Answers
Answer:
[tex]\text{C. }60[/tex]
Step-by-step explanation:
Question from image:
"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."
Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.
Checkmarks mark where the 1 can be, the x marks where it cannot be.
[tex]\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}[/tex]
Let's start with the first position:
[tex]\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]
There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in [tex]3!=6[/tex] ways. Therefore, there are [tex]4\cdot 6=\boxed{24}[/tex] possible numbers when 1 is the first digit of the number.
Continue this process with the remaining possible positions for 1.
Second position:
[tex]\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}[/tex]
There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in [tex]3!=6[/tex] ways. Therefore, there are [tex]3\cdot 6=\boxed{18}[/tex] possible numbers when 1 is the second digit of the number.
The pattern continues. Next there will be 2 places to place the 2. For each of these, there are [tex]3!=6[/tex] ways to rearrange the remaining 3 digits for a total of [tex]2\cdot 6=\boxed{12}[/tex] possible numbers when 1 is the third digit of the number.
Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still [tex]3!=6[/tex] ways to rearrange the remaining three numbers. Therefore, there are [tex]1\cdot 6=\boxed{6}[/tex] possible numbers when 1 is the fourth digit of the number.
Thus, there are [tex]24+18+12+6=\boxed{60}[/tex] numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.
Related Questions
61/2×(8/9÷13/18)+(3/4) of 31/5
Answers
Answer:
[tex]\frac{10969}{260}[/tex]
Step-by-step explanation:
What is the angular velocity of a point that rotates through
radians in 24 second
What’s the answer?
Answers
Answer:
Option A
Step-by-step explanation:
Angular velocity of an object is defined by,
Angular velocity (w) = [tex]\frac{\triangle \theta}{\triangle t}[/tex]
Here, Δθ = Change in angle of rotation
Δt = Duration or time
In this question Δθ = [tex]\frac{7\pi }{2}[/tex] radians and Δt = 24 seconds
Therefore, angular velocity = [tex]\frac{\frac{7\pi }{2} }{24}[/tex]
= [tex]\frac{7\pi }{48}[/tex] radians per second
Option A is the answer.
Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.
Answers
Answer: To find the average rate of change, evaluate the function at the given points.
Evaluate the difference of the function at the given points.
Divide the difference of the function at the given points with the difference of the given points.
Step-by-step explanation:
The Average of rate is -1.
Everytime it goes up by one the y goes down by 1 so it would be -1.
The average rate of change of the function in the table given is: -1.
What is Average Rate of Chnge of a Function?Average rate of change of a function = change in y / change in x = rise/run.
Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):
Average rate of change of the function = (7 - 5)/(-2 - 0)
Average rate of change of the function = 2/-2
Average rate of change of the function = -1.
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what two numbers add up to 55 and multiply to -375
Answers
Answer:
-6.13406 and 61.13406
Step-by-step explanation:
x + y = 55
x × y = -375
y = 55 - x
x × (55 - x) = -375
55x -x² = -375
x² - 55x - 375 = 0
solution of a quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
a=1
b=-55
c=-375
x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =
= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =
= 5/2 × (11 ± sqrt(181)) =
= 61.13406... or -6.13406...
y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =
= -6.13406... or 61.13406...
solve algebraically for z : 360000 + 102 = 200000 + 104z NEED ANSWER ASAP PLEASE HELP
Answers
Answer:
z = 1539.44230769
Step-by-step explanation:
360000 + 102 = 360102
360102 - 200000 = 160102
160102/104z = 1539.44230769
z = 1539.44230769
Which relationship has a zero slope?
Answers
Answer:
b has zero slop mark me as a brilliant
Which statement is necessarily true if is an altitude to the hypotenuse of right ? A. ≅ B. C. D. ∠BAC ≅ ∠BDC
Answers
Answer:
Step-by-step explanation:
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answers
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
Does this graph represent a function? Why or why not?
Answers
Answer:
B yes, because it pases the vertical line test
hey !! solve it
[tex] \sqrt{44 \times 11} [/tex]
Answers
Step-by-step explanation:
✓44×11
=✓2²×11²
=22
!!!!????!!!!!!
Answer:
22
Step-by-step explanation:
First, multiply 11 and 44
11 × 44 = 484
[tex]\sqrt{484}[/tex] = 22
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Have a great summer :)
Two large parallel metal plates carry opposite charges. They are separated by 85mm. The work done by the field is 6x10-3J and its field exerts on a particle with charge +8µC. Calculate the surface charge density on each plate.
