Using the fundamental counting theorem, it is found that 17,576,000 different license plates can be manufactured.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
Since repetition is allowed, for the 3 letters, there are 26 outcomes, hence [tex]n_1 = n_2 = n_3 = 26[/tex].For the 3 numbers, there are 10 outcomes, hence [tex]n_4 = n_5 = n_6 = 10[/tex]Then:
[tex]N = 26^3 \times 10^3 = 17576000[/tex]
17,576,000 different license plates can be manufactured.
To learn more about the fundamental counting theorem, you can take a look at https://brainly.com/question/24314866
HELP!!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the multiplication expressions to the exponential expressions.
Answer:
Step-by-step explanation:
Convert 4pie/5 to degrees. 135° 144° 216° 225°
[tex]\huge \bf༆ Answer ༄[/tex]
For converting radians to degree, we multiply the value in radian by [tex] \dfrac{180}{π}[/tex]
That is ~
[tex] \sf \dfrac{4 \cancel\pi}{ \cancel5} \times \dfrac{ \cancel{180} \: \: {}^{36} }{ \cancel\pi} [/tex][tex] \sf4 \times 36[/tex][tex] \sf144 \degree[/tex]can someone help me with this math problem
Answer:
It is congruent to the angle F, as they are similar triangles.
Describe how to find all the points on a baseball field that are equidistant from second base and third base.
In the figure, m∠DBE=50. Find each of the following.
m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC
From the given diagram, the following statements are true:
AB = BC
3y = 5y - 22
3y - 5y = -22
-2y = -22
y = 11
Similarly, m<DBE = 50 degrees
m<BED = 90 - m<DBE
m<BED = 90 - 50
m<BED = 40 degrees
Since BE = BC = 3y
BE = BC = 3(11) = 33
Also, 7x - 2 = 40
7x = 40 + 2
7x = 42
x = 6
Get the measure of m<BEA
m<BEA = 7x - 2
m<BEA = 7(6) - 2
m<BEA = 40 degrees
Learn more on angles here: https://brainly.com/question/16281260
How do you know when to rewrite square trinomials and difference of squares binomials as separate factors? How can sums and differences of cubes be identified for factoring?
Answer:
Step-by-step explanation:
You asked: How do you know when to rewrite square trinomials and difference of squares binomials as separate factors? First, and mostly obviously is when the directions say to factor the given expression. Next, if you're given an equation and asked to solve it. You set it equal to 0 and factor the perfect square trinomial or the difference of squares binomial. Set each factor equal zero and solve. This is a little bit oversimplified but, solutions are roots are zeros are x-intercepts, so if you are asked to find any of those things. Set your equation equal to zero, factor and solve. Also, if you have a rational expression (a fraction with a polynomial on top and a polynomial on the bottom) you would need to factor in order to simplify, to sketch a graph without technology. Anytime you need to simplify, factoring is good to try.
You also asked: How can sums and differences of cubes be identified for factoring? The sum or difference of cubes is in the form a^3 + b^3 or a^3 - b^3
You can memorize how to factor these a^3 + b^3 = (a+b)(a^2 - ab + b^2) and
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
If you take the trouble to multiply these two factors back together you will see how four terms drop out and you get a binomial. Also the is an acronym SOAP to help you memorize it. Factoring cubes is used in the same way as you previous question. To factor, to solve, to simply, to graph. This was a really general question. I hope this helps.
Find the equation for the circle with center (8,−8) and radius of length 2
Step-by-step explanation:
(x-8)²+(y--8)²=(2)²
x²-16x+64+y²+16y+64=4
x²+y²-16x+16y+124=0
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
[tex]y = {x}^{2} [/tex]
[tex]y = 4x[/tex]
; about the y-axis
well, first off, when it comes to volumes by rotation, we'd want to graph them, Check the picture below. Our rotation over the axis will give us a "washer", so we'll be using the washer method.
now, our axis of rotation is the y-axis or namely x = 0, x = 0 is a vertical line, meaning we have to put the functions in y-terms, that is in f(y) form
[tex]y = x^2\implies \pm\sqrt{y}=x\implies \boxed{\pm\sqrt{y}=f(y)} \\\\\\ y = 4x\implies \cfrac{y}{4}=x\implies \boxed{\cfrac{y}{4}=g(y)}[/tex]
if we look at the picture, the parabola is the farthest from the axis of rotation and the line is the closest, or namely R² and r² respectively.
the way I get the area for R² and r², is by using the same I do with "area under the curve", so if I say call the axis of rotation h(y), the way I get the area is
R => f(y) - h(y)
r => g(y) - h(y)
so let's proceed.
[tex]\textit{area under the curve}\\ \begin{array}{llll} \sqrt{y}- 0\implies &\sqrt{y}\\ \frac{y}{4}-0\implies &\frac{y}{4} \end{array}\qquad \qquad \begin{array}{llll} \stackrel{R^2}{(\sqrt{y})^2}-\stackrel{r^2}{\left( \frac{y}{4} \right)^2}\\[-0.5em] \hrulefill\\ y\qquad -\qquad \frac{y^2}{16} \end{array}[/tex]
now, we want to get the area enclosed by both, and thus we'd need their points of intersection, setting both to [tex]\sqrt{y}=\cfrac{y}{4}[/tex] which in short gives us the bounds of 0 and 16.
