Approximate the value of the given integral by use of the trapezoidal rule, using the given value of n. 5 9 -dx, n= 10 2 x + x 1 ... 5 9 so dx = (Round to four decimal places as needed.) + X 1 X
Answers
The approximate value of the integral is -9.0167.
To approximate the value of the given integral using the trapezoidal rule with n = 10, we divide the interval [5, 9] into 10 subintervals and apply the formula for the trapezoidal rule.
The trapezoidal rule states that the integral of a function f(x) over an interval [a, b] can be approximated as follows:
∫[a to b] f(x) dx ≈ (b - a) * [f(a) + f(b)] / 2
In this case, the integral we need to approximate is:
∫[5 to 9] (2x + x²) dx
We divide the interval [5, 9] into 10 subintervals of equal width:
Subinterval 1: [5, 5.4]
Subinterval 2: [5.4, 5.8]
...
Subinterval 10: [8.6, 9]
The width of each subinterval is h = (9 - 5) / 10 = 0.4
Now we calculate the approximation using the trapezoidal rule:
Approximation = h * [f(a) + 2(f(x1) + f(x2) + ... + f(xn-1)) + f(b)]
For each subinterval, we evaluate the function at both endpoints and sum the values.
Finally, we sum the approximations for each subinterval to obtain the approximate value of the integral. In this case, the approximate value is -9.0167 (rounded to four decimal places).
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Related Questions
A pharmaceutical company wants to test the effectiveness of a new allergy drug. The company identifies 250 females 30-35 years old who suffer from severe allergies. The subjects are randomly assigned into two groups. One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug. After six months, the subjects' symptoms are studied and compared. Answer parts (a) through (c) below.
Answers
After six months, the subjects' symptoms are studied and compared. Answer parts are given below.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
A pharmaceutical company wants to test the effectiveness of a new allergy drug.
The company identifies 250 females 30–35 years old who suffer from severe allergies.
The subjects are randomly assigned into two groups.
One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.
After six months, the subjects' symptoms are studied and compared.
Here, 30-35 year-old girls are used to test the new allergy medication's effects.
(a)
Females between the ages of 30 and 35 who are the test subjects are the experimental units.
The new allergy medication, whose results are being studied, is the remedy.
It's best to choose C.
(b)
A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.
In this case, choice B is preferable.
(c)
If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.
In this case, choice A is preferable.
Therefore, all the correct choices are given above.
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The complete question is given in the image.
Which of the following statements is false?
• A. A square is a regular quadrilateral.
B. A rectangle is an equiangular quadrilateral.
C. Adjacent angles in a parallelogram are complementary.
•D. Opposite sides of a parallelogram are congruent.
Answers
The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.
What are the type of angles in a parallelogram ?In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.
Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.
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Determine the global extreme values of the function on the given set without using calculus f(x, y) = 8e-(2x2+8y2), 2x2 + 8y2 52 fmin = fmax =
Answers
The maximum value of the function on the given set is 8e⁻²⁶. Therefore, fmin = 8e⁻⁵² and fmax = 8e⁻²⁶.
To determine the global extreme values of the function f(x, y) = 8e-(2x² + 8y²) on the given set 2x² + 8y² ≤ 52, we can use the fact that the function is decreasing as the argument (2x² + 8y²) increases. Therefore, we want to maximize the value of 2x² + 8y² while staying within the given set. The maximum value of 2x² + 8y² on this set is 52, which is the boundary of the set.
When 2x² + 8y² = 52, we have f(x, y) = 8e-(2x² + 8y²) = 8e⁻⁵² = 8e-52. This is the minimum value of the function on the given set.
Since the function is decreasing as the argument increases, the maximum value of the function occurs at the boundary points where 2x² + 8y² = 52. Therefore, we can find the maximum value by evaluating the function at the four boundary points:
f(±√13, ±√3) = 8e-(2(√13)2+8(√3)2) = 8e-26
The maximum value of the function on the given set is 8e⁻²⁶. Therefore, fmin = 8e⁻⁵² and fmax = 8e⁻²⁶.
