The probability in a random 5-letter string that the letters A and B will be next to each other is 0.4
For A and B to be next to each other in the string of letters, consider the AB combination as a single letter. Then there are 4 letters AB, C, D, E.
There are 4! number of ways to arrange these 4 letters.
4!= 24 ways
We know AB can be arranged in 2 ways ( AB or BA)
Thus there are 2*4! = 2 * 24 = 48 ways of arranging the letters such that AB are next to each other in the random Five-letter string
The total number of letters in the set is 5 and hence the total number of ways the letters can be arranged without A and B necessarily being next to each other is 5!= 120
The probability that in the random five-letter string( in which each letter appears only once with all such strings equally likely) the letters A and B are next to each other= 48/120 = 0.4
another sum using probability:
brainly.com/question/18803944
#SPJ4
I need help with my mathWrite the slope-intercept form of the equation of each line
Answer:
y = -1
Explanation:
The slope-intercept form of the equation of a line has the form:
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
So, replacing (x1, y1) by (1, -1) and (x2, y2) by (2, -1), we get:
[tex]m=\frac{-1-(-1)}{2-1}=\frac{-1+1}{1}=\frac{0}{1}=0[/tex]On the other hand, the y-intercept is the point where the line crosses the y-axis. So, the y-intercept is -1.
Finally, the equation of the line in the slope-intercept form is:
y = 0x - 1
y = -1
So, the answer is y = -1
Part A Write the multiplication expression shown by the model. Do not solve the problem. Part B
Explain the expression written in Part A. Include the final product and how it is shown with the model.
active attachment
The multiplication expression is L×w
The expression is written as N= r+ g + w + b
The final product = 200 boxes
How to determine the expressionIt is important to note that the formula for calculating the area of a rectangle is expressed as;
Area = lw
Where;
l is the length of the rectanglew is the width of the rectangleThe area can be determined by multiplying the length and the width and also by then adding the boxes.
Mathematically, we have;
10( 4 + 5 + 4 + 7)
Also
L × w = r + g + w + b
Hence, we have that L×w is a multiplication expression.
Total number of boxes for the length = 20
Total number of boxes for the width = 10
Total area = L×w = 20×10=200
Number of red boxes = 46Number of green boxes = 46Number of blue boxes = 46Number of white boxes = 62We then have;
N= r+ g + w + b
but r = g = b
Also,
L×B = 3r + w
Hence, a multiplication expression is an expression in which variables or numbers are being multiplied.
Learn more about algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
solve the systems using equal values.y= 2xy= -3x + 5
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!
1. The quadratic function f(x) has roots of −4 and 2 and point (1, −5) lies on f(x). What is the equation of f(x)?
f(x) = (x − 2)(x + 4)
f(x) = (x − 2)(x − 4)
f(x) = 4(x − 2)(x + 4)
f(x) = 4(x − 2)(x − 4)
2. What is the standard form of the equation of a quadratic function with roots of 2 and −5 that passes through (1, −3)?
y = −0.5x2 + 1.5x − 5
y = −0.5x2 + 1.5x + 5
y = 0.5x2 + 1.5x − 5
y = 0.5x2 + 1.5x + 5
Answer: For 1 it is A - f(x)=(x-2)(x+4) and for 2 it is C - y = 0.5x^2 + 1.5x − 5
Step-by-step explanation:
Just use Desmos
It takes Allie 456
minutes to drive to the store. From the store, it takes her 734
minutes to drive to the car wash. How many minutes does it take Allie to drive to the store and then to the car wash?
It takes 1190 minutes for Allie to drive to the store and then to the car wash.
According to the question,
We have the following information:
Time taken by Allie to drive to the store = 456 minutes
Time taken by Allie to drive to the car wash from the store = 734 minutes
Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.
(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)
Now,
The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store
The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes
The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes
Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.
