Answer:
a. The sum of the interior angles of a regular polygon with n sides can be found using the formula (n-2) x 180 degrees. Using this formula, we know the sum of the interior angles of a pentagon is (5-2) x 180 = 540 degrees. Since the sum of the interior angles of a polygon increases by 180 degrees for each additional side, we can guess that the sum of the interior angles of a 17-gon would be (17-2) x 180 = 2700 degrees.
b. For concave polygons, the sum of the interior angles may not follow the same pattern as that of regular polygons. It is possible for the sum of the interior angles of a concave polygon to be greater or less than the sum of the interior angles of a regular polygon with the same number of sides. So, it is difficult to make an accurate guess without more information about the specific shape of the concave 17-gon.
c. The sum of the exterior angles of any convex polygon always equals 360 degrees because each exterior angle is supplementary to its adjacent interior angle. In other words, the exterior angle and the adjacent interior angle form a straight line, which is 180 degrees. Since there are n exterior angles in an n-sided polygon, the sum of all the exterior angles is n x 180 degrees. However, each exterior angle is counted once for each vertex, and there are n vertices, so we need to divide by n to get the total sum of exterior angles, which is (n x 180) / n = 180 degrees.
d. For a concave polygon, the sum of the exterior angles may be greater than or less than 360 degrees, depending on the shape of the polygon. In a concave polygon, some of the exterior angles will be greater than 180 degrees, which means that their adjacent interior angles will be less than 180 degrees. Since the sum of the exterior angles is equal to the sum of the adjacent interior angles, some of the exterior angles will need to be subtracted from 360 degrees to get the total sum of exterior angles. However, without more information about the specific shape of the concave polygon, it is difficult to make an accurate guess.
Answer:
a. The sum of the angle measures of the regular pentagon is 540 degrees, and the sum of the angle measures of the concave pentagon is 720 degrees. Both of these polygons have five sides. If we assume that the sum of the angle measures of a polygon with n sides is proportional to n, we can use the ratios of the number of sides in each polygon to make an estimate for the sum of the interior angles of a 17-gon. The ratio of the number of sides in a 17-gon to the number of sides in a regular pentagon is 17/5. If we multiply the sum of the angle measures of the regular pentagon by this ratio, we get an estimate for the sum of the angle measures of a 17-gon:
540 * (17/5) = 1836 degrees.
So, we would guess that the sum of the interior angles of a 17-gon is 1836 degrees.
b. We can use a similar reasoning as in part (a) to estimate the sum of the interior angles of a concave 17-gon. The ratio of the number of sides in a concave pentagon to the number of sides in a concave 17-gon is 5/17. If we multiply the sum of the angle measures of the concave pentagon by this ratio, we get an estimate for the sum of the angle measures of a concave 17-gon:
720 * (5/17) = 211.76 degrees.
So, we would guess that the sum of the interior angles of a concave 17-gon is 211.76 degrees.
c. The sum of the exterior angles of a convex polygon always equals 360 degrees because the exterior angle at each vertex of the polygon is equal to the sum of the two adjacent interior angles. If we add up all of the exterior angles of a polygon, we are essentially adding up all of the vertex angles twice (once for each adjacent exterior angle). Therefore, the sum of the exterior angles of a convex polygon is equal to 2 times the sum of the interior angles. Since the sum of the interior angles of any n-sided polygon is (n-2)*180 degrees, the sum of the exterior angles is:
2 * (n-2) * 180 = 360(n-2) degrees.
d. It is not possible to make a generalization about the sum of the exterior angles of a concave polygon, because the sum of the exterior angles of a concave polygon can be greater than, less than, or equal to 360 degrees, depending on the polygon's shape. The sum of the exterior angles of a concave polygon can be greater than 360 degrees if the polygon has one or more reflex angles, which are angles greater than 180 degrees. In this case, the exterior angle at each vertex is less than the adjacent interior angle, so the sum of the exterior angles is greater than 360 degrees. On the other hand, if a concave polygon has no reflex angles, the sum of the exterior angles will be less than 360 degrees.
