For all real numbers a, b, and c, which of the following
expressions is equal to l a-b-c | ?

(a) Total words: 32,768

(b) Words without repeated letters: 6,720

(c) Words starting with "aha": 15

(d) Words starting with "aha" or ending with "bah" or both: 26

(e) Words without repeated letters and without the sub-word "bad": 6,700

a) Since we have 8 letters to choose from (a, b, c, d, e, f, g, h) and we're forming 5-letter words, the total number of words is given by 8⁵

Total words = 8⁵ = 32,768

b) For the first letter, we have 8 choices. After choosing the first letter, we have 7 choices left for the second letter, then 6 choices for the third letter, 5 choices for the fourth letter, and finally 4 choices for the fifth letter (since no repeats are allowed). So the total number of words without repeated letters is:

Total words without repeats = 8 × 7 × 6 × 5 × 4 = 6720

c) To count the number of 5-letter words that start with the sub-word "aha", we can fix the first three letters to be "aha" and then count the number of ways to choose the remaining two letters from the remaining six letters. The number of ways to do this is given by:

(₂⁶) = 6!/2!×4! = 15

Therefore, there are 15 5-letter words that start with the sub-word "aha"

d) To count the number of 5-letter words that either start with "aha" or end with "bah" or both, we can add the number of words that start with "aha" to the number of words that end with "bah" and then subtract the number of words that start with "aha" and end with "bah" (to avoid double counting).

The number of words that start with "aha" is 15 (as we found in part (c)). The number of words that end with "bah" can be found in the same way, by fixing the last three letters to be "bah" and then counting the number of ways to choose the first two letters from the remaining six letters. The number of ways to do this is given by:

(₂⁶) = 6!/2!×4! = 15

Therefore, there are 15 5-letter words that end with "bah".

To count the number of words that start with "aha" and end with "bah", we can fix the first three letters to be "aha" and the last three letters to be "bah", and then count the number of ways to choose the middle letter from the remaining four letters. The number of ways to do this is given by:

(₁⁴) = 4

Therefore, there are 4 5-letter words that start with "aha" and end with "bah".

Adding the number of words that start with "aha" to the number of words that end with "bah" and then subtracting the number of words that start with "aha" and end with "bah", we get:

15 + 15 - 4 = 26

Therefore, there are 26 5-letter words that either start with "aha" or end with "bah" or both

e) To count the number of 5-letter words containing no repeats that also do not contain the sub-word "bad", we can use the permutation formula to count the number of 5-letter words containing no repeats, and then subtract the number of 5-letter words containing no repeats that contain the sub-word "bad".

The number of 5-letter words containing no repeats is given by:

P(8, 5) = 8!/4! = 6720

To count the number of 5-letter words containing no repeats that contain the sub-word "bad", we can fix the first two letters to be "ba" and then count the number of ways to choose the remaining three letters from the remaining six letters that are not "b", "a", or "d". The number of ways to do this is given by:

(₃⁶) = 20

Therefore, there are 20 5-letter words containing no repeats that contain the sub-word "bad".

Subtracting the number of 5-letter words containing no repeats that contain the sub-word "bad" from the total number of 5-letter words containing no repeats, we get:

6720−20=6700

Therefore, there are 6700 5-letter words containing no repeats that also do not contain the sub-word "bad.

Learn more about Permutation here

https://brainly.com/question/29990226

#SPJ4

(a) The recurrence relation for the number of ways Elf can climb n stairs if each step covers either 1 or 2 or 3 stairs is aₙ = aₙ₋₁ + aₙ₋₂ + aₙ₋₃  .

(b) the number of ways Elf can climb 4 stairs is 7 ways .

In the question ,

Let number of ways to climb n stairs = aₙ .

Part (a) ,

So , in order to climb n stairs,  elf must either start with a step of one stair and then climb n - 1 stairs (which is done in aₙ₋₁ ways) or

start with a step of two stairs and then climb (n - 2) stairs (which is done in aₙ₋₂  ways) , or else

start with a step of three stairs and then climb (n - 3) stairs (which is done in aₙ₋₃  ways) .