To know more about minutes here
https://brainly.com/question/15600126
#SPJ1
Find the sum of the following infinite series.1/3−2/21+4/147−8/1029+···
Given:
The series is 1/3−2/21+4/147−8/1029+··
Explanation:
For the given series, the first term is,
[tex]a=\frac{1}{3}[/tex]The common ratio is,
[tex]\begin{gathered} r=\frac{-\frac{2}{21}}{\frac{1}{3}} \\ =-\frac{2}{21}\cdot\frac{3}{1} \\ =-\frac{2}{7} \end{gathered}[/tex]The formula for the sum of infinite series is,
[tex]S_{\infty}=\frac{a}{1-r}[/tex]Substitute the values in the formula to determine the sum of infinite series.
[tex]\begin{gathered} S_{\infty}=\frac{\frac{1}{3}}{1-(-\frac{2}{7})} \\ =\frac{\frac{1}{3}}{\frac{9}{7}} \\ =\frac{1}{3}\times\frac{7}{9} \\ =\frac{7}{27} \end{gathered}[/tex]Answer: 7/27
A computer retail store has 10 personal computers in stock. A buyer wants to purchase 4of them. Unkown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random.A. In how many different ways can the 4 computers be chosen?Answer: 210B. What is the probability that exactly one of the computers will be defective?Answer:
A.
The number of different ways the computers can be chosen is given by a combination of 10 choose 4.
A combination of n choose p is given by the formula below:
[tex]C(n,p)=\frac{n!}{p!(n-p)!}[/tex]So we have:
[tex]C(10,4)=\frac{10!}{4!(10-4)!}=\frac{10\cdot9\cdot8\cdot7\cdot6!}{4\cdot3\cdot2\cdot6!}=210[/tex]B.
If the first computer chosen is the one defective, the probability of the first PC being defective is 4/10, the probability of the second one not being defective will be 6/9, for the third not being defective is 5/8 and for the fourth not being defective is 4/7.
Since the defective PC can be any of the 4 bought, we need to multiply the probability above by 4. So the final probability is:
[tex]P=4\cdot\frac{4}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}\cdot\frac{4}{7}=0.3809[/tex]In 2022, a company made a profit of $1.38 million. That amount is $2.54 million more than the profit from 2021.
What is the profit from 2021? Write & solve an Algebraic Equation.
Answer: 6x+2xz*52-35^5=
Step-by-step explanation: rs:p=4436x
Answer: The profit from 2021 = $ -1.16 Million ($1.16 Million loss)
Step-by-step explanation:
Profit for 2022 = $ 1.38 Million
Profit for 2021 = Profit for 2022 - $ 2.54 Million
Algebraic equation:
p2021 = p2022 -$ 2.54 Million
p2021 = $ 1.38 Million - $ 2.54 Million
p2021 = $ -1.16 Million
What is the wavelength of a gamma ray with a frequency of 1.0 × 10¹⁹ Hz? 19 x [?] x 10?] m c = 3.0 x 108 m/s
The wave length of the gamma ray with a frequency of 1.0 x 10¹⁹ is 3 x 10⁻¹¹
Wave length:
Wavelength refers the distance between two peaks (or troughs) of a wave, and is therefore measured in meters.
The formula for calculating wave length is,
λ = c/v
where,
c = 3.0 × 10⁸, i.e. the speed of light, and
λ = wavelength , and
ν = frequency .
Given,
Here we have the frequency as 1.0 x 10¹⁹.
Now we need to find the wave length of the gamma ray.
Here we know that value of c = 3 x 10⁸
And the value of v = 1.0 x 10¹⁹
Wen we apply the value on the formula then we get,
λ = ( 3 x 10⁸) / ( 1.0 x 10¹⁹)
When we simplify it, then we get,
v = 3 x 10⁻¹¹
Therefore, the wavelength of the gamma ray is 3 x 10⁻¹¹.
