Standard automobile license plates in a country display 1 numbers, followed by 2 letters, followed by 4 numbers. how many different standard plates are possible in this system? (assume repetitions of letters and numbers are allowed.)
there are 10 numbers ( 0-9)
there are 26 letters ( A-Z)
10 x 26 x 26 x 10 x 10 x 10 x 10 =67,600,000 possible combinations
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. find the number?
Answer:x equals 12
Step-by-step explanation:
4x+40=100-x
add x to both sides
5x+40=100
Subtract 40 on both sides
5x=60
divide both sides by 5
x=12
The number is 12 from the obtained equation.
Given that, When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number be x.
4 times a number is increased by 40
=4x+40
100 is decreased by the number
= 100-x
So, equation is 4x+40=100-x
4x+x=100-40
⇒ 5x = 60
⇒ x=12
Therefore, the number is 12 from the obtained equation.
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The bacteria in a container quadruples every day. if there are initially 100 bacteria, write an equation that models the number of bacteria a after d days. how many bacteria will there be after 1 week?
Answer:
[tex]a = 100 * 4^{d}[/tex]
In a 1 week there would be 1,638,400 bacteria
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
Since the amount of bacteria are quadrupling every day this means that the bacteria are compounding, meaning that every time they quadruple the next day the new amount is quadrupled. Thus growing exponentially every time.
So to solve this we would need to create an exponential equation that calculates the amount of bacteria after a certain amount of days, like so...
[tex]a = 100 * 4^{d}[/tex]
If we want to calculate the number of bacteria after 1 week , we would substitute d for 7 and solve for a.
[tex]a = 100 * 4^{7}[/tex]
[tex]a = 100 * 16,384[/tex]
[tex]a = 1,638,400[/tex]
In a 1 week there would be 1,638,400 bacteria
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions?
a. 15,504
b. 20,145
c. 23,670
d. 25,890
P = 3^7 x 11^2 and Q = 3^4 x 7^3 x 11. Write as the product of prime factors the LCM of P and Q
The LCM of P and Q is found by taking the highest powers of the common prime factors from both numbers, which results in LCM(P, Q) = 37 x 73 x 112.
Explanation:To find the Least Common Multiple (LCM) of P and Q when given as products of prime factors, we look for the highest powers of the prime factors that appear in either P or Q. In this case:
P = 37 x 112Q = 34 x 73 x 11For prime factor 3, the highest power in P and Q is 37. For prime factor 11, the highest power is 112 (from P). Since prime factor 7 only appears in Q, we include it in its highest power, which is 73. Combining these, the LCM of P and Q as the product of prime factors is:
LCM(P, Q) = 37 x 73 x 112
A certain kind of bacteria growing on your kitchen counter doubles every 30 mins.. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 180 mins.
write the following inequality in slope intercept form. -6+2y less than or equal to 42
Answer: The required slpe-intercept form of the given inequality is
[tex]y\leq 0\times x+24.[/tex]
Step-by-step explanation: We are given to write the following inequality in the slope-intercept form :
[tex]-6+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope intercept form of a straight line with slope m and y-intercept c is given by
[tex]y=mx+c.[/tex]
Writing equation (i) in slope-intercept form, we have
[tex]-6+2y\leq 42\\\\\Rightarrow 2y\leq 42+6\\\\\Rightarrow 2y\leq 48\\\\\Rightarrow y\leq 24\\\\\Rightarrow y\leq 0\times x+24,[/tex]
where slope, m = 0 and y-intercept, c = 24.
Thus, the required slpe-intercept form of the given inequality is
[tex]y\leq 0\times x+24.[/tex]
A cylindrical tree trunk is 14 yards high from the ground up to the lowest branch, and it measures 4 yards around. What is the volume of wood in this section of the trunk?