Step-by-step explanation:
2. Two players A and B are competing at a trivia quiz game involving a series of questions. On any individual question, the probabilities that A and B give the correct answer areαandβrespectively, for all questions, with outcomes for different questions being independent. The game finishes when a player wins by answering a question correctly. Compute the probability that A wins if
a) A answers the first question,
b) B answers the first question.
a) The probability that A wins if A answers the first question is α / (α + β).
b) The probability that A wins if B answers the first question is βα+β.
a) If A answers the first question, then the game will be over only if A answers the first question correctly, which has a probability of α. If A answers incorrectly, then B gets to answer the next question, and we are in the same situation but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:
P(A wins | A answers first) = α + (1 - α)β P(A wins | B answers first)
b) If B answers the first question, then we are in the same situation as in part a) but with A's and B's roles reversed. Therefore, the probability that A wins in this case is given by:
P(A wins | B answers first) = β P(A wins | A answers first) + (1 - β)β P(A wins | B answers first)
We can solve these equations for P(A wins | A answers first) and P(A wins | B answers first) using algebraic manipulation. For example, we can rearrange the equation in part a) to get:
P(A wins | A answers first) = α / (1 - (1 - α)β)
Similarly, we can rearrange the equation in part b) to get:
P(A wins | B answers first) = β / (1 - (1 - β)α)
Note that these probabilities depend on the values of α and β, which represent the abilities of A and B to answer questions correctly.
Learn more about probability here: brainly.com/question/30034780
#SPJ4
The sum of the base and the height of a triangle is 22 cm. Find the dimensions for which the area is a maximum. The triangle with maximum area has a height of_____cm and a base of cm_____.
The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.
We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:
b + h = 22
We want to find the dimensions of the triangle that will give us the maximum area.
The formula for the area of a triangle is A = (1/2)bh.
We can use the equation b + h = 22 to solve for one of the variables in terms of the other.
we can solve for h:
h = 22 - b
Substituting this into the formula for the area, we get:
A = (1/2)b(22 - b)
The equation 0 = 11b - (1/2)b² can be rearranged to:
(1/2)b² - 11b = 0
We can then use the quadratic formula to solve for "b"
b = 11 ± 11
So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:
h = 22 - 11 = 11 cm
Triangle has a base of 11 cm and a height of 11 cm.
To practice more questions about area of triangle:
https://brainly.com/question/21735282
#SPJ11
what are the X intercept of the graph of the following equation y=x^2 - 64
Step-by-step explanation:
Here is one way :
at the x-axis intercepts , the value of 'y' = 0 (obviously)
0 = x^2 -64
x^2 = 64
x = ± 8
a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:
The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.
What is the z-score?The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.
z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5
The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.
z = {x-μ}/{σ} = {-20-0}/{8} = −2.5
The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.
Learn more about Z-score here:
https://brainly.com/question/15016913
#SPJ11
Suppose Alice uses the RSA methods as follows. She starts with a mes- sage consisting of several letters, and assigns a = 1,b=2, -2=26. She then encrypts each letters separately. For example, if her message is cat, she calculates 3 = mod n 19 = 2 mod n and 209 = mod n. Then she sends the encrypted message {G}=1,2,3 to Bob. Explain how Eva can find the message without factoring n. In particular, suppose n=8881 and e=13. Eva intercepts the message q=4461; = 794; e = 2015,C4 = 2015,3 = 3603 Find the message without factoring 8881.
The solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.