To know more about Wave length here.
https://brainly.com/question/10715783
#SPJ1
Complete the steps to find the value of x
Answer:
2x=128⁰ x=64⁰
Step-by-step explanation:
since they are corresponding angles, the other side (2x) will also be 128⁰. This means that x=64⁰
and 2x=128⁰
Is the bottom answer correct.
Answer:
I believe so
Step-by-step explanation:
PLEASE ANSWER QUICK THIS IS DUE TODAY!!
-6+7m = 6m - m
Answer:
m = 3
Step-by-step explanation:
Hello!
We can solve for m by isolating the variable.
Solve for m-6 + 7m = 6m - m-6 + 7m = 5m => Simplify7m = 5m + 6 => Add 6 to both sides2m = 6 => Simplifym = 3 => Divide by 2The value of m is 3.
Solve for y 2(4y+7)=62
Answer:
2 (4y+7) = 62. y=6
Step-by-step explanation:
2 (4y+7) Distribute the 2
8y+14=62. use subtraction to cancel out
-14 -14
8y=48. Use division to cancel out
/8. /8
y=6
Find the value of x.
Step-by-step explanation:
even though the line segment pieces of the horizontal and the inclined lines are of different lengths, but the ratio between the pieces of the same line must be the same.
in other words
x/27 = (32-18)/18 = 14/18 = 7/9
9x/27 = 7
x/3 = 7
x = 7×3 = 21
(1,-3),y=-4x-1 in slope intercept form
The following question has two parts. First, answer part A. Then, answer part B.
Use the model to answer the questions.
A rectangle is divided into two sections by a vertical line. The left section is labeled inside with 260. The right section is labeled inside with B. The left edge of the rectangle is labeled 13. Across the top outside of the rectangle, the sections are labeled A tens, a plus sign above the vertical line, and C.
Part A
Carter wants to use the model above to solve 273÷13. Explain how he would find parts A, B, and C of the model.
Part B
The final quotient for 273÷13 is
The knowledge of place value helped in solving 273÷13 with a rectangular model developed by Carter
The part labelled A is 26 tens
The part labelled B is 13 units
The part labelled C is 13 ones
How to determine parts A, B, and C using rectangular model developed by Carterinformation given in the question
A rectangle is divided into two sections by a vertical line
The left section is labeled inside with 260
The left edge of the rectangle is labeled 13
other information is in the attached diagram
How to used the model
Carter's model is a rectangle of length 273 and breadth 13.
273 / 13 = 21
This means that dividing the length into 13 places each unit is 13
273 - 13 = 260
hence the 260 represents 20 units, since one unit is subtracted
The knowledge of place value help to get the numbers to be arranged in tens and ones
putting the numbers in tens is done by dividing by 10
= 260 / 10
= 26
hence, A in tens is equivalent to 26
putting the numbers in ones is dine by dividing by 1
C = 13 / 1
C = 13 ones
a unit is 13, B = 13
B covers same space as C so they are equal
Learn more about using rectangular models :
https://brainly.com/question/27271326
#SPJ1
David has a wooden board that is 6 feet long. how many pieces can be cut from the board if the length of each piece is 1/3 of a foot
total length = 6 ft
length of the piece = 1/3
[tex]\text{Number of pieces = 6 / }\frac{1}{3}\text{ = }\frac{\frac{6}{1}}{\frac{1}{3}}\text{ = }\frac{6x\text{ 3}}{1\text{ x 1}}=\text{ }\frac{18}{1}\text{ = 18}[/tex]There will be 18 pieces
What is 4325 + 970 step by step explanation pls
50 pointssss!!!!
if N is a nonzero integer, then n+1 divided by n is always greater than 1
Find a counter example to show its false
Answer: Plugging in -1 for n.
Step-by-step explanation:
Equation:
(n+1) / n
Given the equation above what can we plug in for n to make the equation less than or equal to 1?
(-1 + 1) / -1 = 0/-1 = 0
Inputting negative one will cause the statement to be false.
