SOLUTION
This is a permutation problem.
a) To find the number of possible two digits codes
[tex]^6P_2[/tex][tex]^6P_2=\frac{6!}{(6-2)!}[/tex][tex]\begin{gathered} =\frac{6!}{4!} \\ =\frac{720}{24} \\ =30\text{ ways} \end{gathered}[/tex]There are 30 possible two-digit codes pattern.
b) To find the number of three digits codes
[tex]\begin{gathered} ^6P_3=\text{ }\frac{6!}{(6-3)!} \\ \text{ =}\frac{6!}{3!} \\ \text{ =}\frac{720}{6} \\ \text{ = 120 ways} \end{gathered}[/tex]There are 120 possible three-digit codes pattern.
Any other pattern can be calculated using
[tex]\begin{gathered} ^6P_r \\ \text{where r is the number of digits code (1,2,3,4,5,6)} \end{gathered}[/tex]So to predict the number of possible five-digit codes will be:
[tex]^6P_5[/tex][tex]\begin{gathered} =\frac{6!}{(6-5)!} \\ =\frac{6!}{1!} \\ =720\text{ways} \end{gathered}[/tex]There are 720 different possible five-digit codes
the answer of this question is 720 ways
x+y+z=12x+4y+2z = -6-x+9y-3z=-49 Can someone please help me solve this system of equation?
Let's begin by listing out the information given to us:
[tex]\begin{gathered} x+y+z=1 \\ 2x+4y+2z=-6 \\ -x+9y-3z=-49 \end{gathered}[/tex]To solve this 3 variable equation, let's eliminate one of the variables
add equation 1 & 3, we have:
[tex]\begin{gathered} x-x+y+9y+z-3z=1-49 \\ 10y-2z=-48 \\ Make\text{ z the }subject,we\text{ have:} \\ -2z=-10y-48 \\ divide\text{ through by -2} \\ z=5y+24 \end{gathered}[/tex]Substitute z into equation 1, 2 & 3
[tex]\begin{gathered} x+y+5y+24=1 \\ x+6y=1-24 \\ x+6y=-23 \end{gathered}[/tex][tex]\begin{gathered} 2x+4y+2\left(5y+24\right)=-6 \\ 2x+4y+10y+48=-6 \\ 2x+14y=-6-48 \\ 2x+14y=-54 \end{gathered}[/tex][tex]\begin{gathered} -x+9y-3\left(5y+24\right)=-49 \\ -x+9y-15y-72=-49 \\ -x-6y=-49+72 \\ -x-6y=23 \end{gathered}[/tex]Solve as a simultaneous equation, we have:
[tex]\begin{gathered} x+6y=-23 \\ 2x+14y=-54 \\ \text{Multiply the top equation by 2 \& subtract it from the bottom equation} \\ 2\cdot(x+6y=-23)\Rightarrow2x+12y=-46 \\ 2x+14y=-54-(2x+12y=-46) \\ 2x-2x+14y-12y=-54-(-46) \\ 2y=-8 \\ y=-4 \end{gathered}[/tex]Substitute y = -4 into x + 6y = -23, we have:
[tex]\begin{gathered} x+6\left(-4\right)=-23 \\ x-24=-23 \\ x=-23+24 \\ x=1 \end{gathered}[/tex]Substitute y = -4 into z = 5y + 24, we have:
[tex]\begin{gathered} z=5\left(-4\right)+24 \\ z=-20+24 \\ z=4 \end{gathered}[/tex]Write an equation for the inverse variation represented by the table.x -3, -1, 1/2, 2/3y 4, 12, -24, -18
By definition, Inverse variation equations have the following form:
[tex]y=\frac{k}{x}[/tex]Where "k" is the Constant of variation.
Given the values shown in the table, you can find the value of "k":
- Choose a point from the table. This could be:
[tex](-3,4)[/tex]Notice that:
[tex]\begin{gathered} x=-3 \\ y=4 \end{gathered}[/tex]- Substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{-3} \\ \\ (4)(-3)=k \\ k=-12 \end{gathered}[/tex]Knowing the Constant of variation, you can write the following equation:
[tex]y=\frac{-12}{x}[/tex]The answer is:
[tex]y=\frac{-12}{x}[/tex]I need help with part b, c ii, and d
Recall that:
[tex]\text{average speed=}\frac{total\text{ distance}}{total\text{ time}}.[/tex](b) Since Marcos traveled for 2 hours and 17 minutes a distance of 155 miles, then Marco's average speed for the 155 miles trip is:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](c ii) Since Devon also traveled the 155 miles in 2hours and 17 minutes but at a constant speed, then the constant speed at which he traveled is equal to his average speed, which is equal to:
[tex]\frac{155mi}{(2+\frac{17}{60})h}=\frac{155mi}{\frac{137}{60}h}=\frac{9300}{137}miles\text{ per hour}\approx67.89miles\text{ per hour.}[/tex](d) Marco needs to drive 2 miles in 5 minutes to be able to complete the 155 miles trip in 2 hours and 17 minutes, then he must drive at a constant speed of:
[tex]\frac{2mi}{5\min }=\frac{2mi}{\frac{5}{60}h}=\frac{120mi}{5h}=24\text{miles per hour.}[/tex]Answer:
(b) 67.89 miles per hour.