From the above analysis the recurrence relation, can be written as valid for all n ≥ 3:  aₙ = aₙ₋₁ + aₙ₋₂ + aₙ₋₃ .

the initial conditions are ; a₀ = 1 , a₁ = 1 and a₂ = 2 .

Part(b)

each term in the sequence aₙ is sum of previous three terms .

we have to find the number of ways are there for the Elf to climb four stairs ; that is a₄ .

So , a₃ = a₂ + a₁ + a₀ = 2 + 1 + 1 = 4

a₄ = a₃ + a₂ + a₁ = 4 + 2 + 1 = 7

So , there are 7 ways .

Therefore , (a) the recurrence relation is aₙ = aₙ₋₁ + aₙ₋₂ + aₙ₋₃ ,

(b) the number of ways are 7 ways .

Learn more about Recurrence Relation here

https://brainly.com/question/14189799

#SPJ4

The probability of getting a sum of 7,the probability of getting a sum of 11, the probability of getting a sum of 7 or 11 are 1/6,1/18 and 2/9 respectively and the outcomes are mutually exclusive.

Given, a green and a red fair die are rolled.

To find:

likelihood of getting a total of seven.

likelihood of drawing the number 11.

likelihood of earning a 7 or an 11.

Do these results preclude one another?

Let's look at the results of the first two dice rolls first.

There are a total of 36 outcomes.

{(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

a. Getting a sum equal to 7, we have following outcomes:

{(1, 6), (2,5), (3, 4), (4,3), (5, 2),(6,1)}

6 possible outcomes for this event.

The following is the formula for an event's probability, E:

P(E)= No of favourable outcomes/ Total Outcomes

P(E) = 6/36 =1/6

b. Getting a sum equal to 11, we have following outcomes:

{(5,6), (6,5)}

2 possible outcomes for this event.

The following is the formula for an event's probability, E:

P(E)= No of favourable outcomes/ Total Outcomes

P(E) = 2/36 =1/18

c. Probability of getting a sum of 7 or 11?

Following possible outcomes are there:

{(1, 6), (2,5), (3, 4), (4,3), (5, 2),(6,1),(5,6), (6,5)}

Total 8 possible outcomes:

The following is the formula for an event's probability, E:

P(E)= No of favourable outcomes/ Total Outcomes

P(E) = 8/36 =2/9

d. Are these outcomes mutually exclusive?

Due to the lack of a similar result from both dice, these events are mutually incompatible.

Hence,The probabilities of getting a sum of 7, a sum of 11, a sum of 7 or 11 are 1/6, 1/18, and 2/9, respectively. The options are also mutually exclusive.

To learn more about mutually exclusive click here:

brainly.com/question/28565577

#SPJ4

Answer:

5600

plz mark brainllest

Answer:

117 degrees

Step-by-step explanation:

These two angles are the same

Answer:

120 miles

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

2 divided by .5 = 4 ( 4 half’s equal 2 )

4 times 30 miles = 120 ( each for represents 30 )

Answer:

1/5

Step-by-step explanation:

F=200/1000 = 2/10 = 1/5 Pretty simple just convert to the same unit if it doesn't make sense watch videos about the topic of unit conversion :D

Answer:

i just did that earler lol

Step-by-step explanation:

Answer:

Step-by-step explanation:

Standard Deviation, σ: 12.363631141376

Count, N: 8

Sum, Σx: 303

Mean, μ: 37.875

Variance, σ2:  152.859375

Steps

σ2 =  

Σ(xi - μ)2

N

=  

(32 - 37.875)2 + ... + (45 - 37.875)2

8

=  

1222.875

8

=  152.859375

σ =  √152.859375

=  12.363631141376

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

To know more about parallelepiped, visit:

https://brainly.com/question/30627222

#SPJ11

Answer:

18 golf balls in all, 1/18 is the answer

Step-by-step explanation:

Answer:

1. 18

2. {blue, magenta, purple}

3. P(blue) = 1/2

P(magenta) = 7/18

P(purple) = 1/9

Step-by-step explanation:

Total balls:

9 + 7 + 2 = 18

Sample space: all possible outcomes

{blue, magenta, purple}

P(blue) = 9/18 = 1/2

P(magenta) = 7/18

P(purple) = 2/18 = 1/9

The standard score of the given X value is -0.00

Now, let's calculate the standard score (z-score) of the given X value, X = 36.5, where μ = 36.7 and σ = 32.5.