Suppose Alice uses the RSA methods as follows. She starts with a message consisting of several letters, and assigns a = 1,b=2, -2=26. She then encrypts each letter separately. For example, if her message is cat, she calculates 3 = mod n 19 = 2 mod n and 209 = mod n. Then she sends the encrypted message {G}=1,2,3 to Bob.The solution to the given question is as follows:Eva knows that n = 8881 = 79 × 112, where p = 79 and q = 112 are primes.Using the extended Euclidean algorithm and the fact that 13*5081 = 1 (mod 8880), one can compute the inverse of e modulo 8880 as d ≡ 5081 ≡ -3805 (mod 8880).To compute the message, Alice encrypts each letter of the message separately using the encryption function y ≡ x13 (mod 8881).Eva receives {G}=1,2,3 from Alice, and hence she wants to decipher it by computing 13 ≡ y ≡ G13 (mod 8881), where y is the message.To compute y, we have 1^{13} ≡ 1 (mod 8881), 2^{13} ≡ 8192 ≡ - 6889 + 2 (mod 8881) since 8192 = 2 × 4096 and 4096 = 8881 - 4785, hence, 2^{13} ≡ - 4785 × 2 + 2 (mod 8881), i.e., 2^{13} ≡ 2311 (mod 8881), and 3^{13} ≡ 3 × 3^{12} ≡ 3 × (3^{4})^{3} ≡ 3 × 6561^{3} ≡ 3 × 4299 ≡ 12897 ≡ 2557 (mod 8881).Therefore, the decrypted message is {y} = (2311, 2557, 2015) and hence the original message is CAT.Hence, the solution is {y} = (2311, 2557, 2015) and hence the original message is CAT.
Learn more about Original
brainly.com/question/28490920
#SPJ11
X
The diagram shows part of a
regular decagon. Work out
the size of the angle marked
X
Answer:
144°
Step-by-step explanation:
x = (10 - 2)(180)/10 = 144
Reduce each expression to a polynomial
((y-b)^(2))/(y-b+1)+(y-b)/(y-b+1)
The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.
In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:
((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)
Now, we can combine the two terms in the equation by finding a common denominator:
(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)
Next, we can combine the terms in the numerator by factoring out (y-b):
[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)
Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:
(y-b)(y-b+1)/(y-b+1) = y-b
Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1) after being simplified, is equivalent to the polynomial y-b.
Learn more about polynomials :
https://brainly.com/question/30127172
#SPJ4
3.
Point out the five-fold health hazards prevalent in Nepal.
4.
Why is life expectancy of the Nepalese very low? Give reasons.
the Minister of Health in Nenal. What programme
The five fold health hazards prevalent in Nepal are respiratory diseases due to high altitude, Germ cell mutagenicity, Carcinogenicity, Reproductive toxicity and sanitation related issues which causes diarrhea, cholera like diseases.
Nepal is a small country in hilly region of Himalayas between China and India. It has not developed much in terms of health care facilities and advanced treatment methods due to which people migrate to India for treatments in several extreme diseases. The low life expectancy is because of poor employment which causes financial insecurity and hence people are either malnourished, or die of lack of proper treatment.
The Nepal Health Sector Program – Implementation Plan (NHSP-IP) has been developed in order to meet the Health Sector Strategy which has its agenda to improvise the needs of the people in near future.
Learn more about life expectancy at:
https://brainly.com/question/17427164
#SPJ4
WILL GIVE BRAINLIEST HELP
Answer:
D= 7(2g-H)/U
Step-by-step explanation:
A shipping company is packing a box with one cubic centimeters blocks. The box is 14 centimeters long. 12 centimeters wide and 16 centimeters high. How many one cubic centimeter blocks will fill the box ?
The shipping company will need 2,688 one cubic centimeter blocks to fill the box.
The volume of the box can be calculated as:
Volume = length x width x height
Volume = 14 cm x 12 cm x 16 cm
Volume = 2,688 cubic cm
Since each block is also one cubic cm in volume, we can simply divide the total volume of the box by the volume of one block to find the number of blocks needed to fill the box:
Number of blocks = Volume of box / Volume of one block
Number of blocks = 2,688 cubic cm / 1 cubic cm
Number of blocks = 2,688
Learn more about volume here
brainly.com/question/23952628
#SPJ4
An online bookstore is having a one-day sale. Softcover books are $4, hardcover books are $7, magazines are $3, and all digital downloads of books are $2. Let's say 150 customers purchased books in one form or another that day. Below are the frequencies in which customers purchased books:
Books: Purchases:
Softcover 42
Hardcover 28
Magazine 23
Digital Download 57
Based on the data above, which is the correct relative frequency with discrete random variable X = "the amount of money for a book?"