(c ii) 67.89 miles per hour.
(d) 24 miles per hour.
find the length of the gray arc in terms of pi
Given
a: angle
a = 60
r: radius
r = 3
Procedure
The length of an arc depends on the radius of a circle and the central angle θ
[tex]\begin{gathered} s=\theta r \\ s=\frac{1}{3}\pi\cdot3 \\ s=\pi \end{gathered}[/tex]The answer would be s = pi
A If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
If y = x + 2 and y = -2x + 8, what do you know about x + 2 and -2x + 8?
we have
y=x+2
y=-2x+8
Solve the system of equations
equate both equations
x+2=-2x+8
x+2x=8-2
3x=6
x=2
Find the value of y
y=(2)+2
y=4
the solution is (2,4)
that means
(2,4) is a common point , that satisfy both equations
What is the reference angle for 289°? A. 71° B. 19° C. 11° D. 89°
Given:
Angle θ=289°.
For angles from 270° to 360°, the reference angle can be calculated by subtracting the given angle from 360° .
The reference angle of θ can be calculated as:
[tex]\begin{gathered} 360\degree-\theta=360\degree-289\degree \\ =71\degree \end{gathered}[/tex]Therefore, reference angle of 289° is 71°.
Find the distance between the (3,3) and (10,3) coordinates and write the result in the empty box. plsss helppppppppppp
Answer: 7
Step-by-step explanation:
Distance (d) = √(10 - 3)2 + (3 - 3)2
=√(7)2 + (0)2
=√49
=7
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43524
[tex]\frac{d32423657565\mod{43242}}{dx}_{564564}[/tex]4tet
54
Simplify the expression -3n-8-7n + 17
We simplify by combining like terms
therefore
[tex]\begin{gathered} -3n-8-7n+17 \\ =-3n-7n-8+17 \\ =-10n+9 \end{gathered}[/tex]Please help with #4. The directions are with the pic below.
sphere: 12 pounds
cylinder: 108 pounds
Explanation:
Data:
. From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
. From balance B:
3 cubes = 5 spheres
Since 1 cube = 20 pounds
=> From balance B:
3 cubes * 20 pounds = 5 spheres
60 pounds = 5 sphere
60 / 5 = 5 / 5
12 pounds = 1 sphere
=> From balance A:
3 cubes + 1 sphere = 1 cylinder + 2 spheres
3 spheres * 20 pounds + 1 sphere * 12 pounds = 1 cylinder + 2 spheres * 12 pounds
120 pounds + 12 pounds = 1 cylinder + 24 pounds
132 pounds = 1 cylinder + 24 pounds
132 pounds - 24 pounds = 1 cylinder + 24 pounds - 24 pounds
108 pounds = 1 cylinder
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!!!!!
Answer:
Option 2
Step-by-step explanation:
hope this helps
In the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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5000 + 300 + 8 in standard form
The given arithmetic expression is:
5000 + 300 + 8
This sum can be computed as shown below:
Therefore, 5000 + 300 + 8 = 5308
Convert 5308 to standard form
[tex]5308\text{ = 5.308 }\times10^3[/tex]
Use log, 20.356, log, 3 0.503, and log, 5 0.835 to approximate the value of the given logarithm to 3 decimal places. Assume that b>0 and b + 1.
log, 625
X
A
Answer:
3.34
Step-by-step explanation:
625 is 5^4
Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],
log_b(5^4) = 4*log_b(5)
4*0.835 = 3.34
identify the rate, base and portion.What percent of 126 is 44.1
In this problem, we have that
Base=126 (represents the 100%)
Portion=44.1
Find out the percentage
100/126=x/44.1
solve for x
x=(100/126)*44.1
x=35%
The percentage is 35%
Determine whether point (4, -3) lies on the line with equation y = -2x + 5 by using substitution and by graphing.