Please help me!! I really need it (:
it is a linear equation
if you take the negative of x and subtract 1 you get Y
so the answer is A
PLEASE HELP! A square piece of paper 144 mm on a side is folded in half along a diagonal. The result is a 45 -45-90 triangle. What is the length of the hypotenuse
A:140 mm
B:12 square root 2
C:280mm
D: 140 square root 2
find a positive angle less than one rotation that is coterminal with 750 degrees
To solve this problem, all you have to do is to subtract 360 degrees (equivalent to 1 rotation) from the given angle until the answer is less than 360 degrees.
1st subtraction: 750 – 360 = 390 degrees
2nd subtraction: 390 – 360 = 30 degrees
Therefore the positive angle less than one rotation that is coterminal with 750 degrees is 30 degrees.
the equation of line AB is y = 1/5x -1 write an equation of a line perpendicular to line AB in slope intercept form that contains point (1, -2)
A contractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 What is the variance?
The variance of the five bedroom house is 864.
The formula varianceσ²
[tex]=\frac{X^2}{N} -u^2[/tex]
To get the value of X²
= 100²+100²+120²+120²+180²
= 81200
The number is N = 5
u = mean
[tex]u = \frac{100+100+120+120+180}{5}[/tex]
u = 124
The values in the variance formula
[tex]\frac{81200}{5} -124^2[/tex]
16240-15376
= 864
The variance is 864
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What is #3 step by step?
If 5x + x2>100 then x is not
For what values of x and y are the triangles congruent?
a. x=-4. y=-4
b. x=-4, y=4
c. x=4, y=7
d. x=7, y=4
an air traffic controller spots two planes at the same altitude flying toward each other. Their flight paths form a right angle at point p. One plane is 150 miles from point P and is moving at 450 miles per hour. The other plane is 200 miles from point P and is moving at 450 miles per hour. What is the distance s between the planes as a function of time t?
The problem states that the paths of the two planes form a right triangle, therefore this means that the distance between the two is the hypotenuse. Given that information, we can use the hypotenuse formula for finding the distance formula:
c^2 = a^2 + b^2 ---> 1
Where c is the hypotenuse, in this case the distance between the two planes.
First let us find the value of a. We know that one plane is 150 miles from point P and this distance is decreasing by a rate of 450 miles per hour, therefore a is:
a = 150 – 450 t ---> 2
We also know that the other plane is 200 miles away and this distance decreases by a rate of 450 miles per hour also, therefore b is:
b = 200 – 450 t ---> 3
Substituting equations 2 and 3 to 1:
c^2 = (150 - 450 t)^2 + (200 – 450 t)^2
c^2 = 22500 – 135000t + 202500t^2 + 40000 – 180000t + + 202500t^2
c^2 = 405,000 t^2 – 315,000 t + 62,500 (ANSWER)
What is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane?
Answer:
The answer is rotational symmetry.
Step-by-step explanation:
The Rotational symmetry is the quality a design has if it maintains all characteristics when it is rotated about a point lying in its plane. A shape is said to possess rotational symmetry when it still looks the same after we rotate it.
given g(x)=Squareroot x-4 and h(x)=2x-8, what are the restriction on the domain of gofh?
x>?
The domain of the (goh)(x) will be [6, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
g(x) = √(x - 4) and h(x) = 2x - 8
Then the function f of g (x) will be
(goh)(x) = g(h(x))
(goh)(x) = √((2x - 8) - 4)
(goh)(x) = √(2x - 12)
Then the domain of the (goh)(x) will be
We know that the value under the square root should be greater than zero.
2x - 12 ≥ 0
2x ≥ 12
x ≥ 6
The domain of the (goh)(x) will be [6, ∞).
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Find the sale price when the original price is $37.00 and the discount rate is 44%.
a.
$20.72
c.
$35.37
b.
$16.28
d.
$1.63
Please select the best answer from the choices provided
What is the product of the rational expressions shown below? Make sure your answer is in reduced form. x+2/x-5 times 8x/x+2
A 8x/x-5
B8x/x-5
C 8/x+2
D8/ x-5
x+2 cancels out and leaves 8x/x-5
Also, Answer A and B are the same
Given that the two triangles are similar, solve for x if AU = 20x + 108, UB = 273, BC = 703, UV = 444, AV = 372 and AC = 589. You must show all of your work to receive credit.
