Answer:
Step-by-step explanation:
ham 3.45x
Gabe purchased a razor for $13.99, a refill pack of razor blades for $5.75, shaving cream for $3.29 and lotion for $7.35. He has a $.65 coupon for the shaving cream and a $3.00 rebate for the razor.
Answer:
13.99 + 5.75 + 3.29 + 7.35 = 30.38
30.38 - .65 - 3.00 = 26.73
Step-by-step explanation:
Hope this helps! =D
Answer:
$26.73
Step-by-step explanation:
razor = $13.99 - $3.00(rebate) = $10.99
refill pack of razor blades = $5.75
shaving cream = $3.29 - $0.65(coupon) = $2.64
lotion = $7.35
Lat year, Kaitlin opened an invetment account with $5200 . At the end of the year, the amount in the account ha decreaed by 7% . How much i thi decreae in dollar? How much money wa in her account at the end of lat year?
The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.
This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.
This can be expressed algebraically as:
Let x = amount in Kaitlin's account at the end of the year
Initial Amount (x) = 5200
Decrease (%) = 0.07
Decrease in Dollars = x * 0.07
Decrease in Dollars = 5200 * 0.07
Decrease in Dollars = 364
Amount in Account at the End of the Year = 5200 - 364
Amount in Account at the End of the Year = 4836
Learn more about amount here:
https://brainly.com/question/8082054
#SPJ4
Select the correct answer.
What is the y-intercept of function f?
(-3x - 2,
-∞ <
-x + 1,
-2 ≤ x ≤ 3
2x + 5,
3 ≤ x < 00
f(x)
=
OA. -1
OB. 5
O C. 1
OD. -2
< -2
The y-intercept of function f is 1.
f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3 = 2x + 5, 3 ≤ x < ∞
For y-intercept, x =0, f(x) = -x + 1 [∵ -2 < 0 < 3]
f(0) = -0 + 1 = 1
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.
This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.
To learn more about function refer to:
brainly.com/question/11624077
#SPJ1
Taylan i elling platic and wooden frame. He old 7 total frame. The number of platic frame Taylan old wa 5 le than twice the number of wooden frame. How many of each type of frame did Taylan ell?
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames
Let x = number of wooden frames
Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:
x + (x * 2) < 7
2x < 7
x < 7/2
x = 3
Therefore, Taylan sold 3 wooden frames and 5 plastic frames.
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
Learn more about inequality here
https://brainly.com/question/28823603
#SPJ4
Dupe's age
and Olu's
age
add
up to 25 years.
Eight years ago, Dupe was twice as old as
Olu. How old are they now?
Dupes's age is 14 year and Olu's age is 11 year now.
What is linear algebraic equations?
Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.
Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.
Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:
x + y = 25
(x - 8) = 2(y - 8)
This system of linear equations can be transformed into the following by using a little algebraic trickery:
x + y = 25
x - 2y = -8
To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.
Learn more about linear algebraic equations click here:
https://brainly.com/question/12788590
#SPJ1
A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base. The mountain is a triangle, the length of the snow line is 2. 4 times the height of the snow covered part of the mountain. If the snow covers 1,200,000 square feet of part of the mountain, how high is the mountain?
The height of the mountain is 10000ft.
Now, According to the question:
A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base.
The snow covers 1,200,000 square feet of part of the mountain.
We know that:
Area of triangle = 1/2 × base × height
Area of a triangle = 1/2 × 2.4 h × h
1200000 = 2.4[tex]h^2[/tex]/2
cross multiply
1200000 × 2 = 2.4[tex]h^2[/tex]
2400000 = 2.4[tex]h^2[/tex]
Divide both sides by 2.4
[tex]h^2[/tex] = 2400000/2.4
[tex]h^2[/tex] = 1000000
h = √1000000
h = 1000 ft.
The height of the mountain = 1000 ft. + 9000 ft. = 10000 ft.