The correct relative frequency for X is:
X: $2 $3 $4 $7
P(X): 0.38 0.15 0.28 0.19
How to find the relative frequency for the discrete random variable X ?
First we need to determine the probability of each value of X occurring based on the given data.
We can use the following formula to calculate the probability of a particular value of X:
P(X = x) = f(x)/n
Where
f(x) is the frequency of the value x n is the total number of purchases (150)Let's calculate the probabilities for each value of X:
P(X = $2) = 57/150 = 0.38
P(X = $3) = 23/150 = 0.15
P(X = $4) = 42/150 = 0.28
P(X = $7) = 28/150 = 0.19
Therefore, the correct relative frequency for X is:
X: $2 $3 $4 $7
P(X): 0.38 0.15 0.28 0.19
Learn more about probability here : brainly.com/question/251701
#SPJ1
What is the difference between the simple and compound interest if you borrow $3,000 at a 6% interest rate for 2 years?
$180.00
$10.00
$6.00
$80.00
Answer:
Correct option is C)
Simple interest =
100
3000×6×2
=360
Compound interest =3000(1+
100
6
)
2
−3000=18×20.6=370.8
∴ Difference is Rs.10.8.
you can convert this value to $$
or simply the answer will be 2. $10
(hob-evzw-zjw) come
Answer:
B is your answer.
10.80$ which you just round to 10. 10 is your answer.
Step-by-step explanation:
For simple interest, the formula is:
Simple Interest = Principal × Rate × Time
For compound interest, the formula is:
Compound Interest = Principal × (1 + Rate)^Time - Principal
Let's calculate the values:
Principal = $3,000
Rate = 6% or 0.06
Time = 2 years
Simple Interest = $3,000 × 0.06 × 2 = $360
To calculate compound interest, we need to use the formula:
Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000
= $3,000 × (1.06)^2 - $3,000
= $3,000 × 1.1236 - $3,000
= $3,370.80 - $3,000
= $370.80
The difference between simple and compound interest is:
$370.80 - $360 = $10.80
Which of the following is equivalent to 3/8? -0.6, square root of 100, 2/5, -2/3, 0.35217534
The οptiοn in the questiοn that is equivalent tο 3/8 is 2/5.
Equivalent- Meaning in MathematicsThe term "equivalent" in math refers tο twο meanings, numbers, οr quantities that are the same. The equivalence οf twο such quantities shall be denοted by a bar οver an equivalent symbοl οr Equivalent Sign. It alsο means a lοgical equivalence between twο values οr a set οf quantities. Equivalence is similar but mοre universal than equality. If twο sets οf equatiοns have the same sοlutiοns, we might cοnsider them similar, but they are nοt identical.
Hοw tο calculate the equivalent οf 3/8?We can simplify 3/8 and 2/5 sο that they have a cοmmοn denοminatοr:
3/8 = 3*(5/5)/(85/5) = 15/40
2/5 = 2(8/8)/(5*8/8) = 16/40
Since 15/40 and 16/40 have the same denοminatοr, we can cοmpare their numeratοrs tο see which is larger:
15/40 < 16/40
Since 16/40 is larger, we can cοnclude that 2/5 is greater than 3/8.
Therefοre, the οptiοn that is equivalent tο 3/8 is 2/5.
Learn more about equivalent at
https://brainly.com/question/14672772
#SPJ1
A middle school teacher estimates that 170 parents will attend the back to school informational meeting. A total of 147 parents actually attended the meeting. What is the percent error of the teacher's estimate rounded to the nearest tenth of a percent
The percent error from the real and estimated values is 16%.
