78,624,000 different license plates are possible if letters and digits cannot be repeated.
For the letters:
There are 26 letters in the English alphabet, and we need to choose three of them without repetition.
This can be calculated as a permutation of 26 letters taken 3 at a time:
P(26, 3) = 26! / (26 - 3)!
= 26! / 23!
= 26 x 25 x 24
= 15,600
For the digits:
There are 10 digits (0-9), and we need to choose four of them without repetition.
This can be calculated as a permutation of 10 digits taken 4 at a time:
P(10, 4) = 10! / (10 - 4)! = 10! / 6!
= 10 x 9 x 8 x 7
= 5,040
To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:
Total possibilities = P(26, 3) x P(10, 4)
= 15,600 x 5,040
= 78,624,000
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p, q and r are prime numbers such that pqr3=270.
Work out the values of p, q and r.
b. Work out the highest common factor of 270 and 105.
The highest common factor of 270 and 105 is 15.
How to find the highest common factorfinding the prime factorization of 270.
The prime factorization of 270 can be written as:
270 = 2 * 3^3 * 5
From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.
So the values of p, q, and r are:
p = 2
q = 3
r = 5
Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.
The prime factorization of 270 is:
270 = 2 * 3^3 * 5
The prime factorization of 105 is:
105 = 3 * 5 * 7
To find the HCF, we need to find the common factors and choose the highest one.
The common factors of 270 and 105 are 3 and 5.
The highest common factor of 270 and 105 is 3 * 5 = 15.
Therefore, the highest common factor of 270 and 105 is 15.
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6 sin =5 solve to the nearest 0.1
Step-by-step explanation:
sin Φ = 5/6 = .8333
Arcsin ( sin Φ) = arcsin (.8333)
Φ = 56.4 degrees
‼️WILL MARK BRAINLIEST, IF HELPFUL‼️
Answer:
A - The height of the parallelogram is equal to the radius of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - The area of the circle is equal to the circumference times the radius.Step-by-step explanation:
Make a plan:
We can use the radius of the circle to calculate the height of the parallelogramWe can use the circumference of the circle to calculate the base of the parallelogramWe can use the parallelogram - like shape to show that the area of the circle is equal to the area of the parallelogram.Solve the problem:
A - The height of the parallelogram is equal to the circumference of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - we can use the parallelogram-like shape to show that the area of the circle is equal to the area of the parallelogram. The area of the parallelogram is equal to the base times the height. However, the area of the circle is equal to the circumference times the radius.Draw the conclusion:
A - The height of the parallelogram is equal to the radius of the circleB - The base of the parallelogram is equal to the circumference of the circle.C - The area of the circle is equal to the circumference times the radius.Hope this helps!
Alex tested three brands of batteries to learn which would last the longest in a flashlight. He placed two brand “A” batteries in a flashing, turned the flashlight on, and measured the time and the light shined. He repeated the experiment with battery brands “B” and “C” using the same flashlight. He recorded the data on the bar graph below.
Which of these is an accurate conclusion that Alex can make about the batteries he tested?
A. Brand “C batteries lasted twice as long as brand “A” batteries.
B. Brand “C” batteries listed three times longer than brand “B” batteries
C. The light was twice as bright with brand “A” batteries than with brand “B” batteries.
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
The correct statement regarding the bar graph is given as follows:
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
What does a bar graph show?A bar graph shows the output considering a given input.
Hence the bar graph in this problem shows the average lifetime for each battery type, given as follows:
Brand A: 270 minutes.Brand B: 120 minutes.Brand C: 360 minutes.Brand C has triple the length of Brand B, hence the correct statement is given by option D.
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The dot plot displays data from 14 random samples, each consisting of 30 middle school students. Each dot represents the mean number of sports played per year by students in the sample.
Which number best represents the mean number of sports played by middle school students? Write your answer as a decimal to the nearest tenth.
__ sports
Part B
Find and interpret the variability in the distribution. Round the MAD to the nearest hundredth.
The MAD is about_____ sport(s). The majority of the sample means are within ______ sport(s) of the mean. This means our estimate is likely not far off from the true mean.
The best representation of the mean number of sports played by middle school students is 2.75 sports and the MAD is about 0.84 sports.
To find the best representation of the mean number of sports played by middle school students, we need to calculate the median of the given data.
The median represents the central tendency of the data and is less affected by extreme values.
Arranging the means of the samples in ascending order, we have:
1, 1, 2, 2.5, 3, 3, 3.5, 4
Since there are eight values, the median will be the average of the fourth and fifth values:
(2.5 + 3) / 2 = 2.75
Variability in the Distribution
Summing up the absolute deviations:
1.75 + 1.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0.75 + 1.25 = 6.75
To find the MAD, we divide the sum of the absolute deviations by the total number of data points:
MAD = 6.75 / 8 = 0.84
Therefore, the MAD is about 0.84 sports.