Learn more about Area of triangle at:
https://brainly.com/question/19305981
#SPJ4
Can 90 over 60 be simplify
Answer:
30/20 = 6/4 = 2/3 (I hope this makes sense)
Step-by-step explanation:
U are dividing by LCM
Karen is trying to get to the MRT station, which is 7
10
km away
from where she parked her car. She has already walked for 2
5
km. How much farther does she have to walk to reach the MRT
station?
answer quickly please and please send solution if possible
Answer:
The answer is 685 km hopefully I understood your question and helped you ☻
Step-by-step explanation:
710 km - 25 = 685
Find the equation for the plane through P0 (−1,−7,2) perpendicular to the following line. x= −1+t , y= −7−5t , z= −2t , −[infinity]
The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30
The plane is passing through point P₀(-1, -7, 2)
And the parametric equation of the line is:
x = -1+t , y= -7-5t , z= -2t
L: (-1, -7, -2) + t(1, -5, -2)
The required plane passes through P₀ and perpendicular to line L.
The direction vector of L is V = <1, -5, -2>.
The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is
1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0
The equation of plane P passing through point P₀ (-1, -7, 2) is:
1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0
(x + 1) - 5(y + 7) - 2(z - 2) = 0
x - 5y-2z + 1 - 35 + 4 = 0
x - 5y - 2z = 30 is the required equation of the plane
Learn more about the equation of the plane here:
brainly.com/question/27190150
#SPJ4
The complete question is:
Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t
For this polynomial function, state the coordinate points of the zeros
The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).
How determine the zeros of the polynomial?The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.
For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.
Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.
f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
Step 2: Factor the polynomial to solve for x.
[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
x([tex]x^{2}[/tex] - 3x + 4) = 0
Step 3: Factor the quadratic equation.
x(x - 1)(x - 2) = 0
Step 4: Set each factor equal to 0 and solve for x.
x = 0, x = 1, x = 2
Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.
When x = 0, y = 4
When x = 1, y = 0
When x = 2, y = 0
Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).
To learn more about polynomial, visit
brainly.com/question/11536910
#SPJ1
What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, f ( x ) decreases in value. As x increases in value, f ( x ) decreases in value. B. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) increases in value. C. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) decreases in value. D. As x decreases in value, f ( x ) decreases in value. As x increases in value, f ( x ) increases in value.
The end behavior of the radical function represented by this graph is option C. As x decreases in value, f ( x ) increases in value. As x increases in value, f ( x ) decreases in value.
What is a radical function on graph?A radical function is a type of mathematical function that includes a radical symbol, such as a square root sign (√) or cube root sign (3√), in its equation.
The graph of a radical function is a curve that may open upward or downward, depending on the specific function. For example, the graph of the square root function, y = √x, starts at the point (0,0) and extends upward and to the right, creating a "V" shape. As the input (x) increases, the output (y) also increases, but at a decreasing rate.
Therefore, the correct answer is as given above
learn more about functions: https://brainly.com/question/10439235
#SPJ1
a spherical balloon is inflated so that its volume is increasing at the rate 6 cm^3/min. at what rate is the radius increasing when the radius is 3 cm
The radius is increasing at rate of [tex]\frac{10}{36\pi } \\[/tex]
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V=
[tex]V=\frac{4}{3} \pi r^3\\dv/dt=6\\Given\\radius=3cm\\[/tex]
so, we need to find dr/dt
Since there is no t in our equation. So differentiate using chain rule
[tex]\frac{dv}{dt} =\frac{dv}{dr} *\frac{dr}{dt} \\[/tex]
Since, in question it is given dv/dt=6
[tex]6=\frac{dv}{dr} .\frac{dr}{dt} \\[/tex]
To find dv/dr differentiate
[tex]4/3\pi r^3\\dv/dr(\frac{4}{3} \pi r^3)=4\pi r^2\\6=4\pi r^2\frac{dr}{dt} \\[/tex]
Dividing
[tex]\frac{10}{4\pi (3)^2} =dr/dt\\dr/dt=\frac{10}{36\pi } \\[/tex]
Learn more about sphere at https://brainly.com/question/30355719
#SPJ4
The radius is increasing at rate of 10/36π
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V= 4/3 πr³
dv/dt =6
Given r = 3 cm.
so, we need to find dr/dt
Since there is not in our equation. So differentiate using chain rule
dv/dt =dv/dr * dr/dt
Since, in question it is given dv/dt=6
6 =dv/dr * dr/dt
To find dv/dr differentiate
dv/dr (4/3πr³) = 4πr²
6 = 4πr² dr/dt
Finally,
dv/dt = 10/36π
Hence, The radius is increasing at rate of 10/36π
Learn more about radius at
brainly.com/question/13449316
#SPJ4
Brian invests £7900 into his bank account.