What is percent error?The difference between a precise value and an approximation to it is the approximation error in a data value. Either an absolute mistake or a relative error can be used to describe this error. It is possible for measurement mistake or computing machine precision to produce an approximation error. The percent error is the distinction between the estimated value and the real value in relation to the actual value. In other terms, the relative error is multiplied by 100 to calculate the percent error.
The estimated value= 170
the real value= 147
Percent error ={ (170-147)/147}*100= 0.1564*100
Percent error = 15.64% ≈ 16%
To know more about percent error, visit
https://brainly.com/question/29107960
#SPJ1
$80 selling price 8% rate of sales tax. find the sales tax and the total cost
Answer:
sales tax 6.40
total cost 86.40
Step-by-step explanation:
First we need to find the sales tax.
80 * 8%
80 *.08 = 6.40
Add this to the original price.
80+6.40
86.40
The total cost is 86.40
A professor grades students on a normal curve. For any grade x, based on the a course mean and standard deviation developed over years of testing, the following applies: D:--1.60 < x < -0.4σ How many A, B, C and D grades are given per 100 students?
The proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students.
What is the z-score?
Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below the mean. Standard deviation is essentially a reflection of the amount of variability within a given data set.
Assuming that the grading follows a standard normal distribution (i.e., with a mean of 0 and a standard deviation of 1), we can use the z-score formula to find the proportions of students that fall within each grade range:
For an A grade: z-score > 1.65
For a B grade: 0.67 < z-score ≤ 1.65
For a C grade: -0.40 < z-score ≤ 0.67
For a D grade: -1.60 < z-score ≤ -0.40
To convert from the standard normal distribution to the distribution with the course mean and standard deviation, we can use the formula:
z-score = (x - mean) / standard deviation
We don't know the actual mean and standard deviation for the course, so we'll use the given range for the D grade (-1.60 < x < -0.4σ) to estimate the standard deviation. Since the D grade range is 1.2 standard deviations wide (from -1.60 to -0.4σ), we can solve for the standard deviation:
1.2σ = -1.60
σ = -1.60 / 1.2
σ = 1.33
(Note that we have a negative value for σ, which is not possible for a standard deviation. This is because we are using the estimated value of σ to convert from the standard normal distribution to the course distribution, which may not perfectly match the actual distribution of grades.)
Now we can use the z-score formula with the estimated mean and standard deviation to find the proportions of students in each grade range:
For an A grade: z-score > 1.65
z-score = (x - mean) / standard deviation
z-score = (1.65 - 0) / 1.33
z-score = 1.24
From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score greater than 1.24 is about 0.107. So for every 100 students, we can expect about:
A grades: 100 * 0.107 = 10.7 or approximately 11
For a B grade: 0.67 < z-score ≤ 1.65
z-score = (0.67 - 0) / 1.33
z-score = 0.50
From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between 0.50 and 1.24 is about 0.205. So for every 100 students, we can expect about:
B grades: 100 * 0.205 = 20.5 or approximately 21
For a C grade: -0.40 < z-score ≤ 0.67
z-score = (-0.40 - 0) / 1.33
z-score = -0.30
From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -0.30 and 0.50 is about 0.307. So for every 100 students, we can expect about:
C grades: 100 * 0.307 = 30.7 or approximately 31
For a D grade: -1.60 < z-score ≤ -0.40
z-score = (-1.60 - 0) / 1.33
z-score = -1.20
Hence, From standard normal distribution tables or a calculator, we can find that the proportion of students with a z-score between -1.20 and -0.30 is about 0.304. So for every 100 students,
To learn more about the z-score visit:
https://brainly.com/question/25638875
#SPJ1
Find the value of N.
4 + 5 -3 = N
8 x 3 - 5 = N
15 ÷ 3 + 10 = N
8 + 3 -1 x 2 = N
14 x 3 - 2 = N
( 3 + 5 ) x 2 = N
10 + 7 + 2 x 1 = N
16 ÷ 8 + 4 = N
7 + 5 ÷ 5 = N
20 ÷ 4 x 6 = N
Answer:
1. n=6
2. n=19
3. n=15
4. n=20
5. n=40
6. n=16
7. n=19
8. n=6
9. n=2.4
10. n=30
Step-by-step explanation:
remember the priorities :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
inside every category you go usually from left to right, but you can use the commutative property where applicable.