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Find the solution set for the equation. |9x-5|+3=8
Answer: 10/9, 0
Step-by-step explanation:
Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?
There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
How to solveThe Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.
Given:
The class has 42 students.
12 boys and 15 girls are said to know how to read three-letter words in English.
19 boys and 17 girls are said to know how to identify all letters of the alphabet.
None of the students in the class is able to write a sentence of five words if dictated to them.
There are in total 22 boys and 20 girls in the class.
Read three-letter words |
|____________|______________|
| | |
| Boys (12) | Girls (15) | Can read three-letter words
|____________|______________|
| | |
| Boys (10) | Girls (13) | Cannot read three-letter words
_______|____________|______________|
| | |
| Boys (9) | Girls (13) | Can identify all letters
|____________|______________|
| | |
| Boys (13) | Girls (7) | Cannot identify all letters
|____________|______________|
To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:
Boys who cannot read a letter or a three-letter word: 10 + 13 = 23
Girls who cannot read a letter or a three-letter word: 13 + 7 = 20
Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.
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Simplify the expression
log₂8³x
Answer:
We can simplify the expression log₂8³x using the following logarithmic rule:
logₐb^c = c * logₐb
Using this rule, we can rewrite the expression as:
log₂8³x = 3log₂8 + log₂x
We can further simplify by recognizing that 8 can be expressed as a power of 2:
8 = 2³
Substituting this in, we get:
3log₂8 + log₂x = 3log₂(2³) + log₂x = 3 * 3 + log₂x = 9 + log₂x
Therefore, the simplified expression is:
log₂8³x = 9 + log₂x
Step-by-step explanation:
Can someone help me? Write a rule for nth term of the arithmetic sequence with a1=7 and the common difference is 3
Answer:
[tex]a_n=3n+4[/tex]
Step-by-step explanation:
If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:
[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]
Urgent!!!
cos4α + 2 Sin² 2α
Answer:
Step-by-step explanation:
cos4α + 2 Sin² 2α is a trigonometric expression that involves the cosine and sine functions of the angle α. This expression can be simplified using trigonometric identities to get:
cos4α + 2 Sin² 2α = (cos² 2α)² + 2 (Sin 2α)²
This simplification involves using the double angle identity for sine and the identity for the square of cosine.
Brainliest Pls
Answer:1
Step-by-step explanation:
cos(4α) + 2sin²(2α)
First, let's expand cos(4α)
cos(4α) = cos²(2α) - sin²(2α)
Now, let's substitute this expression back into the original equation:
cos(4α) + 2sin²(2α) = (cos²(2α) - sin²(2α)) + 2sin²(2α)
= cos²(2α) + sin²(2α)=1 by
cos²(α) + sin²(α)=1
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of
your response as Part A, Part B, and Part C.
Part A: Suppose event A and event B are mutually exclusive. Is the statement P(A and B)-0 true?
Part 9: Explain why or why not to support your answer to Part A.
Part C: Provide an example to support your explanation.
Part A :
Yes, the statement is true that P( A and B ) = 0 .
Given,
Event A and Event B are mutually exclusive.
Thus P ( A and B ) = 0
Part B:
A and B are mutually exclusive events if they do not occur at the same time.
This means that A and B do not share any common outcomes and
P(A and B) = 0.
Part C:
Let,
The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.
A and B do not have any numbers in common so P(A and B) = 0.
Hence, A and B are mutually exclusive.
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prove that
(z^a/z^b)^c * (z^b/z^c)^a * (z^c/z^a)^b =1
Step-by-step explanation:
remember, when we multiply the same base, we add the exponents, when we divide the same base we subtract the exponents.
when we have exponent of exponent, we multiply the exponents.
so,
the expression is
(z^ac / z^bc) × (z^ab / z^ac) × (z^bc / z^ab) = 1
we have in there the commutative and associative properties of multiplication : the sequence of operands do not matter at all.
and therefore we have in there the terms :
z^ac / z^ac
z^bc / z^bc
z^ab / z^ab
all three are 1
and so the main expression is
1 × 1 × 1 = 1
which is true, of course, and therefore the original equation is true.
The EPA fuel economy estimates for automobiles models tested recently found them to be
normally distributed with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What is
the percentile rank of an automobile that has a fuel economy of 35 mpg?