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write 71.38 in word form
Answers
seventy-one and thirty-eight hundreths
mLON is a straight angle.
mMON = 8x - 13
mLOM = 7x – 17°
Find MON
Answers
Answer:MON=99
Step-by-step explanation:
8x-13+7x-17=180
15x=210
x=14
Answer:
Step-by-step explanation:
8x - 13 + 7x - 17 =180
15x - 30 = 180
15x = 210
x = 14
8(14) - 13= 112 - 13 = 99
the bill for three bags of peanuts on two medium drinks at the movies with 11.15 dollars is a bag of peanuts cost to $35 how much was 1 drink
Answers
Answer:
5.575
Step-by-step explanation:
divide it by 2 its easy
a. name the vertex of <4 b. Name the sides of <1 c. Write another Name for <5 d. classify each angle
Answers
Answer:
A. vertex B
B. Side BC and BD
C. Angle EBD
Step-by-step explanation:
An angle is an undefined term in plane geometry.
The vertex of \(\angle 4\) is BThe sides of \(\angle 1\) are BC and BDAnother name for \(\angle 5\) is \(\angle DBE\).\(\angle FBC\) is a right angle\(\angle EBF\) is an obtuse angle \(\angle ABC\) is a straight angle.\(\angle EBC = 144\)\(\angle ABE =13.5\)Vertex of \(\angle 4\)
The vertex of an angle is the point where the rays that form the angle meet.
From the diagram, rays BE and BA meet at point B to form \(\angle 4\).
Hence, the name of the vertex is B
Sides of \(\angle 1\)
The sides of an angle are the rays or sides that form the angle
\(\angle 1\) is formed by rays BC and BD
Hence, the sides are BC and BD
Another name for \(\angle 5\)
An angle can be named by combining the sides and the vertex.
The sides of \(\angle 5\) are DB and BE, while the vertex is B
This means that rays DB and BE meet at point B
Hence, another name is \(\angle DBE\)
Classify the angles
Angles are classified based on the measure
\(\angle FBC\) is a right angle, because \(\angle FBC = 90^o\)
\(\angle EBF\) is an obtuse angle because \(\angle EBF\) is greater than \(90^o\) but less than \(180^o\)
\(\angle ABC\) is a straight angle, because \(\angle ABC= 180^o\)
Angle bisector
The line or ray that divides an angle into equal halves is an angle bisector.
Ray BE is an angle bisector, because it divides \(\angle DBA\) into two equal halves.
Find \(\angle EBC\)
We have:
\(\angle EBD = 36\)
\(\angle DBC = 108\)
\(\angle EBC\) is calculated using:
\(\angle EBC = \angle EBD +\angle DBC\)
\(\angle EBC = 108+36\)
\(\angle EBC = 144\)
Find \(\angle ABE\)
We have:
\(\angle EBF = 117\)
\(\angle DBC = 108\)
\(\angle ABE\) is calculated using:
\(\angle EBF = \angle ABE +\angle EBD + \angle ABF\)
Where
\(\angle ABF = 90\)
\(\angle ABE = \angle EBD\)
So, we have:
\(117 = \angle ABE +\angle ABE + \angle 90\)
\(117 = 2\angle ABE + 90\)
Collect like terms
\(2\angle ABE =117 - 90\)
\(2\angle ABE =27\)
Divide both sides by 2
\(\angle ABE =13.5\)
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help last question A semicircular mat has a diameter of 18 m. What is the area of the mat?
Answers
Answer:
127.2
Step-by-step explanation:
The area of a semicircle is:
\(\frac{\pi r^{2} }{2}\)
So to figure it out we first find the diameter:
18÷2=9
Then we plug it into the equation
\(\frac{9^{2}\pi }{2} = \frac{81\pi}{2}\) Which we can put into a calculator to get 127.2345... so we round to 1 d.p to get our answer, 127.2 (the fifth digit, 3, rounds down)
The area formula for a semicircle is
(pie)(radius^2). So divide 18 (the diameter) by 2 to find the radius, and it’ll be 9. The when you solve it, it should be 127.235.
PLEASE HELP, WILL VOTE BRAINLIEST
Write an explicit function to represent the following sequence.
3,9, 27, 81,...
Answers
Answer:
The equation would be if y is the numbers in the sequence (like 3, 9, 27) and x is the is the number in the order (like 3 is 1, 9 is 2, 81 is 4) the the equation would be y = 3^x.
Step-by-step explanation:
Find the area, in square meters, of an equilateral triangle with a perimeter of 36 m.
Answers
Answer:
If an equilateral triangle has a perimeter of 36 meters, then each side of the triangle is 36 ÷ 3 = 12 meters long.