If two triangles are similar then the corresponding sides are in proportion. Thus,
AB / AU = BC / UV = AC / AV
AB / (20x+108) = 703 / 444
Where AB is equivalent to:
AB = AU + UB
AB = 20x + 108 + 273
AB = 20x + 381
Therefore going back to the first equation:
(20x + 381) / (20x + 108) = 703/444
444 (20x + 381) = 703 (20x + 108)
8880x + 169164 = 14060x + 75924
14060x - 8880x = 169164 – 75924
5180 x = 93240
x = 93240 / 5180
x = 18
Answer:
x = 18
Step-by-step explanation:
You want the value of x, given similar triangles ABC and AUV with ...
AU = 20x +108AV = 372UB = 273AC = 589Similar trianglesCorresponding sides, or their parts, of similar triangles are proportional. In this geometry, this means ...
[tex]\dfrac{AU}{UB}=\dfrac{AV}{VC}[/tex]
We know that VC = AC -AV = 589 -372 = 217, so we can write the proportion as ...
[tex]\dfrac{20x +108}{273}=\dfrac{372}{217}= \dfrac{12}{7}\\\\7(20x+108)=273(12)\qquad\text{multiply by $273\cdot12$}\\\\140x = 2520\qquad\text{subtract 756}\\\\x=\dfrac{2520}{140}=18[/tex]
The value of x is 18.
A die is rolled 12 times find the probability of rolling exactly 12 ones
Answer:
[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Solution to the problem
We assume that the die is fair and the probability of obatin a one is 1/6.
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=12, p=1/6)[/tex]
And we want to find this probability:
[tex] P(X=12)[/tex]
And if we replace we got:
[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]
George's page contains twice as many typed words as bills page and bills page contains 50 fewer words than Charlie's page. If each person can type 60 words per minute, after one minute, the difference between twice the number of words on bills page and the number of words on Charlie's page is 210. How many words did bills page contain initially? Use a table to organize the information.
The number of bacteria in a petri dishes 524 and growing at a rate of 7% every month how many bacteria will be there in seven months
7% = 0.07
since it is growing add that to 1 = 1.07
now that is to the power of length of time 1.07^7
now multiply
524 x 1.07^7 = 841.429 ( round answer as needed)
What is the awnser to -10x+3(4x-2)=6
The function $f$ satisfies \[f(x) + f(2x + y) + 5 x y = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.
PLEASE help me!!!!! and can you show me how you did it please!?!
A school typically sells 500 yearbooks each year for $50 each.
The economics class does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price.The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Let X represent the number of $5 decreases in price. If the expression that represents the revenue is written in the form R(X)=(500+ax)(50-bx). Find the values of a and b.
Answer: a=100 and b=5
Step-by-step explanation:
Given: A school typically sells 500 yearbooks each year for $50 each.
The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.
Let x represents the number of $5 decreases in price.
Then the new price (in dollars)=50-5x
Total yearbook sold=500+100x
If the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.
Then the revenue function will be [tex]R(X)=(500+100x)(50-5x)[/tex]
On comparing this with the given revenue expression we get
a=100 and b=5.
In this exercise we have to calculate the values of A and B, so we have to:
[tex]A=100\\B=5[/tex]
Since the equation is:
[tex]R(X)=(500+ax)(50-bx)[/tex]
And the following information was given:
A school typically sells 500 yearbooks each year for $50 each.The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.So knowing that by increasing 100 more books sold this is equal to A and the decrease in value is going to be equal to b.
[tex]R(X)=(500+100x)(50-5x)[/tex]
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A man travelled 3/8 of his journey by a rail 1/4 by a taxi 1/8 by and the remaining 2km on foot what is the length of his total journey?