The formula for calculating the standard score is:

z = (X - μ) / σ

where z is the standard score, X is the score you want to calculate the standard score for, μ is the mean of the dataset, and σ is the standard deviation of the dataset.

So, plugging in the values we have:

z = (36.5 - 36.7) / 32.5

z = -0.02 / 32.5

z = -0.000615

Rounding this answer to two decimal places, we get:

z = -0.00

Therefore, the standard score of the X value 36.5, given the mean μ = 36.7 and standard deviation σ = 32.5, is -0.00. This indicates that the score of 36.5 is very close to the mean score of the dataset, which is not surprising given that the standard deviation is quite large at 32.5.

To know more about score here.

https://brainly.com/question/24210074

#SPJ4

Complete Question:

Calculate the standard score of the given X value, X = 36.5, where μ = 36.7 and σ= 32.5. Round your answer to two decimal places.

For the polynomial 149³ - 2, the value of greatest common factor is obtained as 1.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

The polynomial 149³ - 2 represented in normal form is 3307947.

The GCF of 3307947 is 1.

The polynomial 149³ - 2 cannot be factored by the method of factoring out the greatest common factor, because there is no common factor other than 1.

So the answer is -

149³ - 2

Therefore, the GCF of 149³ - 2 is 1.

To learn more about polynomial from the given link

https://brainly.com/question/24662212

#SPJ1

The diagonals of a parallelogram intersecting at right angles do not guarantee that the parallelogram is a rectangle. A rectangle is a specific type of parallelogram with additional properties, such as right angles in all corners.

The statement that "a parallelogram must be a rectangle if its diagonals" is incorrect. A parallelogram can have its diagonals intersect at right angles without being a rectangle.

A rectangle is a special type of parallelogram where all four angles are right angles (90 degrees). In a rectangle, the diagonals are congruent, bisect each other, and intersect at right angles. However, not all parallelograms with intersecting diagonals at right angles are rectangles.Consider the example of a rhombus. A rhombus is a parallelogram where all four sides are congruent, but its angles are not necessarily right angles. If the diagonals of a rhombus intersect at right angles, it does not transform into a rectangle. Instead, it remains a rhombus.

Furthermore, there are other types of quadrilaterals that are parallelograms with diagonals intersecting at right angles but are not rectangles. Examples include squares and certain types of kites. Squares have all the properties of a rectangle, including right angles and congruent diagonals. On the other hand, kites have congruent diagonals that intersect at right angles, but their angles are not all right angles.In conclusion, the diagonals of a parallelogram intersecting at right angles do not guarantee that the parallelogram is a rectangle. A rectangle is a specific type of parallelogram with additional properties, such as right angles in all corners.

Learn more about Rectangle here,https://brainly.com/question/2607596

#SPJ11

Answer:

Ok

Step-by-step explanation:

The values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3

To multiply matrix, we follow patterns depending on the type of matrix. Thus, from the given matrix, we can say that;

(1 * -1) + (0 * -1) + (1 * 3) = a

-1 + 0 + 3 = a

a = 2

Similarly;

(1 * -1) + (0 * 2) + (1 * 4) = b

-1 + 0 + 4 = b

b = 3

Thus, the values of a and b of the given matrix multiplication is gotten as; a = 2 and b = 3

Read more about Matrices at; https://brainly.com/question/11989522

#SPJ1

Answer:

180cm²

Step-by-step explanation:

Area of the frame = area of the frame+ painting - area of painting.