4 + 5 - 3 = 4 + 5 - 3 = 4 + 5 - 3 = 4 - 3 + 5 = 6
8×3 - 5 = 24 - 5 = 19
15/3 + 10 = 5 + 10 = 15
8 + 3 - 1×2 = 8 + 3 - 2 = 9
14×3 - 2 = 42 - 2 = 40
(3 + 5)×2 = 8×2 = 16
10 + 7 + 2×1 = 10 + 7 + 2 = 19
16/8 + 4 = 2 + 4 = 6
7 + 5/5 = 7 + 1 = 8
20/4×6 = 5×6 = 30
How do I solve this?
Answer:
X+4
Step-by-step explanation:
Area = l *b
x^2 + 13x + 36 = (X+9) * b
x^2 + 9x + 4x + 36 = (X+9) * b
X(X+9) + 4(X+9) = (X+9) * b
(X+4) (X+9) = (X+9) * b
b = (X+4)
I NEED HELP ON THIS ASAP!!
Answer:
(a) {0 ≤ x ≤ 60; 0 ≤ y ≤ 90; x + y ≤ 120}
(b) p = 50x +75y; 30 tons of loam and 90 tons of peat will maximize profit
Step-by-step explanation:
You want a graph of constraints and the solution to the problem of maximizing profit from sale of 60 tons of loam and 90 tons of peat at a profit of $50/t and $75/t, respectively, if at most 120 tons can be sold.
(a) ConstraintsLet x and y represent tons of loam and peat, respectively. Then the constraints can be written as the inequalities ...
0 ≤ x ≤ 60 . . . . . can only sell as much as is available0 ≤ y ≤ 90 . . . . . can only sell as much as is availablex + y ≤ 120 . . . . . can sell a maximum of 120 tons(b) Objective functionWe want to maximize profit, so maximize ...
p = 50x +75y
GraphThe attached graph shows the graphs of the inequalities. The restrictions on the variables confine the applicable graph to the first quadrant.
The black line shows the objective function. The value of the profit function is maximized when the line is as far from the origin as possible. The boundary point of the constraint solution space that maximizes profit is (x, y) = (30, 90).
Sale of 30 tons of loam and 90 tons of peat soil will maximize profit.
__
Additional comment
Since selling peat is the most profitable, profit will be maximized when we sell as much peat as possible. Sale of only 90 tons is possible, so profit will be maximized when we sell that many, then make up the rest of the 120 ton maximum by selling loam. We don't need a graph or a list of constraints to figure that out.
Suppose V = {S, A, a, b}, T = {a, b), S is the start symbol with productions S ® bS, S ® aA, A ® aS, A ® bA, A ® a, S ® b. Find a derivation of each of the following. A) bbabbab
(3 Marks)
b) bbbaab
This question is related to formal languages and automata theory, specifically to the topic of context-free grammar and derivations.
a) bbabbab:
S -> bS (Apply S -> bS)
-> bbS (Apply S -> bS)
-> bbbA (Apply S -> aA)
-> bbbaS (Apply A -> aS)
-> bbbaaS (Apply S -> aA)
-> bbbaaa (Apply A -> a)
Therefore, the derivation of bbabbab is S -> bS -> bbS -> bbbA -> bbbaS -> bbbaaS -> bbbaaa -> bbabbab.
b) bbbaab:
S -> bS (Apply S -> bS)
-> bbS (Apply S -> bS)
-> bbbA (Apply S -> aA)
-> bbbaS (Apply A -> aS)
-> bbbaaS (Apply S -> aA)
-> bbbaaa (Apply A -> a)
-> bbbaab (Apply A -> b)
Therefore, the derivation of bbbaab is S -> bS -> bbS -> bbbA -> bbbaS -> bbbaaS -> bbbaaa -> bbbaab.