Answer:
11n
Step-by-step explanation:
1)bowl a contains 2 red chips; bowl b contains two white chips; and bowl c contains 1 red chip and 1 white chip. a bowl is selected at random, and one chip is taken at random from that bowl. what is the probability of selecting a white chip? if the selected chip is white, what is the probability that the other chip in the bowl is red?
Probability that selected chip is white: 1/2
Probability that the other chip in the bowl is red given if the selected chip is white: 1/3
Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:
P(A) = P(B) = P(C) = 1/3
The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.
Let W be the event that a white chip is randomly selected.
Attached is the picture solution.
You can learn more about probability from:
https://brainly.com/question/11234923
#SPJ4
(3x³ - 8x² + 16x - 1) ÷ (x − 1) answer ?
Answer:
[tex]= \frac{-125x^3-1}{x-1}[/tex]
if the expected frequencies rule for chi-square had been violated by the data, which categories could be combined together in a meaningful way to increase the expected frequencies?
If the chi-square test's expected frequencies rule is broken, either the row or the column is combined to provide a higher frequency that can be used to run the independence test.
Generally speaking, if more than 20% of the anticipated frequencies have a value of less than 5, Chi-Square should not be used (it does not matter what the observed frequencies are).
Both the chi-square test and Fisher's exact test are inappropriate if the sampled values' independence is broken. This presumption will be broken if the same subject results in more than one observation in the contingency table.
There are distinct assumptions for each non-parametric test as well. The data in the cells should represent frequencies or counts of cases rather than percentages or other data transformations, according to the Chi-presumptions. square's The variables' levels are mutually exclusive.
To know more about chi-square refer to the given link:
https://brainly.com/question/14082240?referrer=searchResults
#SPJ4
URGENT HELP!!
Approximate the correlation of the data shown below?
The approximate correlation of the data shown on the diagram above is: C. -0.5.
The question says we should approximate the correlation using the given scatter plot. Below shows a detailed explanation on how to do a rough estimation of the possible value of the correlation.
What is the Approximate Correlation of a Data?
Correlation Coefficient, r, is a numerical value of -1 to 1, which tells how strongly related two variables are. If the points on a scatter plot form a trendline that slopes upwards, it is a positive correlation. If it slopes downwards, it is a negative correlation.
The magnitude of the correlation coefficient is dependent on how father apart the points are from each other along a trend line. If they are much farther apart from each other, the correlation coefficient would far from 1 and -1, and close to zero. If they are closer, it would be close to 1 or -1, and far from 0.
The scatter plot shows the data points are moderately spaced from each other and the trendline slopes downwards. Therefore, the best estimate for the correlation is: C. -0.5.
Learn more about correlation on:
https://brainly.com/question/4219149
#SPJ1
Alberto's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 adult tickets and 14 student tickets for a total of $84. The school took in $105 on the second day by selling 12 adult tickets and 7 student tickets. What is the price each of one adult ticket and one student ticket?
Answer:
Adult: $7
Student $3
Step-by-step explanation:
Hello!
We can use a system of linear equations to find the solution.
Let the price of adult tickets be x, and the price of student tickets are y.
The price of Day 1 can be represented by 6x + 14y = 84, and the second day can be represented by 12x + 7y = 105.
We can solve the system by graphing both equations on a coordinate plane and finding the point of intersection.
The point of intersection happens at x-coordinate 7 and y-coordinate 3. Recall that x is assigned to the price of adult tickets, and y is assigned to student tickets.
The price of adult tickets is $7, and the price of student tickets is $3.
Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,-8) and (1,4)
Answer: (8,
-4) and (3,8)
Step-by-step explanation:
Find the ordered pair $(x,y)$ if
\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Thanks
In accordance with the system of linear equations, the ordered pair is (x, y) = (1, 2).