He receives 2. 3% per year compound interest.
How much will Brian have after 5 years?
Give your answer to the nearest penny where appropriate
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 7900\\ r=rate\to 2.3\%\to \frac{2.3}{100}\dotfill &0.023\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 7900\left(1+\frac{0.023}{1}\right)^{1\cdot 5} \implies A=7900(1.023)^5\implies A \approx 8851.26[/tex]
In 1957 an earthquake in Alaska
measured about 9.0 on the Richter
scale. An earthquake with magnitude 6.0 occurred in Japan in early 2007. How many times more intense was the earthquake in Alaska than the one in Japan?
The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.
How much more intense the earthquake in Alaska and find ratio of amplitude?To determine how much more intense the earthquake in Alaska was than the one in Japan, we can use the formula:(magnitude of Alaska earthquake / magnitude of Japan earthquake) = (9.0 / 6.0) = 1.5This means that the earthquake in Alaska was 1.5 times more intense than the one in Japan.Alternatively, we can use the logarithmic relationship of the Richter scale to calculate the ratio of amplitude.(10^(magnitude of Alaska earthquake)/10^(magnitude of Japan earthquake)) = (10^9.0/10^6.0) = (1000000000/1000000) = 1000This means that the amplitude of the earthquake in Alaska was 1000 times greater than the one in Japan.So the answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.To learn more about ratio of amplitude refer:
brainly.com/question/3613222
#SPJ1
imagine that a recent study found that people who eat large amounts of bananas get bitten by mosquitoes on average more often than people who eat smaller amounts of bananas. what causal relationship can we conclude from this study alone?
It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.
Cause and Effect of Bananas and Mosquito BitesTo determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.
If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.
Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.
It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.
Learn more about Cause and Effect of Bananas and Mosquito Bites here:
https://brainly.com/question/3222241
#SPJ4
an element in a ring is called an idempotent if . prove that the only idempotents in an integral domain are and . find a ring with a idempotent not equal to 0 or 1.
A ring with a idempotent not equal to 0 or 1 is 3 and 4.
Make (R,+) a domain that is integral.
As a commutative ring with two elements, R, ab = 0 when either an or b are equal to zero.
If a ∈ R is an idempotent element, then a ≠ 0,a ≠ 1 will result.
[tex]a^{2}[/tex] = a
We can take multiple of 1 because the same number return if we multiply 1 to any number.
[tex]a^{2}[/tex] = a·1
Subtract a·1 on both side, we get
[tex]a^{2}[/tex] - a·1 = 0
Taking a common
a(a -1) = 0
(a -1) = 0 or a =0
R has no zero divisors.
So, a = 1 or a = 0
As a result, the only idempotent elements in the integral domain R are 0 and 1.
A ring that is not equal to 0 or 1 and is idempotent.
A ring with respect to addition and multiplication is the set R = 0 through 5.
Let 3 ∈ R,
[tex]3^{2}[/tex] = 6+3 = 0+3 = 3
Let 4 ∈ R.
[tex]4^{2}[/tex] = 16 = 12+4 = 2
Hence, 3 and 4 are idempotent elements other than 0 and 1
To learn more about idempotent element link is here
brainly.com/question/15297309
#SPJ4
The complete question is:
An element x in a ring is called an idempotent if [tex]x^2[/tex] = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with an idempotent x not equal to 0 or 1.
Dana sees a street sign and a pine tree. The street sign is 8 feet tall and casts a shadow that is 15 feet long. What is the height of the pine tree if the pine tree's shadow is 30 feet long?
Hi, I am trying to solve a the sin graph y=1-3sin(3/2)Theta. can someone explain to me how to get the y-values for each x value?
