There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
What is permutation?
A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.
So, the number of desired cases are,
= [tex]\frac{7_P_3(24)^4}{2} = 34836480[/tex]
Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.
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Write a compound inequality for the graph shown below. Use x for your variable.
The interval is [4, 6], and the compound inequality is 2 ≤ x < 5 as indicated on the number line.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign.
It is an illustration of inequity.
This shows that the left half, 5x 4, is bigger than the right part, 2x + 3.
So, the blue line runs from 12 and then to 5.
The solid dot at position 2 denotes inclusion, whereas the hollow dot at position 5 denotes exclusion.
Now,
x ≥ 2 and x < 5
Combine:
2 ≤ x < 5
Therefore, the interval is [4, 6], and the compound inequality is 2 ≤ x < 5 as indicated on the number line.
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Henry has a length of ribbon that is 6 1/4 feet long He needs 1 1/12 feet of ribbon to make a bow.
The answer to this Question based on Length is Yes he can easily make a bow with that
What is Length?
Length is a measurement of distance or size. It is the greatest of the three linear dimensions and is often denoted by the letter “L”. Length is commonly used to measure the size of objects, the distance between two points, or the magnitude of a displacement. Length can be measured in a variety of units such as inches, feet, meters, kilometers, or miles. Length is also used to determine the area of a two-dimensional shape, the volume of a three-dimensional shape, and the circumference of a circle. Length is an important concept in mathematics, physics, engineering, and other scientific disciplines. Length can also be used to describe how long something lasts, such as the length of a movie or a song.
we can see that length of henry ribbon that is available is 6 1/4 feet long ribbon which means 25/4 feet ribbon
= 6.25 feet of ribbon
whereas length of ribbon he needs is 1 1/12 feet ribbon to make a bow which is equal to
13/12 = 1.08 feet ribbon and he has 6.25 feet available hence he can easily make a bow with that
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h(x)=(32)x−1 the outputs
The possible outputs of the function for different values of [x] are given below.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.Given is the following function -
h(x) = 32x - 1
We can write the output for the given function as -
[x] h(x) = 32x - 1 h(x)
1 {32 x 1 - 1 = 31} 31
2 {32 x 2 - 1 = 63} 63
3 {32 x 3 - 1 = 95} 95
4 {32 x 4 - 1 = 127} 127
Therefore, the possible outputs of the function for different values of [x] are given above.
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How long does it take to travel 200 km at 40 km per hour?
Answer:
5 hours
Step-by-step explanation:
Time = 200÷40 = 5 hours.
A five-card hand is dealt at random from a standard deck. What is the probability that the hand contains exactly two face cards?
By using the concept of probability, it can be calculated that
Probability that the hand contains exactly two face cards = [tex]\frac{209}{833}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
From the set of five cards, two cards can be chosen in [tex]{5 \choose 2}[/tex] ways = 10 ways
Number of face cards = 12
Number of non face cards = 52 - 12 = 40
Probability that the hand contains exactly two face cards = [tex]{5 \choose 2}\times \frac{12}{52} \times \frac {11}{51} \times \frac{40}{50} \times\frac{39}{49}\times \frac{38}{48}\\[/tex]
[tex]\frac{209}{833}[/tex]
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what is x^(1.5-x)=3/2
Please help this for algebra! :)
Answer: y= -8x + 9.5
Step-by-step explanation:
The equation for slope intercept form is y=mx+b
b is the y-intercept; we see that it is located at (0, 9.5), so b is 9.5
The slope is rise/run
We see that the y decrease by 8 and x increases by 1, so the slope is -8/1
So the answer is y= -8x + 9.5
A lap around the track is 1/4 of a mile. Josie completes a lap in 1.3 minutes. If she continues at the same pace, how long will it take her to complete
a mile? Express your answer as a decimal in simplified form..
minutes
Answer:
5.2 or 5:12
Step-by-step explanation:
1.3*4 = 5.2 or 5:12. That's a pretty fast mile.
Problem
The sum of 3 consecutive even numbers is 132.
What is the third number in this sequence?