90th Percentile
O 5th Percentile
O 95th Percentile
10th Percentile
Step-by-step explanation:
(35-24.8) / 6.2 = z-score of + 1.645 corresponding to .9495 =
~ 95th percentile
(10)
In 2008, the average new car price was approximately $27,700. In 2010,
the average new car price had increased to $29,200. Assuming a linear
relationship, what will be the approximate new car price in 2014?
A $33,700
B. $32,200
C. $30,700
D. $29,950
The approximate price of the new car in 2014 is:
B. $32,200
How to find the approximate new car price in 2014?The general form of a linear equation is given by:
y = mx + c
where y is the future price of the car, x is the number of years, m is the rate of change of price and c is the initial price of the car
c = $27,700
m = ($29,200 - $27,700)/(2010 - 2008)
m = 1500/2
m = $750 per year
In 2014, x = 2014 - 2008 = 6 years
Substituting into y = mx + c:
y = 750(6) + 27,700
y = 4500 + 27700
y = $32,200
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Find the slope of the line.
A. 3/2
B. -2/3
C. 4/3
D. -3/4
Answer:
-3/4, answer D
Step-by-step explanation:
Slope = rise/run. The equation is (y2-y1)/(x2-x1).
So let's pick 2 points. There are pink dots on (-2,2) and (6,-4), so we'll use those points.
slope = (2-(-4))/(-2-6)
slope = (2+4)/(-2-6)
slope = (6)/-8, which we can simplify by dividing the numerator and denominator each by 2.
slope = -3/4
Just as a quick check, this makes sense because as x increases, y decreases so we should expect the slope to be negative.
Answer:
Step-by-step explanation:
Use 2 points from the line: (-2, 2) and (6, -4)
slope = y2 -y1 = -4 - 2 = -6 = - 3
x2 - x1 6 - -2 8 4
The slope is choice D -3/4
what is 300 in word form
Answer:
Three Hundred.
What is the X intercepts of f(x) =-2x^2 + 10x - 7
Evaluate
--(5-1)(5²).
Answer:
100
Step-by-step explanation:
You want the value of --(5-1)(5²).
Minus signsThe even number of leading minus signs cancel each other, so the effect is as if there were no leading minus signs.
--(5 -1)(5²)
= --(4)(25)
= --(100)
= -(-100)
= 100
__
Additional comment
As always, the value of a numeric expression can be found using a calculator.
<95141404393>
WHAT IS THE FIRST STEP TO SOLVE 3(4x + 5) = 12
A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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Maxine's credit card has an APR of 27.99%. If her current monthly balance, before interest, is $1,834.50, what will her monthly interest charge be? (4 points) $42.78 $42.79 $51.67 $65.54
Answer:
(b) $42.79
Step-by-step explanation:
You want the monthly interest charge on a balance of $1834.50 when the annual rate is 27.99%.
Monthly rateThe monthly interest rate is the annual rate divided by 12. This means the interest charge is ...
I = Prt . . . . . interest on P at annual rate r for t years
I = $1834.50 × 0.2799 × 1/12 ≈ $42.79
Her monthly interest charge will be $42.79.
A simple gable roof is to cover a span of 32 feet. If it is to have a 7:12 pitch, how tall will the ridgeline be above the house?
The ridgeline will be 18.67 feet above the house.
What will be the height of the ridgeline above the house?Generally, a height refers to the measurement of someone or something from head to foot or from base to top.
To find the height of the ridgeline, we will use the formula: Height = (Pitch / 12) * Span
Given data:
Pitch = 7
Span = 32 feet
Inputting the values, we have:
Height = (7 / 12) * 32
Height = 0.5833 * 32
Height = 18.6656
Height = 18.67 feet.
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Pleaseee help me I’ve been stuck on this fool like 30 minutes can’t miss this or I restart the whole lesson pleease help
The properties of equality that shows justification of how the equation is solved is explained below.
How to Apply the Properties of Equality to Solve an Equation?Given the equation, 17/3 - 3/4x = 1/2x + 5, we have the following steps and justification which explains the property of equality that was used:
17/3 - 3/4x = 1/2x + 5 [given]
17/3 - 3/4x - 17/3 = 1/2x + 5 - 17/3 [subtraction property of equality]
3/4x = 1/2x - 2/3 [simplification]
3/4x - 1/2x = 1/2x - 2/3 - 1/2x [subtraction property of equality]
-5/4x = -2/3 [simplification]
-5/4x * -4/5 = -2/3 * -4/5 [multiplication property of equality]
x = 8/15 [simplification]
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Write a sin function that has a midline of y=3, and amplitude of 2, and a period of 3/4.