To find the area of an equilateral triangle, we can use the formula:
Area = (sqrt(3) / 4) x (side)^2
Plugging in the value for the side, we get:
Area = (sqrt(3) / 4) x (12)^2
Area = (sqrt(3) / 4) x 144
Area = 36 x sqrt(3)
Therefore, the area of the equilateral triangle is 36 times the square root of 3, which is approximately 62.353 square meters (rounded to three decimal places).
A truck is loaded with packages. The truck's
trailer is 12 feet high by 5 1/2 feet wide by 15 1/2 feet long. What is the volume of the trailer?
A. 97 1/4
B. 19 1/2
C. 252
D. 1,023
Answers
The volume of the trailer is 97 1/4 cubic feet. The calculation is based on multiplying the height, width, and length of the trailer.
To calculate the volume of the trailer, we multiply the three dimensions: height, width, and length.
The height of the trailer is given as 12 feet, the width is 5 1/2 feet, and the length is 15 1/2 feet. To multiply these measurements, we convert the mixed fractions into improper fractions. The width can be expressed as 11/2 feet, and the length as 31/2 feet.
Now, we multiply the three dimensions:
12 feet × 11/2 feet × 31/2 feet = (12 × 11 × 31) / (2 × 2 × 2) = 4074 / 8 = 509 1/4 cubic feet.
Therefore, the volume of the trailer is 509 1/4 cubic feet.
However, since the answer choices provided are not in mixed fraction format, we convert 509 1/4 to an improper fraction, which is 2049/4. The nearest answer choice is 97 1/4 cubic feet (97.25 in decimal form), which accurately represents the volume of the trailer. Thus, the correct answer is A. 97 1/4.
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A geologist gathered data about the total shoreline and maximum depth of several area lakes and organized the data into this table.
Total Shoreline (miles) 22 17 10 23 12 35 7
Maximum Depth (feet) 101 85 59 113 64 158 33
She then used a graphing tool to display the data in a scatter plot, with x representing the total miles of shoreline and y representing the maximum depth. She also used the graphing tool to find the equation of the line of best fit:
y = 4.26x + 10.908.
Based on the line of best fit, what is the approximate maximum depth of a lake that has 31 miles of shoreline?
Answers
Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft
How to interpret a Line of best fit?The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.
Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.
However, when the geologist found the graph, she arrived at an equation of best fit as;
y = 4.26x + 10.908.
Thus, for 31 miles of shoreline, the approximate maximum depth is;
Approximate maximum depth = 4.26(31) + 10.908.
Approximate maximum depth = 142.968 ft
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Answer:
143 feet
Step-by-step explanation:
its technically 142 and change but edmentum rounds up
The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
Answers
Answer:
Step-by-step explanation:
Correct option is A)
Find the greatest common factor.
42²x² + 42²x+ 40²
Enter the correct answer.
Answers
Answer:
4a^2
Step-by-step explanation:
\(4a^2x^2+4a^2x+4a^2= \\\\4a^2(x^2+x+1)\)
Therefore, the largest common factor is 4a^2. Hope this helps!
(For 160,000 it takes 18ms to sort each half. Then merging together the two sorted halves with 80,000 numbers in each of them takes 40-218 = 4 ms. For 320,000 elements, it will take 240 to sort each half and 24 to merge the sorted halves with 160,000 numbers in each, for the total of 240+8 = 88 ms.)
Answers
For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.
The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.
When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.
Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.
Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.
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Find the value of X
Answers
Explanation: since x is next to 138 it’s a supplementary. Therefore, you do 180 -138 which is 42
the only calculated fields you can create in access are those involving addition and subtraction. True or false?
Answers
Answer:
false
Step-by-step explanation:
False.
Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.
In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.
Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.
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find the median of the numbers
Answers
Answer:
8
Step-by-step explanation:
There are 3 numbers on each side of 8, which makes 8 the median because it is in the middle.
if there are an even number on each side it leaves the middle number to be the median.
Liz wants to determine which sport students like to play the most at her school. Which method will MOST LIKELY produce a random sample?
Liz randomly surveys 10 of her friends.
Liz randomly surveys 10 girls at her school.
Liz randomly surveys 10 students at her school.
Liz randomly surveys 10 athletes at her school
Answers
Answer:
10 students
Step-by-step explanation:
It will give the broadest spectrum of answers. If it asked which sport most athletes played at her school you would've been asked what sport most athletes play
If I am wrong please correct me
Liz randomly surveys 10 students at her school and will MOST LIKELY produce a random sample so option (C) will be correct.