Learn more about automata theory at
brainly.com/question/31044784
#SPJ4
Anna has n number of nickels. She has less than 45 cents. Which inequality could
be used to find the value of n?
A $0.05n< $0.45
B $0.05n > $0.45
C $0.05n ≤ $0.45
D $0.05n ≥ 0.45
Answer:
A $0.05n< $0.45
Step-by-step explanation:
It is given that she has "less than" rather than "less than or equal to" 45 cents. Therefore, your answer will contain the "less than" sign, which is signified as <.
Therefore, being the only answer with <, your answer will be A.
A nickel is $0.05, therefore:
$0.05 of n is less than $0.45, or $0.05n< $0.45
A) $0.05n < $0.45 is your answer.
~
Learn more about inequalities, here:
https://brainly.com/question/4410289
Part III: Short Answer Items (Worth 3 points) Instruction: Write the most simplified answer on the blank space provided for each of them. 11. If the price of an item is Birr 9,500 before VAT, then the total cost of the item including VAT
According to the VAT rate, the total cost of the item including VAT is Birr 10,925 assuming a VAT rate of 15%.
What is VAT rate ?
VAT (Value Added Tax) rate is a percentage that is added to the price of goods or services. VAT is usually charged on top of the base price of a product or service, and the total price is calculated as (base price) + (base price x VAT rate). The VAT rate is typically set by the government and may be subject to change over time.
To find the total cost of the item including VAT, we need to know the VAT rate.
Let's assume the VAT rate is 15%. To calculate the VAT amount, we can multiply the price before VAT by the VAT rate:
VAT amount = 0.15 x 9,500 = Birr 1,425
The total cost of the item including VAT is the sum of the price before VAT and the VAT amount:
Total cost = 9,500 + 1,425 = Birr 10,925
Therefore, the total cost of the item including VAT is Birr 10,925 assuming a VAT rate of 15%.
To know more about VAT rate visit:
brainly.com/question/28165138
#SPJ1
After 6 new students entered the Happy Hearts Childcare Center and 2 students exited, there were 3 times as many students as before. How many students were present before students entered and exited the center?
Answer: 2
Step-by-step explanation:
If there are three times as many students when there are 6 students you do 6 divided by three to give you two.
Problem: Power Output. In each case, find your average power in watts. Assume that riding a bike burns 100 Calories per mile. If you ride at a speed of 20 miles per hour, what is your average power output, in watts?
The average power output of a bike rider at a speed of 20 miles per hour is 556 W
Given, Riding a bike burns 100 Calories per mile. Speed of riding a bike is 20 miles per hour. Power is a measure of the rate at which work is done over time.
Therefore, the formula for average power is given by,
P = W/t
Where, P is power, W is work and t is time.
Now, We know that riding a bike burns 100 Calories per mile, but we have to find out the work done.
So, work done = 100 Calories × distance traveled= 100 × 1.609 × 1000 = 160900 J
Time taken = distance/speed= 1.609/20 = 0.08045 hours
Putting values in the formula of power, we get,
P = W/t= 160900/0.08045= 1999999.9 J/hour
Converting hour to seconds,1 hour = 3600 seconds1 J/s = 1 watt1 J/hour = 1 / 3600 watt
Therefore, power = 1999999.9 / 3600= 555.5556 watts (approx)
Therefore, the average power output of a bike rider at a speed of 20 miles per hour is 556 W (approx). Answer: 556
Learn more about average power output:https://brainly.com/question/14558400
#SPJ11
The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59 F and a
standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean
temperature is recorded. What is the standard deviation of the sampling distribution of the sample mean for all
possible random samples of size 10 from this population?
The standard deviation of the sampling distribution of the sample mean for the given sample size is equal to 3.1623°F.