Answers
Answer:
The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].
Step-by-step explanation:
separation, d = 85 mm
Work, W = 6 x 10^-3 J
charge , Q = 8µC
The potential difference is given by
W = q V
[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]
Let the charge on he capacitor is q.
[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]
Yashoda and Ingrid shared a sum of money in the ratio 3:2, respectively. Ingrid
received $1200. What was Yashoda's share?
Answers
Answer:
Yashoda got 1800
Step-by-step explanation:
Yashoda : Ingrid
3 : 2
Ingrid got 1200
Divide this by 2
1200/2 = 600
Multiply each side by 600
Yashoda : Ingrid
3*600 : 2*600
1800 : 1200
Yashoda got 1800
[tex]128^3+272^3 /128^2-128*272+272^2[/tex]
Answers
wait do you want it step by step or just the answer?
the answer is 400
Topic: Modeling exponential functions
Kathy plans to purchase a car that depreciates
(loses value) at a rate of 14% per year. The initial
cost of the car is $21,000. Which equation
represents the value, v, of the car after 3 years?
1) v = 21,000(0.14)
2) v = 21,000(0.86)
3) v= 21,000(1.14)
4) v= 21,000(0.86)(3)
Answers
Answer:
Step-by-step explanation:
The standard form equation for this type of problem is
[tex]y=a(b)^x[/tex] where a is the initial value, b is the rate of depreciation, and x is the number of years in question. Because the value of the car is going down, b can also be written as (1 - r) where r is the rate of depreciation. For us, then, the equation will look like this:
[tex]y=a(1-r)^x[/tex] and filling in:
[tex]y=21000(1-.14)^3[/tex] which in simplified form is
[tex]y=21000(.86)^3[/tex] which I'm assuming is how choice 4 should look.
hey guys ... just want to make this answer sure... subtract 2x²+3x+6 from 3x²+5x+7=? A)x²+2x+1 or
B)x²+8x+13
Answers
Answer:
answer is A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
3x² + 5x + 7 - (2x² + 3x + 6) ← distribute terms in parenthesis by - 1
= 3x² + 5x + 7 - 2x² - 3x - 6 ← collect like terms
= x² + 2x + 1 → A
Given 15=3(2x+4)−3
Prove x=1
Complete the proof. Provide reasons for 1-6 below. Make sure to number your answers.
Answers
we start with the inside of the para thesis so multiply 2•1 which gives us 2 and we add 4 which gives us 6
now we have 15=3(6)-3
we multiply the 3 and 6 and we get 18
Now we have 15=18-3 so we subtract 18-3 and we get 15
15=15 is the product
The value of x in the expression 15 = 3(2x + 4) - 3 is 1.
What is expression?A number, a variable, or a combination of numbers and variables and operation symbols is called expression.
According to the given question.
We have an expression
[tex]15 = 3(2x+ 4) -3[/tex]
Solve the above expression for x.
Step 1: open the parentheses
[tex]15 = 3(2x + 4) -3[/tex]
⇒ [tex]15 = 6x + 12 -3[/tex]
Step 2: simplify the above expression.
[tex]15 = 6x + 9[/tex]
Step 3: subtract 9 to the both the sides
[tex]15 - 9 = 6x + 9 -9[/tex]
⇒[tex]6 = 6x[/tex]
Step 4: Divide both the sides by 4
⇒ [tex]\frac{6}{6} =\frac{6x}{6}[/tex]
⇒ [tex]x = 1[/tex]
Hence, we proved that x = 1 for the above expression.
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During a sale, a store offered 35% discount on a particular couch that was originally priced at $390. After the sale, the discount price of the camera was increased by 35%. What was the price of the couch after this increase? Round to the nearest cent.
Answers
Answer:
$342.23
Step-by-step explanation:
35/100 x $390 = $136.50
Price of couch after 35% discount
= $390 - $136.50
= $253.50
35/100 x $253.50 = $88.725
Price of couch after the 35% increase
= $253.50 + $88.725
= $342.225
= $342.23 (round off to nearest cents)
A general formula for a parabola is y2=4px.
What is the value of p in the equation y2=−4x?