What is sampling?Sampling is collecting some items in a lot randomly to predict opinions about the lot.
For example; Selection of goods, selection of people
Sampling is a useful technique because if we do it for all samples then it will take time and cost as well.
Given that,
Liz wants to determine which sports students like to play the most at her school.
So her sample also should be from the lot(school).
If she takes 10 girls then it will not gives results for boys.
Hence "Liz randomly surveys 10 students at her school and will MOST LIKELY produce a random sample".
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You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The 107 subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program and the thirst received usual heart care from their personal physicians. In the next three years, only three of the 33 people in the stress management group suffered "cardiac events", defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, seven of the 34 people in the exercise group and 12 out of the 40 patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. What are the success rates of the three treatments in preventing cardiac events?
Answers
The success rates of the three treatments in preventing cardiac events are approximately 90.91% for the stress management program, 79.41% for the exercise program, and 70% for usual heart care.
a. Two-way table:
| Treatment | Cardiac Events | No Cardiac Events |
|-----------|-----------------|----------------------|
| Stress Management | 3 | 30 |
| Exercise | 7 | 27 |
| Usual Care | 12 | 28 |
b. The success rates of the three treatments in preventing cardiac events can be calculated as the percentage of people in each group who did not experience a cardiac event.
- Stress management: 90.9% success rate (30/33)
- Exercise: 79.4% success rate (27/34)
- Usual care: 70% success rate (28/40)
Therefore, the stress management program had the highest success rate in preventing cardiac events, followed by the exercise program and then usual care.
Stress management and its impact on reducing heart attacks. Let's analyze the study results and create a two-way table, as well as calculate the success rates of the three treatments in preventing cardiac events.
a. Two-way table:
| Treatment | Cardiac Events | No Cardiac Events | Total |
|--------------------|----------------|-------------------|-------|
| Stress Management | 3 | 30 | 33 |
| Exercise Program | 7 | 27 | 34 |
| Usual Heart Care | 12 | 28 | 40 |
| Total | 22 | 85 | 107 |
b. Success rates of the three treatments in preventing cardiac events:
1. Stress Management:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (30 / 33) * 100
Success rate ≈ 90.91%
2. Exercise Program:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (27 / 34) * 100
Success rate ≈ 79.41%
3. Usual Heart Care:
Success rate = (No Cardiac Events / Total) * 100
Success rate = (28 / 40) * 100
Success rate = 70%
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1. Find the probability that you will roll a six and then a five when you roll a die twice
2. A bag contains 3 red, 4 blue, and 6 yellow marbles. One Marble is selected at a time, and once a marble is selected, it is replaced, find each probability.
Answers
can someone see if i did them right?
Answers
Answer:
Yes your answer is right. You did well
The surface area of a rectangular prism is 174 square inches. The rectangular base has one side length 3 times the other. The height of the prism is 5 inches. What are the maximum lengths of the sides of the base?A. 6 inches and 18 inchesB. 8.7 inches and 26.1 inchesC. 4.35 inches and 13.05 inchesD. 3 inches and 9 inches
Answers
EXPLANATION:
We are given the following details for a triangular prism;
\(\begin{gathered} \text{Surface area}=174 \\ \text{Width}=w \\ \text{Length}=3w \\ \text{Height}=5 \end{gathered}\)Note that for the rectangular base, one side is 3 times the other. Hence, if the width is w, then the length would be 3 times w.
The surface area of a rectangular prism is;
\(S=2(wl+hl+hw)\)With the side lengths given we can now substitute and we'll have;
\(\begin{gathered} 174=2(\lbrack w\times3w\rbrack+\lbrack5\times3w\rbrack+\lbrack5w\rbrack) \\ 174=2(3w^2+15w+5w) \end{gathered}\)Divide both sides by 2;
\(\begin{gathered} 87=3w^2+15w+5w \\ 87=3w^2+20w \end{gathered}\)We shall now move all terms to one side of the equation;
\(3w^2+20w-87=0\)We can now solve this quadratic equationwith the quadratic equation formula;
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)Where the variables are;
\(a=3,b=20,c=-87\)\(w=\frac{-20\pm\sqrt[]{20^2-4(3)(-87)}}{2(3)}\)\(w=\frac{-20\pm\sqrt[]{400+1044}}{6}\)\(w=\frac{-20\pm\sqrt[]{1444}}{6}\)\(w=\frac{-20\pm38}{6}\)\(w=\frac{38-20}{6},w=\frac{-38-20}{6}\)\(w=3,w=-9\frac{2}{3}\)We now have two solutions. We shall take the positive one since our side lengths cannot be a negative value.
