Answer:
Mean = 7
Median = 8
Mode = 3
Range = 9
Step-by-step explanation:
License plates are made using 2 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is not allowed?
The number of license plates that can be made if repetition of letters and digits is not allowed is 468,000.
We will use the multiplication principle of counting here.
In multiplication principle of counting, if a task can be done in m ways and another task can be done in n ways, then both tasks can be done together in m × n ways. So, the number of ways the license plates can be made without repetition is:
Number of ways to select 2 letters from 26 letters without repetition = 26P2 = 26 × 25
Number of ways to select 3 digits from 10 digits without repetition = 10P3 = 10 × 9 × 8
Hence, using the multiplication principle of counting, the number of license plates that can be made without repetition of letters and digits is:
26 × 25 × 10 × 9 × 8= 468,000.
Therefore, the number of license plates that can be made if repetition of letters and digits is not allowed is 468,000.
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11,900 divided by 34
Please help me fast!!!!!!!!!!
Answer: 4x-12x
Step-by-step explanation:
Distributive preoperty so -6*-2/3=4 and -6*2x= -12x together 4x-12x equals option c
Answer:
You're going to myltiply -6 ×-2/3 which will equal positive 4 and -6 ×2x which is going to equal-12. So your answer is 4-12x
Using dynamic geometry software, Nora calculates the perimeter P and area A of a regular hexagon with a side length of 2 units. The change to the perimeter and area after three, doublings of this side length are listed in the table. Analyze the patterns in the table. Then make a conjecture as to the effects on the perimeter and area of a regular hexagon when the side length is doubled. Explain.
Perimeter:
2 units -> 12 units
4 units -> 24 units
8 units -> 48 units
Area:
2 units -> 10.39 square units
4 units -> 41.57 square units
8 units -> 166.28 square units
Analyzing the patterns in the table, we can observe the following:
Perimeter: When the side length of the regular hexagon is doubled, the perimeter also doubles. For example, when the side length is 2 units, the perimeter is 12 units. When it is doubled to 4 units, the perimeter becomes 24 units. This doubling pattern continues when the side length is doubled to 8 units, resulting in a perimeter of 48 units. Therefore, we can conjecture that doubling the side length of a regular hexagon doubles its perimeter.
Area: When the side length of the regular hexagon is doubled, the area is quadrupled. For instance, when the side length is 2 units, the area is approximately 10.39 square units. When the side length is doubled to 4 units, the area becomes approximately 41.57 square units, which is four times the initial area. Similarly, when the side length is doubled again to 8 units, the area becomes approximately 166.28 square units, which is again four times the previous area. Hence, we can conjecture that doubling the side length of a regular hexagon results in its area being multiplied by four.
These patterns can be explained by considering the properties of regular polygons. In a regular hexagon, all sides are congruent, and the perimeter is the sum of all the side lengths. Therefore, when each side length is doubled, the perimeter doubles as well. Regarding the area, a regular hexagon can be divided into six congruent equilateral triangles. The area of an equilateral triangle is proportional to the square of its side length. When the side length is doubled, the area of each equilateral triangle is quadrupled, resulting in the overall area of the hexagon being multiplied by four.
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Crosby and Adam are working with exponents. Crosby claims that 3² * 3³ = 3⁵. Adam argues that 3² * 3³ = 3⁶. Which one of them is correct?
Answer:
Crosby is correct.
Step-by-step explanation:
You know this is true because if you plug in 3^2 * 3^3, you get 243.
If you type in 3^5, you get 243. If you type in 3^6, you get 729, which is not true.
assume that cans of pepsi are filled so that the actual amount have a mean of 12 oz and a standard deviation of 0.09 oz. suppose that a random sample of 36 cans are examined, 1. what is the mean of this sample mean of 36 cans?
The mean of the sample mean of 36 cans of Pepsi is (11.97, 12.03), by using the standard error of the mean.
To calculate the mean of the sample mean, we need to first calculate the standard error of the mean (SEM) by divide the standard deviation of the population by the square root of the sample size. In this case, the centred deviation is 0.09 oz, which is the standard deviation of the population. And the sample size is 36. Therefore, the SEM of the sample mean is 0.09 / sqrt(36) = 0.015 [1].