For the normally distributed data,
Mean of the population distribution 'μ' = 59F
Population standard deviation 'σ' = 10°F
Sample size 'n' = 10
Formula for the standard deviation of the sampling distribution of the sample mean (also known as the standard error of the mean) is equal to ,
= σ / √(n)
Substitute the value to get the standard deviation of the sampling distribution of the sample mean we get,
= 10°F / √(10)
= 3.1623°F
Therefore, the standard deviation of the sampling distribution of the sample mean for all possible random samples of size 10 from this population is approximately 3.1623°F.
Learn more about standard deviation here
brainly.com/question/30985253
#SPJ4
A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =
The area of the square base = x².
we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...
The dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.
To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.
Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x
Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x² A'(x) = 0 when x = (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
Learn more about Area
brainly.com/question/1561162
#SPJ11
last week Alexander was paid $56 for 7 hours of work. how much money does Alexander's job pay her hour??
Answer:
$56 divided by 7 hours is $8 per hour sh get payed.
For which function does g decrease by 25% every time x increases by 1?
A g(x) = 0.75
B) g(x) = 75
g(x) = 0.25
D g(x) = 25*
We pIug this function into the equation above, we get: g(x+1) = 0.
Assume that g(x) is a function that decreases by 25% for every one increase in x.
This means that if we increase x by one, the vaIue of g(x) wiII be 75% of what it was befοre.
In other words, if g(x) is the function's vaIue at x, then g(x+1) is 0.75 times g. (x).
As a resuIt, we can express g(x+1) in terms of g(x) as foIIows:
g(x+1) = 0.75 * g(x) (x)
Let's see which οption meets this requirement.
A) g(x) = 0.75: When we pIug this function into the equation above, we get:
g(x+1) = 0.75 * 0.75 = 0.5625 * g(x) (x)
This means that increasing x by one increases g(x) by 25%. As a resuIt, this optiοn does not meet the condition.
B) g(x) = 75: When we pIug this function into the equation above, we get:
g(x+1) = 0.75 * 75 = 56.25
This means that increasing x by οne decreases g(x) by more than 25%.
As a resuIt, this option does not meet the condition.
C) g(x) = 0.25: When we pIug this function into the equatiοn above, we get:
g(x+1) = 0.75 * 0.25 = 0.1875 * g(x) (x)
This means that increasing x by one decreases g(x) by more than 25%. As a resuIt, this optiοn does not meet the cοndition.
D) g(x) = 25*: When we pIug this function into the equation above, we get:
g(x+1) = 0.
To knοw more about Function visit:
brainly.com/question/14996337
#SPJ1
Cοmplete question:
For which function does g decrease by 25% every time x increases by 1?
A) g(x) = 0.75
B) g(x) = 75
C) g(x) = 0.25
D) g(x) = 25*
Is this a compound?
First, Gabriel planted the geraniums in a clay pot, and then he placed the pot on a sunny windowsill in his kitchen
A. YES
B. NO
Answer:
yes it is right now you can write it
Should we write reciprocal for 5/6 in this question 5 × 5/6
If the question is simply asking for the product of 5 and 5/6, then writing the reciprocal is not necessary. To multiply fractions, we can simply multiply the numerators and the denominators separately. In this case, we would get:
5 x 5/6 = (5 x 5)/(1 x 6) = 25/6
However, if the question specifically asks for the result to be expressed as a mixed number or a whole number, then we would need to simplify the fraction by converting it to a mixed number or a whole number. In some cases, it may be helpful to write the reciprocal in order to simplify the fraction more easily.
For example, if the question asks us to express 5 x 5/6 as a mixed number or a whole number, we could first write the reciprocal of 5/6 as 6/5, and then multiply it with 5 to get:
5 x 5/6 = 5 x 6/5 = 30/5
We can simplify this fraction by dividing both the numerator and the denominator by 5:
30/5 = 6
Therefore, if the context or the desired result requires the expression 5 x 5/6 to be simplified further, it may be helpful to write the reciprocal of 5/6 to make the simplification process easier. However, in general, it is not necessary to write the reciprocal to multiply fractions.
Find more about reciprocal
brainly.com/question/15212898
#SPJ4