The graph of the function is added as an attachment and the function values are y = 4 for all x values
How to detemrine the function valuesFrom the question, we have the following parameters that can be used in our computation:
y=1-3sin(3/2)Theta
Express properly
So, we have the following representation
y = 1 - 3sin(3/2π)
Next, we create a plot of the graph (see attachment)
From the graph, we can see that the function is a horizontal line at y = 4
This means that for all x values, the y value is constant at 4
Read more about function at
https://brainly.com/question/28532394
#SPJ1
Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
The value of x and y is -10 and 5 respectively in the given equations.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - x + 3y = 5
The second linear equation is - -3x - 2y = 20
On evaluating individually the equation obtained is -
-3x - 2y + x + 3y = 20 + 5
-2x + y = 25
Multiply equation (1) with 3 -
3(x + 3y) = 5 × 3
3x + 9y = 15.....(3)
Adding equation (3) and (2) -
-3x - 2y + (3x + 9y) = 20 + 15
-3x - 2y + 3x + 9y = 35
-2y + 9y = 35
7y = 35
y = 35/7
y = 5
Substituting the value of y in equation (1) -
x + 3y = 5
x + 3(5) = 5
x + 15 = 5
x = 5 - 15
x = -10
Therefore, the value of x and y is -10 and 5 respectively.
To learn more about linear equation from the given link
brainly.com/question/2226590
#SPJ1
Find the length of side x to the nearest tenth.
Considering the figure the side length x is solved to be 6.6
How find the value of xInformation given from the question is interpreted as
√11 = adjacent
x = hypotenuse
The side x is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The side x is calculated using cos, CAH
cos 60 = Adjacent / hypotenuse
cos 60 = √11 / x
x = √11 / cos 60
x = 6.633
x = 6.6 to the nearest tenth
Learn more about SOH CAH TOA here:
https://brainly.com/question/29402966
#SPJ1
Evaluate: 3(x+4)(x+1) / (x+2)(x-2) for x = 4
A.10/3
B.10
C.-10/3
D.-10
the following data are for 30 observations involving two categorical variables, x and y. the categories for x are a, b, and c; the categories for y are 1 and 2. observation x y 1 a 1 2 b 1 3 b 1 4 c 2 5 b 1 6 c 2 7 b 1 8 c 2 9 a 1 10 b 1 11 a 1 12 b 1 13 c 2 14 c 2 15 c 2 observation x y 16 b 2 17 c 1 18 b 1 19 c 1 20 b 1 21 c 2 22 b 1 23 c 2 24 a 1 25 b 1 26 c 2 27 c 2 28 a 1 29 b 1 30 b 2 (a) develop a crosstabulation for the data, with x as the row variable and y as the column variable. y total 1 2 x a b c total (b) compute the row percentages. (round your answers to one decimal place.) y total 1 2 x a b c (c) compute the column percentages. (round your answers to one decimal place.) y 1 2 x a b c total (d) what is the relationship, if any, between x and y? category a values for x are ---select--- for y. category b values for x are ---select--- for y. category c values for x are ---select--- for y. need help?
The row percentage of A is 0% , B is 83.3% and of C is 15.4%.
Percentage describes the relative value of a number. Its shows the 100th part of the number with respect to a number whose value is provided in the problem.
Here various data is given about A, B and C in the format of two tables and this shows the relationship between the two.
Now, the row percentage of A is
[tex]\frac{0}{5} * 100=0%[/tex]%
Then, the row percentage of B is
[tex]\frac{10}{12}*100 = 83.3%[/tex]%
Now, we have to find the row percentage of C
[tex]\frac{2}{13}*100 = 15.4%[/tex].%
Hence, The row percentage of A is 0, the row percentage of B is 83.3% and the row percentage of C is 15.5%.
To Learn more about the percentage visit: https://brainly.com/question/29306119
#SPJ4
Triangle ABC is similar to triangle FGH.
What is the value of x in centimeters?
Triangle ABC is similar to triangle FGH.
And the value of the x is 22.5 centimeters.
What are similar triangles?Those triangles that looks the same but different in sizes.
And in the similar triangle,
the corresponding sides in proportion to each other and corresponding angles are equal to each other.
Given:
Triangle ABC is similar to triangle FGH.
That means, the corresponding sides of the triangles are in proportion to each other.
That means,
13.5/9 = 18/12 = x/15
Now,
18/12 = x/15
x = 270/12
x =22.5 centimeters
Therefore, the value of the x is 22.5 centimeters.