Area of a rectangle = Length × Width

Area of the painting = 20cm×16cm

Area of the painting = 320cm²

Area of the paint+ frame = 25cm×20cm

Area of the paint+ frame = 500cm²

Area of the frame = 500cm²-320cm²

Area of the frame = 180cm²

Hence the area of the frame is 180cm²

The equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

The equation of a line in slope-intercept form is expressed as;

y = mx + b

where;

m is the slope

b is the y-intercept

For two lines to be perpendicular, the product of their slope must be -1

Given the equation 2x - y =7​

Rewrite

y = 2x - 7

The slope of the line is 2, the slope of the line perpendicular must be -1/2. Hence from the given option, the equation that represents a line that is perpendicular to the line represented by 2x - y = 7 is y = -1/2x + 6

Learn more on equation of a line here: https://brainly.com/question/13763238

#SPJ1

8) a) The new fastest time is 56.7 seconds, b) The overall percentage improvement is 19 %.

9) The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

In this problem we have two examples from real life, in which percentages are used. The first is the distance traveled by a runner in a given time and the second is the growth of a person in time. Change in variables based on percentages are described by the following formula:

C' = C · (1 + r / 100)     (1)

Where:

Now we proceed to resolve on each case. 8) a) Please notice that the runner must cover the trail in less time and percentage time must be negative. If we know that C = 70 and r = - 10, then his new fastest time is:

C' = 70 · (1 - 10 / 100)

C' = 70 · 0.90

C' = 63

And again: (C' = 63, r = - 10)

C'' = 63 · (1 - 10 / 100)

C'' = 63 · 0.90

C'' = 56.7

The new fastest time is 56.7 seconds.

b) And the overall percentage improvement is:

r = (|C'' - C| / C) × 100 %

r = (|56.7 - 70| / 70) × 100 %

r = 19 %

The overall percentage improvement is 19 %.

9) If we know that C = 1.25 and r = 10, then the height next year is:

C' = 1.25 · (1 + 10 / 100)

C' = 1.375

And again: (C' = 1.375, r = 12)

C'' = 1.375 · (1 + 12 / 100)

C'' = 1.54

The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

To learn more on percentages: https://brainly.com/question/13450942

#SPJ1

The value of JK is 14.28

Measurement of angle K is 90 degrees

To determine the measurement of the side, we need to note that;

The Pythagorean theorem is a mathematical theorem stating that the square of the longest side of a triangle, called the hypotenuse is equal to the sum of the squares of the other two sides of that triangle.

From the information given, we have that;

Hypotenuse = 20

Adjacent = 14

opposite = JK

Substitute the values

20² = 14² + JK²

find the square values

400 = 196 + JK²

collect like terms

JK² = 204

Find the square root of both sides

JK = 14. 28

The angle K takes the value of a right angle = 90 degrees

Learn about Pythagorean theorem at: https://brainly.com/question/654982

#SPJ1

When calculating car payments with trade-in negative equity, it's important to consider the total amount owed on your current car loan. Negative equity occurs when the value of your trade-in vehicle is less than the remaining loan balance.

To incorporate this into your car payment calculation, subtract the negative equity amount from the trade-in value, and add it to the purchase price of the new car. The resulting total will be the amount financed. You can then use an online car payment calculator, considering factors like interest rate, loan term, and down payment, to determine your monthly payments.

By using a car payment calculator that accounts for trade-in negative equity, you can obtain a more accurate estimate of your monthly payments. This allows you to make an informed decision regarding your budget and financing options. Remember to consider all aspects of the transaction, including trade-in value, remaining loan balance, purchase price, and loan terms, to get a comprehensive understanding of your car payment obligations.

Learn more about  trade-in value here

brainly.com/question/30402782

#SPJ11

To calculate a car payment with trade-in negative equity, you'll need a few pieces of information. Here's what you need:

Loan amount: The total amount you need to borrow for the new car (including the negative equity from your trade-in).

Loan term: The length of the loan in months.

Interest rate: The annual interest rate on the loan.

Trade-in value: The appraised value of your trade-in vehicle.