How to find the values associated to an ordered pair
Ordered pairs are constructions characterized by two components, typically real numbers. The most common form of notation is (x, y). In this problem we need to resolve a system of linear equations to obtain the needed values. We find a system of two equations and two variables:
x + y = (3 - x) + (3 - y)
x - y = (x - 2) + (y - 2)
First, simplify each expression of the system:
First equation:
x + y = 6 - x - y
2 · x + 2 · y = 6
x + y = 3
Second equation:
x - y = (x - 2) + (y - 2)
x - y = x + y - 4
- 2 · y = - 4
y = 2
Second, substitute in the first equation:
x + 2 = 3
x = 1
The ordered pair is (x, y) = (1, 2).
To learn more on ordered pairs: https://brainly.com/question/20379472
#SPJ1
Berti is the Shape Factory's top employee. She has received awards every month for having the top sales
figures so far for the year. If she stays on top, she will receive a $5000 bonus for excellence. She currently has
sold 16, 250 shapes and continues to sell 340 per month.
EMPL
Since there are eight months left in the sales year, Sarita is working hard to catch up. While she has only sold
8,830 shapes, she is working overtime and on weekends so that she can sell 1, 082 per month. Will Sarita
catch up with Berti before the end of the sales year? If so, when?
No, Sarita will not be able to catch up with Berti before the end of the sales year.
Berti currently has sold 16, 250 shapes
She continues to sell 340 per month.
In eight months she will be able to sell
16250 + 8 x 340
= 16250 + 2720
= 18970
Sharita has only sold 8,830 shapes
Working overtime and on weekends so that she can sell 1, 082 per month
In eight months she will be able to sell
8830 + 8 x 1082
8830 + 8656
17486
No, Sarita will not be able to catch up with Berti before the end of the sales year.
To learn more about word problem refer here
https://brainly.com/question/13818690
#SPJ1
Find the area of the entire region round two decimal places
SOLUTION.
The area of the entire region will be to find the area of the isosceles triangle and the semi-circle.
[tex]\begin{gathered} \text{Area of the triangle is } \\ =\frac{1}{2}\times a\times b\times\sin \theta \\ \text{Where } \\ \text{where a and b are two sides and }\theta=angle\text{ betwe}en\text{ the two sides } \end{gathered}[/tex]Then
[tex]\begin{gathered} =\frac{1}{2}\times8\times8\times\sin 72.6 \\ =32\sin 72.6 \\ =30.54\text{unit}^2 \end{gathered}[/tex]The area of the isosceles triangle is 30.354 square units
We need to obtain the diameter of the semi-circle using the cosine rule
We need to obtain the value of x,
[tex]\begin{gathered} x^2=8^2+8^2-2(8)(8)\cos 72,6 \\ x^2=128-128\cos 72.6 \\ x^2=128-38.27 \\ x^2=89.72 \end{gathered}[/tex]Take square root of both sides, we have
[tex]x=\sqrt[]{89.72}=9.74[/tex]Hence, the diameter is 9.74
Then the radius will be
[tex]r=\frac{9.74}{2}=4.87[/tex]The area of the semi-circle is
[tex]\begin{gathered} =\frac{1}{2}\pi r^2 \\ =\frac{1}{2}\times3.14\times4.87^2 \\ =37.24\text{unit}^2 \end{gathered}[/tex]The area of the semi circle is 37.42 square units
Therefore the area of the region will be
[tex]\begin{gathered} =\text{Area ot triangle + Area of semi circle } \\ =30.54+37.42 \\ =67.96uniits^2 \end{gathered}[/tex]Thus
The area of the region is 67.96 units²
Complete the ratio table.
13 11
22
52 44
55
91 77
The complete table using ratios is:
13, 39, 52, 72, and 91. What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.In mathematics, a ratio shows how frequently one number appears in another.For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.In, the column we can notice the pattern of (×2):
11×2 = 2222×2 = 44Now calculate similarly:
This is a ratio method 13, 39, 52, 72, and 91.Therefore, the complete table using ratios is:
13, 39, 52, 72, and 91.To learn more about ratios refer to:
brainly.com/question/12024093
#SPJ13
graph of this equation x=3/5y