Answer:
46
Step-by-step explanation:
because it is ...... maybe
brawdy plastics, inc., produces plastic seat belt retainers for general motors at their plant in buffalo, new york. after final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. how fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. to test this theory, brawdy plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. the following data were collected. excel file: data14-05.xlsx line speed number of defective parts found 20 23 20 21 30 19 30 16 40 15 40 17 50 14 50 11 if required, enter negative values as negative numbers. a. select a scatter diagram with the line speed as the independent variable. a. b. c. d. a b. what does the scatter diagram developed in part (a) indicate about the relationship between the two variables? negative relationship c. use the least squares method to develop the estimated regression equation (to 1 decimal). d. predict the number of defective parts found for a line speed of feet per minute.
a. The scatter diagram indicates that the Number of Defective Parts found increases with Line Speed
b. The regression model is Y = 27.5 - 0.3·X
c. When the line speed is 25 feet per minute, the number of expected defective parts is 20 defective parts.
According to the Question:
The give data is presented as follows'
Line Speed; 20, 20, 30, 30, 40, 40, 50, 50
Number of Defective; 23, 21, 19, 16, 15, 17, 14, 11
Now,
1. From the scatter diagram there is an apparent correlation between increase line speed and the number of defective parts found.
2. The equation for linear regression by the least squares method is presented as follows;
Y = a + b·X
Where;
b = N ∑XY - (∑X) (∑Y) / N ∑X² - (∑X)² -------------------- (1)
and
a = ∑Y - b ∑X / N ---------------------------- (2)
Now, after calculation, we have;
∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8
Putting in equation (1) and (2), we get;
b = (8×4460 - 280×136) / (8×10,800 - 78,400) = -0.3
and,
a = (136 - (-0.3)×280)/8 = 27.5
Therefore, we have the linear regression as follows;
Y = 27.5 - 0.3·X
Therefore, when the line speed is 25 feet per minute, we have;
Y = 27.5 - 0.3 × 25 = 20
The number of defective parts expected to be found when the line speed is 25 feet per minute, Y = 20 defective parts.
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answered
Nakeisha's family took a road trip to Mount Rushmore. Nakeisha fell asleep 18% of the way through the trip. If the total length of the trip was 400 miles, how many miles had they travelled when Nakeisha fell asleep?
2.Select the number below that is irrational.
Answer:
Step-by-step explanation:
the second one
Question 7 (Essay Worth 6 points)
(04.03 MC)
On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
Can drive Cannot drive Row Totals
0.60
Likes to fly
Do not like to fly
Column totals 0.55
0.18
0.45
1.00
Complete the relative frequency table, showing all necessary calculations.
×84 DID
Source C
BIUS x, x Tx
I
E E 99
=
Styles
▾
Format
▼
Font
(
Size
A- A
The completed relative frequency table is given by the image shown at the end of the answer.
How to complete the relative frequency table?First we look at the row total of people who like to fly, which is of 70%, hence:
It is stated in the table that the proportion of those who like to fly and can drive is of 0.32.Hence the relative frequency of those who like to fly and cannot drive is of: 0.7 - 0.32 = 0.38.Amount those who can drive, we have that:
The total is of 0.45.0.32 like to fly.Hence the relative frequency of those who do not like to fly is of: 0.45 - 0.32 = 0.13.Amount those who cannot drive, we have that:
The total is of 0.55.0.38 like to fly.Hence the relative frequency of those who do not like to fly is of: 0.55 - 0.38 = 0.17.Thus the total frequency of the second row is given as follows:
0.17 + 0.13 = 0.30.
Missing InformationThe table is given by the image shown at the end of the answer. I don't know if the values are the same but you will have to follow the same procedure to obtain the missing values.
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Answer:
I took the test
the answer is in the image below
Step-by-step explanation:
which of the following is the most appropriate interpretation of the y-intercept? group of answer choices for a car weighing 68.17 pounds we would expect a fuel efficiency rating of 0 mpg. for a car weighing 6,817 pounds we would expect a fuel efficiency rating of 0 mpg. for a car weighing 0 lbs we would expect a fuel efficiency rating of 6,817 mpg. for a car weighing 0 lbs we would expect a fuel efficiency rating of 68.17 mpg.
The correct interpretation regarding the y-intercept of the least squares regression line is given as follows:
For a car weighing 0 lbs we would expect a fuel efficiency rating of 68.17 mpg.
What is the y-intercept?For a function, the y-intercept represents the value assumed by the output of the function when the input of the function assumes a value of zero.
For the least squares regression line in this problem, the input variable and the output variable are defined as follows:
Input variable: weight of each car.Output variable: fuel efficiency of the car.The y-intercept in this problem has a value of:
68.17.
Meaning that when the weight is of 0 pounds, the fuel efficiency is of 68.17 mpg.