Negative equity: The amount you owe on your trade-in vehicle that is more than its appraised value.

The samples are normally distributed and have equal variances. If these assumptions are not met, alternative tests such as the Mann-Whitney U test or the Welch's t-test may be more appropriate.

To test whether people in Texas read more books than people in Colorado, a two-sample t-test would be appropriate.

The reason for choosing a two-sample t-test is that we are comparing the means of two independent samples (Texas and Colorado), and we want to determine if the difference between these means is statistically significant or if it could be due to random chance.

To understand whether the difference in means is statistically significant, we can calculate the t-statistic and compare it to the critical value from the t-distribution with degrees of freedom equal to the sum of the sample sizes minus two (df = n1 + n2 - 2). If the calculated t-statistic is greater than the critical value, we can reject the null hypothesis that the means are equal and conclude that there is a statistically significant difference between the means.

We can also calculate the p-value associated with the t-statistic and compare it to the significance level (usually 0.05). If the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is a statistically significant difference between the means.

It's important to note that in order to perform a two-sample t-test, we need to assume that the samples are normally distributed and have equal variances. If these assumptions are not met, alternative tests such as the Mann-Whitney U test or the Welch's t-test may be more appropriate.

Learn more about variances here

https://brainly.com/question/30651141

#SPJ11

Answer:

x = 98

Step-by-step explanation:

x and 82 are adjacent angles on a straight line and sum to 180° , then

x + 82 = 180 ( subtract 82 from both sides )

x = 98

The increasing interval of the graph indicates that the longer the farmer waits to harvest their crop after the first strawberries ripen, the higher their profit will be.

Graph is a data structure composed of nodes connected by edges, which represent a relationship between the two notes of are used to represent networks of communication that organized and even extract concept like thought or riders the nodes in the graph are often represent by Circle and it's by line but the other safe of the symbol are also use copper power Bluetooth for a organizing and understanding data and can be used to solve complex problem.

This could be due to the fact that the strawberries continue to ripen over time and that the farmer can take advantage of later-ripening, more mature fruits for better quality and higher prices. Additionally, waiting to harvest also allows for a larger crop size as more fruits will have time to mature. Ultimately, the longer the farmer waits to harvest their crop, the higher the potential profit they can make.

To know more about graph click-
https://brainly.com/question/19040584
#SPJ1

Answer:3/2

Step-by-step explanation: just did the test

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

In its simplest form, a scale factor is the proportion between the model measurement and the actual measurement. The scale factor, as opposed to a scale ratio, does not contrast various measurement units. A model car that is scaled at one-twentieth of its real-world counterpart is said to be that size. The car is also 20 times bigger than the model, according to this statement.

16 feet is the length of a fence. The fence is depicted as being 4 inches tall on a map. Write a ratio comparing the two quantities before attempting to calculate the scale factor of the drawing to the actual fence.

Given triangle side are 6, 6, 8 and scaled triangle is 9,9,12

The corresponding sides are

6/9, 6/9, 8/12

When you simply, we get

2/3, 2/3, 2/3

As all sides have grown by 2/3 times, The scale factor is  2/3. Thus, option A is correct.

Learn more about scale factor

https://brainly.com/question/29047298

#SPJ1

Answer:

77

Step-by-step explanation:

The range of the data is the largest number - the smallest number.

98-21

=77

Hope i helped :)

Answer:

77

Step-by-step explanation:

I just used a range calculator...

The perpendicular distance between the two parallel sides, height h of the trapezium is 8cm

It is important to note the properties of a trapezium;

the formula for area of  trapezium is;

Area = a + b/ 2 ·(h)

Substitute the value

80 = (4 + 16)/ 2  (h)

Add the values

80 = 10h

Divide by the coefficient of h

h = 8cm

Learn about trapezium at: https://brainly.com/question/16904048

#SPJ1

Complete question:

The area of a trapezium is  80cm^2

The lengths of its parallel sides are  4cm and 16cm respectively. Find the perpendicular distance between the two parallel sides.