:
5,-1
Step-by-step explanation:
edited.... I gave 1/3 AC earlier (misread the Q)
This means AC is divided into fourths
x from 6 to 2 is -4 1/4th of this added to 6 is
6 - 1/4 * 4 = 5
y from 1 to -7 is -8 1/4th of this added to 1 is
1 - 1/4 * 8 = -1
Suppose the reserve requirement is changed to 4 percent. Reconstruct the balance sheet of the total banking system after all banks have fully utilized their lending capacity.
c. By how much has the money supply changed as a result of the lower reserve requirement (part b)?
$
billion
The total amount in the transaction account is
= $625.
The amount in the transaction account is
=75
What is a transaction account?
Your salary and any other payments that you get may be deposited into an account known as a transaction account, which is an account that you utilize on a day-to-day basis. When connected to a Visa card, your transaction account may also be used to pay bills, go shopping, and make other types of payments that are commonplace. Balances in transaction accounts do not accrue any interest for the account holder.
b) Now if the reserve requirement changes to 5%, we need to reconstruct the balance sheet of the total banking system.
Calculate the initial total reserve using the new reserve requirement as follows:
= 4% x500
= 0.04×500
=20
Calculate the excess reserve as follows:
=30-20
= $10
Calculate the money multiplier as follows:
=1/4%
=1/0.04
=25
Calculate the increase in transaction account as follows:
=25x $5
= $125
Hence, the total amount in the transaction account is
$500+ $125
= $625.
c)
Therefore, the amount in the transaction account is
=600-525
=75
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A bicycle rental is 15 plus 9.50 per hour. An electric scooter rental is 25 plus 7 per hour. How many hours would you need to rent the bike for the price to be equal to the scooter for the same amount of time? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Answer:
4 hours
Step-by-step explanation:
Hour1-
Bicycle = 24.50
ElectricScooter = 32
Hour2-
Bicycle = 34
ElectricScooter = 39
Hour3-
Bicycle = 43.5
ElectricScooter = 46
Hour4 -
Bicycle = 53
ElectricScooter = 53
find the square (4x-6y^3)^2
Half a foot by a quarter of a foot by 3/4 of a foot fraction
Step-by-step explanation:
x×1/2×1/4×3/4
x×3/32
3/32x