Missing InformationThe missing part of the problem is of:
"For this data set, X represents the weight of each car in hundreds of pounds, and Y represents the predicted fuel efficiency of each car in miles per gallon (mpg). Note that 68.17 is reasonable value for the y-intercept of the least squares regression line. Which of the following is the most appropriate interpretation of the y-intercept?"
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Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of her collection?
Answer: 15 is a 25% increase of 12.
Step-by-step explanation: Difference of 12 and 15 = |12 - 15|/((12 + 15)/2) = 3/13.5 = 0.22222222222222 = 22.222222222222%
a group of nine people are attending the movies together. (a) two of the nine insist on sitting side-by-side. in how many ways can the nine be seated together in a row? 40320 (b) two of the people do not like each other and do not want to sit side-by-side. now how many ways can the nine be seated together in a row?
a group of nine people are attending the movies together . now 40320 ways can the nine be seated together in a row by combination.
(a) The two people who insist on sitting side-by-side can be seated in 1 way. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row is 1 x 7! = 40320.
(b) In this case, the two people who do not like each other can be seated in (7-1)! ways. The remaining 7 people can be seated in 7! ways. Therefore, the total number of ways in which the 9 people can be seated together in a row by combination is (7-1)! x 7! = 40320.
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What is the slope of a line perpendicular to the line whose equation is 15x-18y=-486.
The slope of the line which is perpendicular to the given line is (-6/5).
Describe the negative reciprocal.
The negative reciprocal of a number, let's say "n," is "- (1/n).
We are aware of a line's equation in slope intercept form, y = mx + b, as well as the fact that perpendicular lines have slopes that are reciprocal to each other's negative values.
The slope intercept form of the line 15x - 18y = -486 can be expressed as,
-18y = -15x - 486.
- y = (-15/18)x - (486/18).
- y = (-5/6)x - 27.
y = (5/6)x + 27.
The slope of the supplied line is (5/6), making the perpendicular line's slope (-6/5).
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6x squared - 2x + 1 =0
Answer:
Step-by-step explanation:
6x^2-2x+1=0
6*6=36
36x-2x+1=0
34x+1=0
subtract 1 on both sides
34x=-1
divide both sides by 34
x=-0.0294117647059
Which trigonometric ratio should be used to find height (h) of the escalator? (MGSE9-12.G.SRT.7, MGSE9-12.G.SRT.8)
The trigonometric ratio is sin 10° = h/109
Which ratios in trigonometry are there?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). The branch of geometry known as trigonometry examines the sides and angles of a right-angled triangle.
What three types of trigonometry are there?
Three crucial trigonometric functions—sine, cosine, and tangent—are represented by the abbreviations sin, cos, and tan. tan
Given that :
Hypotenuse = 109 ft
Height = h
Hence sin = height / Hypotenuse
sin 10° = h/109
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The histogram summarizes the percentage of people in each state and the District of Columbia who identify as Hispanic or Latino. Use the drop-down menus to describe the distribution of percentages shown in the histogram.
Can I know if the answers that I choosed are correct?
The smallest and largest possible range in the histogram summarizes the percentage of people in each state and the District of Columbia who identify as Hispanic or Latino is 0 - 4.9 and 45 - 49.9 respectively.
What is percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
The histogram summarizes the percentage of people in each state and the District of Columbia who identify as Hispanic or Latino,
The Hispanic or Latino percentage of the population is shown in the x-axis, whereas the frequency of the population is shown in the y-axis.
Calculate the smallest possible range by considering the graph,
The smallest possible range = 0 - 4.9
Calculate the largest possible range by considering the graph,
The largest possible range = 45 - 49.9
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Answer:
skewed right
Step-by-step explanation:
I am not sure about the numbers, but it's skewed right i had the same question
What is the slope of AB?
m=
A (-6, -4)
B(-3,4)
If 4x - 16 = 32, what is 4x?
Answer: X = -12
Step-by-step explanation:
-4x-16=32
We move all terms to the left:
-4x-16-(32)=0
We add all the numbers together, and all the variables
-4x-48=0
We move all terms containing x to the left, all other terms to the right
-4x=48
x=48/-4
x=-12
Answer:
x=12
Step-by-step explanation:
Given,
4x-16=32
4x=32+16(We transpose LHS to RHS)
4x=48
x=48/4
x=12
Hence, the answer is 12
what is the roots to, x^4-x^2-20=0
The roots of the given equation are √5, - √5, 2i, and - 2i
Roots of a polynomial:The values of a variable for which the provided polynomial equals zero are referred to as a polynomial's roots. If n is the root of a polynomial p(x), then p(n) will be equal to zero.