The mean of the sample mean of 36 cans can be calculated by adding up the values of all 36 cans and dividing by 36. However, without additional information on the values of each can, we cannot determine the exact value of the mean of the sample mean of 36 cans. However, we can say with 95% confidence that the true mean of the population falls within a range of +/- 2 SEM.
Therefore, the 95% confidence interval for the sample mean would be 12 +/- 2 * 0.015, which is (11.97, 12.03).
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A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go, and it steadily rose 3 feet per second.
The equation that shows the relationship between the number of seconds since the boy let the balloon go is y = 3x + 3.
What is a function?A function can be defined as the outputs for a given set of inputs. The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Here,
Given, A little boy accidentally let go of his balloon, and it floated away. It was 3 feet above the ground when he let go this height is our constant value in the function.
It steadily rose 3 feet per second.
Assuming time in seconds to be x and total height is y.
∴ An equation that shows the relationship between the number of seconds since the boy let the balloon go is,
y = 3x + 3
The link between the amount of seconds after the youngster let go of the balloon is shown by the equation y = 3x + 3.
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what are the conditions for using the normal approximation for a sampling distribution of proportions g
The normal approximation for sampling distributions of proportions can be used when the sample size is large enough.
What prerequisites must be met for a sampling distribution of proportions g in order to use the normal approximation?The conditions for using the normal approximation for a sampling distribution of proportions are as follows: The sample size (n) must be sufficiently large (usually 30 or more). The sample proportion (p) should not be close to 0 or 1. The population distribution should be normally distributed.The general rule is that if the sample size (n) is greater than or equal to 30, then the normal approximation can be used. When using the normal approximation for a sampling distribution of proportions, the sample size must be greater than or equal to 30 and the population proportion (p) must be between 5% and 95%. Furthermore, the sample size must be large enough that the expected number of successes (np) and expected number of failures (nq) are both greater than or equal to 10. Finally, the sampling distribution should be approximately normal and the sample should be randomly selected from the population. The normal approximation is a useful tool for estimating confidence intervals and the probability of extreme values, as well as for hypothesis testing. It can be used to estimate the probability of success in a given sample of proportions, which can be helpful when making decisions about a population or understanding the behavior of a system.To learn more about distribution of proportions refer to:
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Suppose a vector v is decomposed into orthogonal components with respect to orthogonal vectors q₁,... qn, so that H r=v-(q²v)9₁ −(q²v)q2 - ·· · (qh' v)¶n ± 0. 91 92 1 This implies that (a) (b) (c) (d) The vectors i are linearly dependent ris orthogonal to vectors q₁,... qn v=0 VE (9₁, ··· 9n) ve
The given expression represents the decomposition of vector v into orthogonal components with respect to orthogonal vectors q₁, ..., qn. The vectors 9₁, ..., 9n are orthogonal projections of v onto q₁, ..., qn, respectively.
The expression Hr = v - (q²v)9₁ - (q²v)q₂ - ... - (qh'v)qn indicates that vector r is obtained by subtracting the orthogonal projections of v onto each of the orthogonal vectors q₁, ..., qn from v itself. Here, (q²v) represents the dot product between q and v.
In part (a), it is implied that the vectors 9₁, ..., 9n are linearly independent. This is because if any of the vectors 9ᵢ were linearly dependent on the others, we could express one of them as a linear combination of the others, leading to redundant information in the decomposition.
In part (b), it is implied that the vectors r and q₁, ..., qn are orthogonal to each other. This follows from the fact that the expression Hr subtracts the orthogonal projections of v onto q₁, ..., qn, resulting in r being orthogonal to each of the q vectors.
In part (c), it is implied that the vector v can be written as the sum of the orthogonal projections of v onto q₁, ..., qn, i.e., v = 9₁ + ... + 9n. This is evident from the decomposition expression, where the vectors 9₁, ..., 9n are subtracted from v to obtain r.
In part (d), it is implied that the vector v is orthogonal to the vector r. This can be seen from the decomposition expression, as the orthogonal projections of v onto q₁, ..., qn are subtracted from v, leaving the remaining component r orthogonal to v.
Overall, the given expression represents the decomposition of vector v into orthogonal components with respect to orthogonal vectors q₁, ..., qn, and the implications (a)-(d) provide insights into the properties of the vectors involved in the decomposition.
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the number of cookies in a shipment of bags are normally distributed, with a mean of 64 and a standard deviation of 4. what percent of bags of cookies will contain between 64 and 68 cookies?
The percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.The number of cookies in a shipment of bags is normally distributed, with a mean of 64 and a standard deviation of 4.
What percentage of bags of cookies will contain between 64 and 68 cookies
When X is normally distributed with mean µ and standard deviation σ, the z-score formula can be used to find the probability that X is between two values.
Z = (X - µ) / σ
First, we convert both 64 and 68 to z-scores:
Z for 64 cookies = (64 - 64) / 4 = 0Z for 68 cookies = (68 - 64) / 4 = 1
Next, we find the probability that X is between these two z-scores using a standard normal distribution table or calculator:
Prob (0 < Z < 1) = 0.3413 - 0.5(0) - 0.159
= 0.1823
So, the percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.
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Peterson and Peterson (1959) conducted an experiment in which participants were asked to remember random letters of the alphabet. They then instructed the participants to count backwards from a three-digit number by threes aloud. The longer the participants spend counting backward, the fewer random letter units they could recall. This inability to recall the original random letters was due in part to____.
The inability to recall the original random letters in the Peterson and Peterson (1959) experiment was due in part to the decay of information in short-term memory (STM).
STM has a limited capacity and duration, which means that information can be lost over time if it is not rehearsed or refreshed.
In this experiment, participants were asked to remember random letters and then count backward from a three-digit number by threes aloud, which served as a distractor task to prevent rehearsal of the letters.As participants spent more time counting backward, the random letters in their STM started to decay, leading to fewer letter units being recalled. This demonstrates the limited duration of STM and how interference from other cognitive tasks can negatively impact the retention of information. The decay of information in STM occurs when it is not actively maintained or rehearsed, making it difficult for individuals to retrieve that information later on.In conclusion, the results of the Peterson and Peterson (1959) experiment highlight the importance of rehearsal in maintaining information in short-term memory and demonstrate the limitations of STM's capacity and duration. The inability to recall the original random letters after engaging in the distractor task can be attributed to the decay of information in STM due to a lack of rehearsal and interference from the counting task.Know more about the short-term memory (STM).
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If Point A located at (-3,6) is reflected across the y axis, and then across the x axis, where will Point A' be located?
Answer:
(3.6)
Step-by-step explanation:
for this the y cordinates are the same while the x points are the opposite signs
Please help I don’t know the answer!!
Answer:
wait do u have a word bank or anything like words to go with it or numbers ????
A cannery processed 1365 pounds of strawberries in 4.5 hours. The cannery processed 3180 pounds in 10 hours.
a. Write a linear equation to model the weight of strawberries S processed in T hours.
b. How many pounds of strawberries can be processed in 11 hours?
what is the volume of the regular pyramid below?
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
This question is incomplete, the missing image is uploaded along this answer below.
What is the volume of the regular pyramid?The volume of pyramid is expressed as;
V = ( 1/3 ) × l × w × h
Given that;
Length l = 8Width W = 8Height h = 6We substitute our given values into the equation above.
V = ( 1/3 ) × 8 × 8 × 6
V = 128 unit³
The volume of the regular pyramid is 128 unit³.
Option D) 128 unit³ is the correct answer.
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Solve for x. (Show ur work)
Which graph shows the solution to this system of in
y>-1/3x+1
y> 2x-3
Answer:
Step-by-step explanation:
the graph is down below
A car travels a distance of 104 miles in 4 hours. What is the speed in miles per hour
Answer:
26
Step-by-step explanation:
104 miles
4 hours
so do 104/4, then you get 26
so 26 miles per an hour
Speed of the car is 26 miles per hour.
What is speed?Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.
Speed formula can be used to find the speed of objects. The formula for the speed of a given body can be expressed as,
Speed = Distance ÷ Time
Given,
Car travels distance = 104 miles
Time taken to travel 104 miles = 4 hours
Speed = distance/ time
Speed of car
= 104/4
= 26 miles per hour
Hence, 26 miles per hour is the speed of car.
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What is the slope of the line shown in the graph?
A)
0
B)
undefined
C) -3
D)- -1/3
Answer:
A) = 0
Step-by-step explanation:
That slope is A), 0 because it is neither increasing or decreasing
a. Connie has $100 in her piggy bank. Ryan has 3 times more than Connie. How much money does Ryan have?