P=−4
P=−1
P=1
P=4
Answers
Answer:
P = -1
Step-by-step explanation:
-1 x 4 = -4
The solution is : p= -1, is the value of p in the equation y^2=−4x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
Explanation:
We have been given parabola along positive side of x-axis with equation
y² = 4px
and, y² = -4x
after equating the values of y² we will get
4px =-4x
Divide each term by x on both left hand side and right hand side we will get
4p= -4
Now, divide each term by 4 on both left hand side and right hand side we will get the final result p=-1
Hence, The solution is : p= -1, is the value of p in the equation y^2=−4x.
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Find C. See the image below
Answers
Answer:
55 degrees
Step-by-step explanation:
First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.
Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35
We can then use the fact that a triangle adds up to 180 degrees here to get
35+90+C=180
C=55 degrees
Sam bought a computer and printer for ₹ 1,15,499. The cost of the computer was ₹ 85,789. What was the cost of the printer?
₹ 29,710
₹ 2,01,228
₹9,73,389
Answers
Answer:
₹29,710
Step-by-step explanation:
We minus ₹ 85,789 from ₹ 1,15,499 to get ₹ 29,710
A pyramid with a triangular base has a volume of 50cm³. If the base and the height of the triangular base are 5cm and 8cm respectively, find the height of the pyramid ?
Answers
Answer:
h = 7.5 cm
Step-by-step explanation:
Firstly, we find the area of the triangular base
Mathematically, we have the area of a triangle as;
A = 1/2 * b * h
A = 1/2 * 5 * 8 = 20 cm^2
Mathematically, we have the formula as;
V= 1/3 * A * h
A is base area and h is height
50 = 1/3 * 20 * h
20h = 3 * 50
20h = 150
h = 150/20
h = 7.5 cm
The graph below shows the solution to which system of inequalities?
Answers
Answer:
A
Step-by-step explanation:
Help please!
Brainliest + 20 points
Answers
Answer:
im not sure but pls gimme brainlyist bc im a dum dum
Step-by-step explanation:
PLEASE HELP - WILL MARK BRAINLIEST w/ explanation (see attachment)
Answers
Answer:
∠ DOC = 26°
Step-by-step explanation:
The secant- secant angle DOC is half the difference of the intercepted arcs, that is
∠ DOC = [tex]\frac{1}{2}[/tex] (AB - CD) = [tex]\frac{1}{2}[/tex] (82 - 30)° = 0.5 × 52° = 26°
Please please help me
Answers
Answer:
may be the answer is 1000.not sure.
Answer:
answer is c 1600
hope it helps
I NEED HELP PLZ it is very much appreciated
Answers
Answer:
C
Step-by-step explanation:
average, average, average
if there is one dot to the right that is far away and 3 dots to the left that are close to the like, estimated distance of the right dot would be 3 and the total distance sum of each dot to the left is 3, so the line would be between the 1 right dot and 3 left dots
Answer:
D
Step-by-step explanation:
D has three dots near to the line
APB is parallel to CTRD. PQRT is a quadrilateral. work out the size of the angle marked x you must show your working
Answers
Answer: X would be 84 degrees.
Step-by-step explanation: APB is a straight angle, which adds up to 180 degrees. TPQ is 90 degrees, and QPB is 32 degrees, so 180-90-32=58. APT is 58 degrees. APT and PTR are alternate interior angles, therefore they have the same angle measure. So PTR is also 58 degrees. A quadrilateral adds up to 360 degrees, so add up the three known angles in the quadrilateral, 58+90+128, which gives you 276 degrees. 360-276=84 degrees, therefore X would be 84 degrees.
(HELP FAST TIMED)Which polynomial is prime x^3+3x^3+2x+6
Answers
Answer:
the third one
Step-by-step explanation:
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree.
the third one is the answer
E)
The parallelogram WXYZ belwo is a rhombus. Find the measure of
angles 1, 2, 3, 4 and 5 given that angle WZY is 60°
w
2
3
1
4
Answer:
60
Answers
Answer:
1. 60°
2. 60°
3. 30°
4. 30°
5. 30°
Step-by-step explanation:
to find angleXYZ suntract 180 from 60
angle ZWX=120°
Angle WXY=60°
The diagnals divide the inteesections in half
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.
Answers
Answer: 7 red marbles.
Step-by-step explanation:
Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.
Then the number of red marbles will be:
= 1/9 × 63
= 7
There are 7 red marbles
The number if blue marbles will be:
= 63 - 7
= 56 blue marbles