Therefore having the width as 3, the length which is 3 times the width is 3 times 3 and that gives 9.
Therefore;
ANSWER:
\(D\colon3\text{inches and 9 inches}\)Explain why 1/3 + 1/4 equals 7/12 and not 2/7
Answers
Answer:
7/12
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
3/12 + 4/12 = 7/12
In AABC, AB = 7 cm, BC = 12 cm, and mZB = 70°.
Find the length of AC to the nearest tenth of a centimeter.
A. 9. 3 cm
B. 12. 8 cm
C. 11. 6 cm
D. 15. 8 cm
Answers
To find the length of AC in triangle ABC, we can use the Law of Cosines. Given that AB = 7 cm, BC = 12 cm, and the measure of angle B, mZB, is 70°, we can calculate the length of AC. The nearest rounded value is 12.8 cm, which corresponds to option B.
In triangle ABC, we can use the Law of Cosines to find the length of AC. The formula is given as:
AC² = AB² + BC² - 2 * AB * BC * cos(m ZB)
Plugging in the known values:
AC² = 7² + 12² - 2 * 7 * 12 * cos(70°)
AC² = 49 + 144 - 168 * cos(70°)
AC² ≈ 193.08
Taking the square root of both sides:
AC ≈ √193.08 ≈ 13.89 cm
Rounding to the nearest tenth of a centimeter, the length of AC is approximately 12.8 cm, corresponding to option B.
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(6x + 6) + ( -3 - 4x )
Answers
Answer:
2x+3 :)
Step-by-step explanation:
If Paul works on Saturdays, he earns $8 per hour (h). plus a $15 bonus for working on the weekend. He wrote a
function, f(h) = 8h + 15 to help calculate how much he would earn working different numbers of hours next Saturday.
How much will Paul earn for working 6 hours and 8 hours?
A)$63, $78
$63, $78
B)$48, $64
$48. $64
C)$63, $79
$63, $79
D) $48, $79
$48, $79
Answers
Answer:
23
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
In a class 5/8 of pupils are boys.If 15 girls are in that class how many boys are there
Answers
Answer:
25
Step-by-step explanation:
If 5/8 are boys then
1 - 5/8 = girls
3/8 = girls
3/8 of the total are girls
Let x = total
3/8 ( x) = 15
8/3 * 3/8 * x = 15 * 8/3
x = 40
There are 40 total students
5/8 are boys
5/8 * 40
25 are boys
Answer:The answer is 25
Step-by-step explanation:
How many license plates can be made using either 3 letters followed by 3 digits or 4 letters followed by 2 digits?
Answers
There can be a total of 63,273,600 license plates that can be made using either 3 letters followed by 3 digits or 4 letters followed by 2 digits.
To determine the number of license plates that can be made using either 3 letters followed by 3 digits or 4 letters followed by 2 digits, we need to calculate the total number of possibilities for each case and then sum them up.
3 letters followed by 3 digits
There are 26 letters in the English alphabet (assuming we're considering only uppercase letters), and 10 digits (0-9). In this case, we have 26 choices for each of the three letters and 10 choices for each of the three digits. Therefore, the number of license plates in this case is:
26 * 26 * 26 * 10 * 10 * 10 = 17,576,000
4 letters followed by 2 digits
Similar to Case 1, we have 26 choices for each of the four letters and 10 choices for each of the two digits. Therefore, the number of license plates in this case is:
26 * 26 * 26 * 26 * 10 * 10 = 45,697,600
To find the total number of license plates, we add the results from both cases:
17,576,000 + 45,697,600 = 63,273,600
Therefore, there can be a total of 63,273,600 license plates that can be made using either 3 letters followed by 3 digits or 4 letters followed by 2 digits.
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⚠️⚠️What should I change ? And why ? ⚠️⚠️
⚠️look at the photo for mor detailed instructions⚠️
DON’T TROLL and if you don’t know don’t answer
Answers
Answer/Step-by-step explanation:
Change the 3rd and 4th input. ALL the input values must be different even if they have the same output values in order to be a function. NONE of the input values should be the same, it just has to be something completely different for it to be correct. It may not be linear, but It will be correct.