The equation of the line is:
[tex]y=-2x+5[/tex]And we need to find if the point (4,-3) lies on the line.
To solve by using substitution, we need to remember that an ordered pair always has the form (x, y) --> the first number is the x-value, and the second number is the y-value.
In this case (4,-3):
x=4
and
y=-3
So now, we substitute the x value into the equation, and if the y-value we get in return is -3 --> the point lies on the line. If not, the point does not lie on the line.
[tex]\begin{gathered} y=-2x+5 \\ \text{Substituting x=4} \\ y=-2(4)+5 \\ y=-8+5 \\ y=-3 \end{gathered}[/tex]We do get -3 as the y-value which matches with the indicated y value of the point.
Thus, by substitution, we confirm that the point lies on the line.
To check the result by graphing, we need to graph the line. The graph of the line is shown in the following image:
In the image, we can see that the marked point on the line is the point we were looking for (4,-3). So we confirm by the graphing method that the point lies on the line.
Answer: It is confirmed by substitution and graphing that the point (4,-3) lies on the line.
A focus group of 12 people is to be chosen randomly from among 24 right-handed people and 5 left-handed people. In order to find the probability that 3 of the people chosen are right-handed, you should use
Let 1 and 2 mean that a person is right-handed or left-handed, respectively.
Consider the probability space as the different groups of 12 people that can be formed with the 29 total people. {(1,1,1,1,1,...1),(2,1,1,1,1,...,1),...}
We need to use the binomial distribution in order to find the answer.
Consider X to be the number of right-handed people in the group.
The probability of X=3 is then:
[tex]Pr(X=3)=\text{ binomial coefficien(}12,3\text{)}(\frac{24}{29})^3(1-\frac{24}{29})^{12-3}[/tex]We used the formula
[tex]\begin{gathered} Pr(X=k)=\text{ binomial coefficient(n,k)}\cdot p^k(1-p)^{n-k} \\ \text{where } \\ k=3 \\ n=12 \\ p=\frac{24}{29} \end{gathered}[/tex]Finally, we need to simplify the expression, as shown below
[tex]\Rightarrow P(X=3)=220(\frac{24}{29})^3(\frac{5}{29})^9=0.0000167[/tex]This is the answer one obtains using the binomial distribution; nevertheless, the actual probability is equal to zero because it is not possible to form a group of 12 people that only contains 3 right-handed people as there are only 5 left-handed people (3+5=8).
Jamal buys a water heater online for $861. If shipping and handling area additional 11% of the price, how many shipping and handling will Jamal pay?
Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.
The equation can be written as d=30g
What is an equation?
An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.
Tyrone's car can travel about 30 miles for each gallon
So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.
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Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you'll find out. Consider AABC, whose vertices are A (2,1), B (3, 3), and C (1,6) ; let AC represent the base of the triangle. Part A Find the equation of the line passing through B and perpendicular to AC.
Answer: y = x/5 + 12/5
Explanation:
The first step is to find the equation of line AC
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept.
The formula for calculating slope of a line is expressed as
m = (y2 - y1)/(x2 - x1)
Considering line AC with points, A(2, 1) and C(1, 6),
x1 = 2, y1 = 1
x2 = 1, y2 = 6
m = (6 - 1)/(1 - 2) = 5/- 1 = - 5
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5
Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5
We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have
3 = 1/5 * 3 + c
3 = 3/5 + c
c = 3 - 3/5
c = 12/5
By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is
y = x/5 + 12/5
Consider the equation cos(2t) = 0.8. Find the smallest positive solution in radians and round your answer to 2 decimal places.
Given:
cos(2t) = 0.8
Take the cos⁻' of both-side of the equation.
cos⁻' cos(2t) = cos⁻'(0.8)
2t = cos⁻'(0.8)
Calculate the value of the right- hand side with your calculator in radians.
2t =0.6435
Divide both-side of the equation by 2
t ≈ 0.32
the figure below has a point marked with a large. First translate to figure 4 units up then give the coordinates of the mark point in the original figure in the final figure.:
Large point coordinates (original)= (1,-4)
To obtain the coordinates of the new point, add 4 to the y coordinate.
(1,-4+4) = (1,0)
I'm trying to simplify negative 5/8 divided by negative 3/4 how do I do that?
20g of radioactive substance decays by 1/2 of it's original
amount every 30 days. How much is left after 10 days.
The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Radioactive decays by 1/2 of its original in 30 days.