Here we have
x⁴- x²- 20 = 0
To find the roots of the Equation factorize the given equation
=> x⁴- x²- 20 = 0
Let t = x²
=> t²- t - 20 = 0
Split the middle term
=> t²- 5t + 4t - 20 = 0
=> t(t - 5) + 4(t - 5) = 0
=> (t - 5) (t + 4) = 0
=> (t - 5) = 0 and (t + 4) = 0
Take t - 5 = 0
=> t = 5 => x² = 5
=> x = ±√5
Take (t + 4) = 0
=> t = - 4 => x² = -4
=> x = ± √- 4
=> x = ± 2i [ ∵ - 1 = i² ]
Therefore,
The roots of the given equation are √5, - √5, 2i, and - 2i
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Determine the range of the following graph
The range of the graph is [-4, 11).
What is graph?A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.
In the given graph,
The value of the x coordinate varies from -8 to 11.
And the values of x shows the domain,
Therefore, domain is (-8, 11).
The y coordinate varies from -4 to 11.
And the values of y coordinate shows the range.
The value of y at 11 is open circle, So it shows open interval.
And at -4 it shows close interval.
So the range of the graph will be [-4, 11)
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Find the equation of the line with Slope = 2 and passing through (2,11). Write your equation in the form
y=mx+b
Answer:
y = 2x + 7
Step-by-step explanation:
Use the formula y - y1 = m(x - x1)
Step-by-step explanation:
formula =y-y1=m(x-x1)
-5x+8=y
I don’t know the answer to this
Answer:
Let x=1
-5*x+8=y
-5*1+8=y
-5+8=y
3=y
Another
Let x=-1
-5*(-1)+8=y
5+8=y
13=y
There are multiple endings I suppose this is a point of intersection question that needs to be done on graph
PLEASE HELP WITH MY MATH HOMEWORK
ill give brainliest
3.) The height of the baseball can be modeled by the function Hs= -16s2+96s where s represents the time in seconds the ball is in the air after it is hit.
a) Write the function in factored form. _____________________
b) The factors from your answer in question 3a reveal something important about the situation. Describe what each of the factors means in terms of the height of the baseball and the time in seconds.
Answer:
a) The factored form of the function Hs= -16s2+96s is Hs = -16(s-3)(s-2).
b) The two factors in the factored form of the function, -16(s-3)(s-2), represent the maximum height of the baseball and the time at which the baseball reaches its maximum height. The first factor, -16, represents the maximum height of the baseball, since a negative value multiplied by the product of two positive values will always be negative. The second factor, (s-3)(s-2), represents the time at which the baseball reaches
or
a) Hs = (-16s + 48)(s - 2)
b) The factor (-16s + 48) represents the initial height of the baseball when it is hit, and the factor (s - 2) represents the time it takes for the baseball to reach its maximum height.
Leveled Practice What conclusion can you make about the system of equations? 6y=12x+36 15y = 45x + 60 The slope of the first equation is second equation. The y-intercept of the first equation is y-intercept of the second equation. The system of equations has the slope of the the solution(s)
Answer:
Both lines intersect at the point (2, 10)
See the attached image
X-y=-6
6x-3y=-9
Can you show the steps please
Answer:
Step-by-step explanation:
x-y=-6 (1)..
6x-3y=9 (2)...
First, multiply (1) by 6:
6x-6y=-36
Now subtract the whole eqaution:
6x-6y=-36
- 6x-3y=9
----------------------
-3y = -45
y=15
Now substitute y into one of the equations:
x-15=-6
x=9
So the answer is x=9, and y=15.
How do you find the actual size of an item from a scale drawing?
To find the actual size of an item, multiply the scale factor by the size of the item in the drawing
The scale factor is the ratio of the measurement of the new figure to the measurement of the original figure
Here, we are drawing an item on the paper, the size of the object on the paper maybe less than or greater than of original item
The dimensions of the actual item will be equal to the product of scale factor and the dimensions of the item on drawing.
If the scale factor is greater than 1, then the actual size will be greater than drawing, if the scale factor is between 0 to 1, then actual size will be less than drawing
Therefore, to find the actual size multiply the scale factor and size of drawing
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