The required sine function is
y = 2 sin (3π/4 (x) + 3
For given function,
A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4
A = 2
T = 3π/4
Since we know
The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
In this case, the midline is 3
⇒ D = 3
Using the generalized equation of sine function,
y = A sin (B (x + C)) + D
y = 2 sin (3π/4 (x + 0) + 3
y = 2 sin (3π/4 (x) + 3
Therefore, the required sine function is
y = 2 sin (3π/4 (x) + 3
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here is my algebra 13 homework screenshot. can somebody please help me! QUICK
The function which has a range of real numbers is f(x) = -x + 2
Range is the set of the values that the function obtains this set is the values that the function obtains when we put an x value in the function.
In f(x) = -x + 2 when we put any value of x we get real number so the function range is ( -∞ , ∞ )
In g(x) = -x² when we put any value of x we get all negative number function range is (-∞ , 0]
In h(x) = [tex]2^{x}[/tex] + 1 when we put any value of x we get all positive number so the function range is (1 , ∞)
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can some one
factor 7a10 - 112a2
The factored of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
How to find the factor 7a10 - 112a2To factor the expression [tex]7a^{10} - 112a^2[/tex] we can identify the greatest common factor (GCF) and factor it out. Let's break down the steps:
The coefficients 7 and 112 have a common factor of 7.
The lowest power of "a" in each term.
In this case, the lowest power of "a" is 2.
Factoring out [tex]7a^2[/tex] from both terms, we get:
[tex]7a^2(a^8 - 16)[/tex]
Therefore, the factored form of [tex]7a^{10} - 112a^2[/tex] is: [tex]7a^2(a^8 - 16)[/tex]
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Which of the following statements is true for ∠a and ∠b in the diagram?
A) m∠a = m∠b
B) m∠a + m∠b = 90°
C) m∠a + m∠b = 180°
D) m∠a – m∠b = 90°
Answer:
A
Step-by-step explanation:
If you look at the angles or use something to measure it you can tell that a and b are opposite sides that are parallel to each other. So they are equal.
How can graph coloring be applied in real-world situations, and what are the challenges and limitations associated with using graph coloring algorithms? Provide specific examples to support your answer.
Answer:
Graph coloring is a widely used concept in real-world situations, particularly in computer science and engineering. It involves assigning colors to the vertices of a graph, with no adjacent vertices having the same color. One real-world application of graph coloring is in scheduling problems, where tasks must be assigned to resources such as workers or machines, with the constraint that no two tasks requiring the same resource can be scheduled at the same time. Another application is in map coloring, where regions on a map are assigned colors in such a way that no two adjacent regions have the same color.
Challenges and limitations associated with using graph coloring algorithms include the exponential increase in computation time as the size of the graph increases, making it difficult to apply the algorithm to very large graphs. Additionally, some graph coloring problems may be NP-hard, meaning that no polynomial-time algorithm is known that can solve them for all possible inputs. This can make it challenging to find an optimal solution, and instead approximate solutions may need to be used.
For example, in telecommunication networks, channel assignment is a common problem of graph coloring. In mobile networks, different channels must be assigned to different cells to avoid interference and ensure efficient use of resources. The channel assignment problem can be formulated as a graph coloring problem, where the vertices represent cells and the edges represent interference.
Another example is in scheduling of sports leagues. In this case, teams are assigned to play on different days and times in such a way that no two teams play against each other more than once and no team plays two games on the same day. This can be formulated as a graph coloring problem, with vertices representing teams and edges representing games between teams.
In conclusion, graph coloring algorithms have numerous real-world applications. While there are challenges and limitations associated with these algorithms, they continue to be an important tool for solving optimization problems in a wide range of fields.
Step-by-step explanation:
what gives the response the sequare of the highwr common fact of 30 and 50
Answer:
GCF of 30 and 50 is 10 :}
Evaluate and simplify the expression g(a+5) - g(5) completely when g(t)=2t^2.
Answer:
The simplified expression for g(a+5) - g(5) is 2a^2 + 20a.
Step-by-step explanation:
To evaluate and simplify the expression g(a+5) - g(5), we need to substitute the function g(t) = 2t^2 into the given expression.
Let's start by evaluating g(a+5):
g(a+5) = 2(a+5)^2
Expanding the expression:
g(a+5) = 2(a^2 + 10a + 25)
g(a+5) = 2a^2 + 20a + 50
Next, let's evaluate g(5):
g(5) = 2(5)^2
g(5) = 2(25)
g(5) = 50
Now we can substitute these values back into the expression g(a+5) - g(5):
g(a+5) - g(5) = (2a^2 + 20a + 50) - 50
Simplifying:
g(a+5) - g(5) = 2a^2 + 20a
Therefore, the simplified expression for g(a+5) - g(5) is 2a^2 + 20a.
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