Joe's equation: 100 cross times 3 equals r
Answer:
Its 300
Step-by-step explanation:
Because 100 x 30 = 300
How many extraneous solutions does the equation have 2m 2m 3 2m 2m 3 1?.
Zero extraneous solutions does the equation have (2m)/(2m+3)-(2m)/(2m-3) = 1.
What is Quadratic Equation?
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable a ≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated.
Given that;
\(\frac{2m}{2m+3}-\frac{2m}{2m-3} = 1\)
⇒ \(\frac{2m(2m-3)-2m(2m+3)}{(2m+3)(2m-1)}=1\)
⇒ \(\frac{4m^2-6m-4m^2-6m}{(4m^2-9)}=1\)
⇒ \(\frac{-12m}{4m^2-9}=1\\\)
⇒ \(-12m = 4m^2-9\)
4m^2 +12m - 9 = 0(1)
The formula for calculating the roots of the quadratic equation ax^2 + bx + c can be utilized because (1) is a quadratic equation.
\(\frac{-b\pm \sqrt{b^2-4ac} }{2a}\)
Variable m is in equation (1), where a = 4, b = 12, and c = -9.
The roots are calculated as:
\(\frac{-12\pm \sqrt{12^2-4\times 4\times (-9)} }{2\times 4}\)
\(\frac{-12\pm \sqrt{2\times 144} }{8}\)
\(\frac{-12\pm 12\sqrt{2} }{8}\)
\(\frac{-3}{2} \pm \frac{3}{2}\sqrt{2}\)
\(\frac{-3}{2} - \frac{3}{2}\sqrt{2} \ and \ \frac{-3}{2} + \frac{3}{2}\sqrt{2}\)
Subsitituting \(\frac{-3}{2} - \frac{3}{2}\sqrt{2}\) in equation (1);
\(9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0\)
0 = 0
The root -3/2 - 3(\(\sqrt{2}\))/2 is therefore not an auxiliary solution.
Now substituting \(\ \frac{-3}{2} + \frac{3}{2}\sqrt{2}\) in equation (1);
\(9+18+18\sqrt{2}-18-18\sqrt{2} -9 = 0\)
0 = 0
Therefore, the root -3/2 + 3(\(\sqrt{2}\))/2 IS NOT AN ADDITIONAL SOLUTION.
The above problem can be solved using either of the two roots.
There is no superfluous solution to the equation (2m)/(2m+3)-(2m)/(2m-3) = 1 as a result.
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Complete this formal proof of B from ~A and AvB in as few lines as possible.
Do cases from left to right! (Left-hand disjunct is the first case.)
1. ~A
2. AvB
Premise
3. |
4. |
5. |
6. |
7.
8.
The formal proof of B from ~A and AvB is completed.
To complete this formal proof of B from ~A and AvB in as few lines as possible, follow these steps:
1. ~A (Premise)
2. AvB (Premise)
3. Assume ~A (Left-hand disjunct, 1st case)
4. B (Disjunction elimination on 2 with 3, i.e., since ~A is true, and AvB is true, B must be true)
5. Assume A (Right-hand disjunct, 2nd case)
6. B (Contradiction elimination on 1 and 5, i.e., A cannot be true since ~A is true, so B must be true)
7. B (Disjunction elimination on 2 with 3-4 and 5-6, i.e., since B is true in both cases, we can conclude B is true)
So, the formal proof of B from ~A and AvB is completed in 7 lines.
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2x3 + 5x2 + 6x + 15
Which of the following is equivalent to the expression above?
A
(x + 3)(2x2 + 5)
B
(x + 5)(2x2 + 3)
с
(x2 + 3)(2x + 5)
D
(x2 + 5)(2x + 3)
Answer:
C
Step-by-step explanation:
Distribute x^2 to 2x and 5, you’ll get 2x^3+5x^2.
The distribute 3 to 2x and 5, you’ll get 6x+15.
You’ll get what the question is asking for.
We need to find the equivalent expression of the given expression.
The required expression is \((x^2+3)(2x+5)\).
The given expression is \(2x^3+5x^2+6x+15\)
Let us solve each option by using the distributive law
\((x+3)(2x^2+5)\\ =2x^3+5x+6x^2+15\)
\((x+5)(2x^2+3)\\ =2x^3+3x+10x^2+15\)
\((x^2+3)(2x+5)\\ =2x^3+5x^2+6x+15\)
\((x^2+5)(2x+3)\\ =2x^3+3x^2+10x+15\)
So, the only option matching with the given expression is C \((x^2+3)(2x+5)\).