[tex]\pi \displaystyle\int_{0}^{16}\left( y - \cfrac{y^2}{16} \right)dy\implies \pi \int_{0}^{16}y\cdot dy-\pi \int_{0}^{16}\cfrac{y^2}{16}\cdot dy\\\\\\\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^{16}-\pi \cdot \left. \cfrac{y^3}{48} \right]_{0}^{16}\implies 128\pi -\cfrac{256\pi }{3}\implies \boxed{\cfrac{128\pi }{3}}[/tex]
The midpoint of AB is M(1, -4). If the coordinates of A are (-3, -6), what are the coordinates of B
Answer:
Step-by-step explanation:
x value of M is 1 - (-3) = 4 units to the right of A
B will be another 4 units to the right of M or x = 1 + 4 = 5
y value of M is -4 - (-6) = 2 units above A
B will be another 2 units above M or y = -4 + 2 = -2
B = (5, -2)
How do I multiply a fraction and a whole number? Please explain step by step to get marked
Any whole number can be written as a fraction. All we do is place the number over 1.
For example, the whole number 7 is the same as the fraction 7/1.
If we wanted to multiply the whole number 7 with the fraction 2/3 then...
[tex]7 * \frac{2}{3}\\\\\frac{7}{1} * \frac{2}{3}\\\\\frac{7*2}{1*3}\\\\\frac{14}{3}\\\\[/tex]
In the jump from the second step to the third step, we multiply straight across. The numerators multiply together. The denominators multiply together. The fraction 14/3 cannot be reduced because 14 and 3 don't have any factors in common other than 1.
Find the HCF of 150 and 250.
Answer:
It is 50
Step-by-step explanation:
Hope this helps
Answer:
50
Step-by-step explanation:
The exponential function y= a(b)^x passes through the points (3,25) and (8,10). Which of the following is closest to the value of b?
If the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833
The given exponential equation is:
[tex]y=ab^x[/tex]
The function passes through the points (3, 25) and (8, 10)
Substitute x = 3 and y = 25 into the function [tex]y=ab^x[/tex]
[tex]25=ab^3[/tex]............................(1)
Substitute x = 8 and y = 10 into the function [tex]y=ab^x[/tex]
[tex]10=ab^8[/tex].............................(2)
Divide equation (2) by equation (1)
[tex]\frac{10}{25}=\frac{ab^8}{ab^3} \\\\0.4=b^5\\\\b=0.4^\frac{1}{5} \\\\b=0.4^{0.2}\\\\b=0.833[/tex]
Therefore, if the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833
Learn more on exponential functions here: https://brainly.com/question/12940982
How do you dived a fraction with a number like for an a example:
4/10 divided 2 = ?
Please explain step by step to get marked as brainliest!
Step-by-step explanation:
I assume you mean how do you divide a fraction by a whole number
In order to divide a fraction by a whole number we must use the KFC rule or the "Keep, flip, change" rule
The "Keep" means we keep the first fraction the same.
Next, we "flip" the second fraction (or in this case number; however it can be made into a fraction by putting it over 1). So now we have 4/10 divided by 1/2
Then we "change" the symbol so instead of dividing the fraction, we change the divide to a multiply.
Lastly, you just multiply the fractions as you usually would and you should end up with 4/20 which simplifies to 1/5 if my maths is correct.
Hope this helps.
Answer:
you can use KCF for this answer as well
Step-by-step explanation:
2 as a fraction would be 2/1
you need 4/10 divided by 2/1
applying KCF, you change it to be 4/10 multiplied by 1/2
solve to get 4/20 or simplified 1/5
hope this helped :)
Define the axis of symmetry, vertex, focus and directrix for
16(y-4)= (x-3)^2
NO LINKS!!
Answer:
see attached
Step-by-step explanation:
The equation is in the form ...
4p(y -k) = (x -h)^2 . . . . . (h, k) is the vertex; p is the focus-vertex distance
Comparing this to your equation, we see ...
p = 4, (h, k) = (3, 4)
p > 0, so the parabola opens upward. The vertex is on the axis of symmetry. That axis has the equation x=x-coordinate of vertex. This tells you ...
vertex: (3, 4)
axis of symmetry: x = 3
focus: (3, 8) . . . . . 4 units up from vertex
directrix: y = 0 . . . horizontal line 4 units down from vertex
Which of the following best describes the slope of the line below?
Answer:
Negative
Step-by-step explanation:
The slope of the line is negative because when looking at the graph, you can see that the line starts in the 2nd quadrant and ends in the 4th.
The price of a video game is $32.99 before tax. Andre bought the video game for 20% off. He then paid 8% sales tax on the discounted price.
Part A: How much did Andre pay in sales tax? Show all work and steps in your solution. (5 points)
Part B: What is the total amount that Andre paid for the video game? Show all work and steps in your solution. (5 points)
Answer:
Step-by-step explanation:
First we need to find the 20% discount.