1/2 of original → 30 days.
Divide both sides by 3
1/6 of original → 10 days
Therefore, in 10 days amount of decays will be,
1/6 of 20 ⇒ 20/6 = 3.33
The amount left = 20 - 3.33 = 16.67.
Hence "The amount of radioactive after 10 days with the same rate of change of decay will be 16.67 g".
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A pancake recipe asked for one and 2/3 times as much milk as flower if two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Let x be the quantity of flour used
Let y be the quantity of milk used
A pancake recipe asked for one and 2/3 times as much milk as flour:
[tex]y=1\frac{2}{3}x[/tex]If two and one half cups of milk is used what quantity of flower would be needed according to the recipe?
Find x when y=2 1/2:
[tex]2\frac{1}{2}=1\frac{2}{3}x[/tex]Write the quantities as fractions;
[tex]\begin{gathered} 2+\frac{1}{2}=(1+\frac{2}{3})x \\ \\ \frac{4}{2}+\frac{1}{2}=(\frac{3}{3}+\frac{2}{3})x \\ \\ \frac{5}{2}=\frac{5}{3}x \end{gathered}[/tex]Solve x:
[tex]x=\frac{\frac{5}{2}}{\frac{5}{3}}=\frac{15}{10}[/tex]Write the answer as a mixed number:
[tex]\frac{15}{10}=\frac{10}{10}+\frac{5}{10}=1+\frac{5}{10}=1+\frac{1}{2}=1\frac{1}{2}[/tex]Then, for 2 1/2 cups of milk would be needed 1 1/2 cups of flourAnswer: 1 1/2Factor 12x² + 19x - 21.O (6x + 7)(2x − 3)—O (4x - 3)(3x + 7)O(6x-7)(2x + 3)(4x + 3)(3x7)
given the expression
[tex]12x^2+19x-21[/tex]we are loking 2 numbers whose multiplication is equal to 12
and other 2 number whose multiplication is equal to 21
the sum of the cross multiplication is equal of 19, as follows
[tex](4x*3x)+((4x*7)+(3x*-3))+(-3*7)[/tex]factor is
[tex]\left(4x-3\right)\left(3x+7\right)[/tex]correct answer option B
What’s eight less than four times a number in algebraic expression
Answer:
4x - 8, 4x just means four of x, and eight less means to subtract 8.
Step-by-step explanation:
Answer:
The answer is 4x - 8 and it equals -32
Please help me come you just tell me the answer I don’t really need you to explain
Given:
[tex]\begin{gathered} \angle JKL=65 \\ \angle KJL=50 \end{gathered}[/tex]Sum of the angle of any triangle is 180
So:
[tex]\begin{gathered} \angle JKL+\angle KJL+\angle KLJ=180 \\ 65+50+\angle KLJ=180 \\ \angle KLJ=180-(65+50) \\ \angle KLJ=180-115 \\ \angle KLJ=65 \end{gathered}[/tex]Then two sides are also equal.
[tex]\begin{gathered} 3x-2=x+10 \\ 3x-x=10+2 \\ 2x=12 \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]So the value of x is 6.
Passing through (- 4,-7) and (1,3) What is the equation of the line in point-slope form
To calculate the equation of the line passing through the points ( -4. -7) and (1, 3):
[tex]\begin{gathered} \text{ Equation of the line can be calculated by the formula } \\ y-y_1=m(x-x_1) \end{gathered}[/tex]where m = slope
(x1, y1) = any of the points given; say points (-4, -7). That is x1= -4, y1 = -7
To calculate the slope, m:
[tex]\begin{gathered} \text{ m = }\frac{y_2-y_{1_{}}}{x_2-x_1}_{} \\ \text{ where }(x_2,y_2)\text{ = (1, 3)} \\ m\text{ = }\frac{3\text{ - (-7)}}{1-(-4)} \\ m=\text{ }\frac{3+7}{1+4}\text{ = }\frac{10}{5} \\ m=2 \end{gathered}[/tex][tex]\begin{gathered} \text{ substituting m = 2, x}_1=-4,y_1=-7\text{ into the formula }y-y_1=m(x-x_1) \\ we\text{ have} \\ y-(-7)=2(x-(-4)\text{ )} \\ y+7=\text{ 2(x+ 4)} \end{gathered}[/tex]The equation of the line in point slope form is y + 7 = 2(x + 4)
Slope The first two sets of points are 9,-24 and 13,-21
We need to find the slope using the points (9, -24) and (13 , -21)
so, the slope = 3/4