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OFFERING 88 POINTS AND BRAINLIEST TO THE FIRST ANSWER PLEASE HELP ME FAST
Answer
\(168in^{2}\)
Step-by-step explanation:
SA=2(wl+hl+hw)
2·(6·2+9·2+9·6)
=168
what is the smallest composite integer n greater than 6885 for which 2 is not a fermat witness?
The smallest composite integer n greater than 6885 for which 2 is not a Fermat witness is n = 6888.
What is the next composite number larger than 6885 where 2 is not a Fermat witness?To find the smallest composite integer n greater than 6885 for which 2 is not a Fermat witness, we need to check if the number n satisfies the condition of the Fermat primality test for the base 2.
According to the Fermat primality test, if a number n is prime, then for any base a, where 1 < a < n, the congruence \(a^(n-1) ≡ 1 (mod n)\) holds.
However, if n is composite, there exists at least one base a that violates the above congruence, making it a Fermat witness for n.
We can start by checking numbers greater than 6885 to determine the smallest composite integer n for which 2 is not a Fermat witness.
Let's check the numbers starting from 6886:
For n = 6886:
\(2^{(6886-1)} \equiv2^{6885} \equiv 1 (mod 6886)\) holds, so 2 is a Fermat witness for n = 6886.
For n = 6887:
\(2^{(6887-1)} \equiv 2^{6886} \equiv 1 (mod 6887)\) holds, so 2 is a Fermat witness for n = 6887.
For n = 6888:
\(2^{(6888-1)} \equiv 2^{6887 }\equiv 2 (mod 6888)\) violates the congruence, so 2 is not a Fermat witness for n = 6888.
Therefore, the smallest composite integer n greater than 6885 for which 2 is not a Fermat witness is n = 6888.
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Answer need ASAP
Add -3 1/6 + 5 3/4 and write it as a reduced mixed number
-3 1/6 + 5 3/4 = ?
Answer: 2 5/6 I think.
Wait no. I just did the math and it would be 2 1/2
he theater club is hosting a one-act competition to raise $1,220 for new costumes. It plans to sell tickets for $8 each and would like to earn within $100 of its goal. This is the equation representing this situation, where t is the number of tickets sold: |8t − 1,220| = 100. Type the correct answer in each box. Use numerals instead of words. To earn within $100 of its goal, the theater club needs to sell a minimum of tickets and a maximum of tickets.
Answer:
i think that your suppose to divide add and subtracct.
Step-by-step explanation:
Hope this helps.
Answer:
140
165
Step-by-step explanation:
To solve the absolute value equation, first rewrite the equation as two separate equations equal to -100 and 100:
8t − 1,220 = -100 8t − 1,220 = 100
8t = 1,120 8t = 1,320
t = 140 t = 165
To earn within $100 of its goal, the theater club needs to sell a minimum of 140 tickets and a maximum of 165 tickets.
How do I do this I need help
Answer and Explanation:
We can find the slope of each line by dividing the change in y by the change in x between two points on the line. In other words:
slope = rise / run
1. 2/5
2. 1/4
3. -1/3
4. -5/2
5. 6/7
6. -6/2 = -3
7. 0/0 = 0
8. -2/6 = -1/3
find three solutions 3(x-3) + 9(7y + 3x) = 6
malai kai tha xaina3521457269026422
Answer:
t's solve for x.
3(x−3)+9(7y+3x)=6
Step 1: Add 9 to both sides.
30x+63y−9+9=6+9
30x+63y=15
Step 2: Add -63y to both sides.
30x+63y+−63y=15+−63y
30x=−63y+15
Step 3: Divide both sides by 30.
30x
30
=
−63y+15
30
x= 21 /10 y 1/2
Answer:
x= -21 / 10 y + 1/2
Step-by-step explanation:
HOPE IT HELPS YOU MARK AS BRAINLIEST
Porfavor alguien me dice cuanto es esto 3×?=20
Answer:
6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
Step-by-step explanation:
Que no se te olvide el punto
Answer:
es imposible
Step-by-step explanation:
3x7=21
se va por uno