$32.99 x .20 = $6.598
The 20% discount is $6.59
We subtract the discount from the original price:
$32.99 - $6.59 = $26.40 (This is price after the discount.)
Now we need to find the amount of the sales tax on the discounted price.
$26.40 x .08 = $2.11 (This is the sales tax on the discounted price.)
The total price Andre paid is the discounted price plus the sales tax.
$26.40 + $2.11 = $28.51
Total price paid: $28.51
PLZ HELPPPPP QUICKLYYYY!!!!!!!!!!!!!
Answer:
root 490
Step-by-step explanation:
A car travels 18 miles on a gallon of gas. The car used 65 gallons of gas last week.compute the number of miles the car traveled?
Answer: 1170 miles
Work Shown:
(18 miles)/(1 gallon) = (x miles)/(65 gallons)
18/1 = x/65
x/65 = 18
x = 65*18
x = 1170
Answer: 1170 miles
1 gallon of gas --> 18 miles
65 gallon of gas --> 18 * 65 (which is 1170 miles)
The volume of a rectangular prism can be computed using the formula V = lwh.
What is the width of a prism that has a volume of 1664 cubic cm a length of 16 cm and a height of 8 cm?
11 cm
13 cm
26 cm
768 cm
Answer:
13cm
Step-by-step explanation:
substitute values we have into the formula:
1664 = 16 x w x 8
rearrange:
1664/16×8 = w
which equals 13
Answer:
13
Step-by-step explanation: just took the test :)
h=-16t^2+72t+100 solve for t
Answer:0
Step-by-step explanation:
hey i'm in the six grade i'm not sure but pls try it
Help please ! Sishsoshsishsjdhshishd
Determine the equation of a circle with center at (8, 10) and radius 6.
1) (X + 8)2 + (y - 10)2 = 36
2) (x + 8)2 + (y + 10)2 = 36
3) (x-8)2 + (y - 10)2 = 36
4)(x - 8)2 + (y - 10)2 = 6
Answer:
Step-by-step explanation:
general equation for a circle at the origin is
x² + y² = r²
if the circle center is (x₀, y₀), the formula is
(x - x₀)² + (y - y₀)² = r²
(x - 8)² + (y - 10)² = 36
1/2+2/3 divided by 1/6
(no links)
[tex]\cfrac{1}{2}+\cfrac{\underline{2}}{3}\implies \cfrac{(3)(1)~~ +~~(2)(\underline{2})}{\underset{\textit{using this LCD}}{6}}\implies \cfrac{3+4}{6}\implies \cfrac{7}{6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{6}\div \cfrac{1}{6}\implies \cfrac{7}{~~\begin{matrix}6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\implies 7[/tex]
If 11% of a number equals 12, find 66% of that number
Answer: 72
Step-by-step explanation:
0.11*a = 12
0.66*a = ?
Hint: We don't need to find a to answer this question! Just find the relationship with these equations.
0.66*a = 6*(0.11*a) = 6*12 = 72
helpp anyone?? :(
No linkssss porfavorr plaesaaje cjkq
Answer:
127/100 = 1.27
1.4
1 whole and 1/3 = 1.5
Step-by-step explanation:
Hope this helps
May I get Braineist pls
Divide 7 divided by 3/5
Express your answer in simplest form.
Answer:
35/5
Step-by-step explanation:
7/1 divded by 3/5. flip 3/5 to its reciprocal so it becomes 5/3, then times 7/1 by 5/3
Which theme is found in this story The Lucky Ticket
Answer:
In "The Lottery Ticket", Chekhov develops the theme that the love of money can destroy one's satisfaction.
Mohal leans a 20-foot ladder against a wall so that it forms an angle of 72° with the
ground. How high up the wall does the ladder reach? Round your answer to the
nearest tenth of a foot if necessary.
Answer:
sin(72°)=x÷20ft.
sin(72°)×20ft.= 19ft 252 inches
the ladder reach 19ft 252 inches tall on the building.
Step-by-step explanation:
What is the slope of the line?
slope:change in x\change in y
Find the value of x need help
Answer:
Step-by-step explanation:
The supplement of 102 = 180 - 102 = 78
It is the interior angle of the given exterior angle.
It is also the enclosed angle of the isosceles triangle
Each of the other two angles = y
180 = 2*y + 78 Subtract 78 from both sides
180 - 78 = 2y Combine
102 = 2y Divide by 2
102 / 2 = y
51 = y
The smaller triangle on your right has 2 equal sides that are marked.
The angle you just found = <2 and the vertically opposite angle of the 51
So <2 = 51
PLS HELP FAST!!
During a snowstorm, Lucy tracked the amount of snow on the ground. When the storm began, there were 4 inches of snow on the ground. For the first 2 hours of the storm, snow fell at a constant rate of 3 inches per hour. The storm then stopped for 5 hours and then started again at a constant rate of 1 inch per hour for the next 7 hours. Make a graph showing the inches of snow on the ground over time using the data that Lucy collected.