To learn more about the similar triangle;
https://brainly.com/question/14926756
#SPJ1
Help me please help thank you and have a great day
Hey Mate,
Answer is (4,3),
Thank you .
The team won the game 114-113. The teams scored only 2s and 3s. The winning team scored 50 baskets and the losing team scored 48 baskets. How many more 3s did the winning team than the losing team?
By using linear equations, The winning team scored 3 less 3s than the losing team.
What are linear equations?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
For winning team
let x=no. of 2s and y=no. of 3s
Therefore, these linear equations will be formed
x+y=50
2x+3y=114
After solving these we get x=36 and y=14
For losing team
let a=no. of 2s and b=no. of 3s
Therefore, these linear equations will be formed
a+b= 48
2a+3b=113
After solving these we get a=31 and b=17
Difference between 3s scored=17-14
Difference between 3s scored=3
To know more about linear equations visit the link
brainly.com/question/29739212?referrer=searchResults
#SPJ1
Hotel P offer two type of room for it cutomer: a Deluxe room and a Suite room. The price per night for the uite room for check-in on Sunday until Thurday i 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday i 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thurday. If the hotel management want to maintain the price difference between the two type of pace, and the price per night for a Suite room for check-in on Sunday until Thurday i $223, what hould be the price per night for a Suite room for check-in on Friday and Saturday?
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.
1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:
$223 / 1.70 = $131.18
2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:
$131.18 x 1.25 = $163.98
3. Calculate the price of a Suite room for check-in on Friday and Saturday:
$163.98 x 1.70 = $278.50
The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ4
mr. and mrs. zeta want to name their baby zeta so that its monogram (first, middle, and last initials) will be in alphabetical order with no letters repeated. how many such monograms are possible?
Mr. and Mrs. Zeta want to make sure that their baby's monogram, which consists of the first, middle, and last initials, is in alphabetical order with no letters repeated. We may utilize the idea of permutations to determine the number of possible monograms.
A permutation is a way to arrange a group of things in a particular sequence. In this instance, we are examining the alphabet's set of letters (from A to Z), and we are trying to determine how many different ways there are to arrange them so that the monogram is composed entirely of unique letters.
The breakdown of the computation is as follows:
There are 26 different alternatives for the first initial (A to Z).
Since the monogram must be in alphabetical sequence, the letter for the second initial must appear after the first initial. There are so 25 possibilities left (the letters that come after the first initial in the alphabet).
There are 24 possibilities left for the final initial (the remaining letters that come after the second initial in the alphabet).
By multiplying the alternatives for each initial, we can calculate the total number of possible monograms using the basic counting principle:
26 x 25 x 24 = 15,600
Because they must be in alphabetical order and contain no repeating letters, there are 15,600 number of monograms are possible .
To know more about permutation at :
brainly.com/question/12468032
#SPJ4
(01.02 MC)
Using the Factor Theorem, which polynomial function has the zeros 3 and 4 - 5i?
The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)
How to determine the polynomialFrom the question, we have the following parameters that can be used in our computation:
zeros 3 and 4 - 5i
The polynomial is represented as
P(x) = (x - zeros)
So, we have
P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))
Expand
So, we have
P(x) = (x - 3)((x - 4)^2 + 25)
Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)
Read more about polynomial at
https://brainly.com/question/7693326
#SPJ1
The table shows conversions of common units of length.
Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers
1 yard = 3 feet
1 yard = 36 inches
Which shows the best path to find the number of centimeters in 1 yard?
The number of centimetres in the 1 yard will be 9.144 cm.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that:-
Metric System Units
1 inch = 2.54 centimetres
1 foot = 0.3048 meters
1 mile = 1.61 kilometres
1 yard = 3 feet
1 yard = 36 inches
First, we will calculate 1 yard to feet.
1 yard = 3 feet
1 feet = 0.3048 meters
1 feet = 3.048 centimeters
1 yard = 3 x 3.048 centimeters
1 yard = 9.144 centimeters
Hence, the length of 1 yard in cm is 9.144 cm.
To know more about unit conversion follow
https://brainly.com/question/28308386
#SPJ1
1) The end behavior of a rational function is equal to
A) Holes
B) Horizontal Asymptote
C) Vertical Asymptote
D) Domain
Answer:
B) Horizontal Asymptote
A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.