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 .
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7. Segment MN has endpoints at M(-12,-5) and N(8, 10). A third point Q is located on MN such that MQ:ON=2:3. Answer the following questions. (a) Find the coordinates of Q. Show how you arrived at your answer.
Answer:
To find the coordinates of Q, we can use the concept of proportional division of line segments.
Given that MQ:ON = 2:3, it means that the ratio of the length of MQ to ON is 2:3.
Let's first find the vector that represents the direction of MN, which is the vector pointing from M to N. We can find this by subtracting the coordinates of M from the coordinates of N:
(8,10) - (-12,-5) = (20, 15)
This is the vector <20,15>
Now, we can find the point Q, which is located two thirds of the way from M to N, by multiplying the vector <20,15> by 2/5 and adding the result to the coordinates of M:
Q = M + (2/5) * <20,15>
= (-12,-5) + (2/5) * <20,15>
= (-12,-5) + <8,6>
= (8,1)
So, the coordinates of Q are (8,1)
An initial investment is $9565. It grows at a rate of 4% a year. Interest is compounded yearly. What is the value after 10 years? Round your answer to the nearest penny.
The future value of the investment after 10 years is $14,158.54.
What is the future value?The future value refers to the value of an investment whose present value is compounded at an interest rate into the future.
We can compute the future value using an online finance calculator as below.
N (# of periods) = 10 years
I/Y (Interest per year) = 4%
PV (Present Value) = $9,565
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $14,158.54
Total Interest = $4,593.54
Thus, in 10 years, the initial investment of $9,565 at 4% a year will grow to $14,158.54.
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Find the image of (-1,3) obtained by translating 2 units down, followed by a rotation of 270 counterclockwise about the origin.
The image of the point (-1, 3) is (1, 1).
What is Translation?A translation is a transformation that moves every point in a figure the same distance in the same direction.
For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .
Given:
Pint( -1, 3).
Translating unit = 2 units down
According to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, move it to your new x-coordinate, and then take the opposite of the x-coordinate and set it as your new y-coordinate:
Extended Rotation Rules
270°-clockwise rotation [90°-counterclockwise rotation] = (x, y) → (-y, x)
270°-counterclockwise rotation [90°-clockwise rotation] =(x, y) → (y, -x)
and, 180°-rotation = (x, y) → (-x, -y)
Thus, the 270°-counterclockwise rotation [90°-clockwise rotation] will be
[-1, 1] moves to [1, 1].
Hence, the translation is (1, 1).
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A 4-pack of coffee mugs costs $2.20. What is the unit price?
Answer:
The unit price for a coffee mug is $0.55.
Step-by-step explanation:
The unit price is simply just the price per unit.
We have a 4-pack of coffee mugs that costs $2.20.
He have 4 units and the price per 4 units.
Lets evaluate the price per 1 unit.
[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]
Lets solve for [tex]x[/tex].
Divide [tex]x[/tex] by 1.
[tex]x=\frac{2.20}{4}[/tex]
Divide 2.20 by 4.
[tex]x=0.55[/tex]
A circle has a circumference of 36 cm. What is the length
of an arc that has a measure of 190°?
The length of an arc that has a measure of 190° is equal to 9 cm.
How to calculate the length of an arc?In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Length of an arc = 2πr × θ/360
Length of an arc = C × θ/360
Where:
r represents the radius of a circle.C represents the circumference of a circle.θ represents the angle subtended by the arc.Substituting the given points into the length of an arc formula, we have the following;
Length of an arc = 36 × 90/360
Length of an arc = 36 × 1/4
Length of an arc = 9 cm.
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Find an equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32
We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,
A(x - x₁) + B(y - y₁) + C(z - z₁) = 0
where, A, B, and C are direction ratios
In the question, the plane passes through point (0, -3,1)
Let (x₁, y₁, z₁) = (0, -3,1)
Using above formula the equation of the plane will be in the form,
A(x -0) + B(y - (-3))+C(z - 1) = 0
Ax + B(y + 3)+C(z - 1) = 0 ..........(1)
The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.
So, their normal to the required plane would be perpendicular to the normal of both the planes.
The normal to the required plane is a cross-product of the normals of planes.
A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k
So, the direction ratios,
A = 16, B = -8, C = 8
So equation (1) becomes,
16x - 8(y + 3) + 8(z - 1) = 0
16x - 8y - 24 + 8z - 8 = 0
16x - 8y + 8z - 32 = 0 is the required equation of the plane
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7. The cost of half a dozen candles is R30. What is the cost of one candle?
Answer: 5R
Step-by-step explanation:
Half a dozen =6 pieces
R30/6=5R
How much is one dozen?
One dozen is equal to 12, so one half of a dozen is 6.
If 6 candles are priced at R30, we can divide R30 by 6 to get the cost of 1 candle.
30 ÷ 6 = 5.
Therefore, each candle costs R5.
I WILL GIVE BRAINLIEST HELPPPPPPP
Answer:
sorry I want to help you but I can't sorry
Step-by-step explanation:
i don't know how to solve this
you have invited 86 people to a meeting. of those people, 12 from the north cannot attend, 4 from the south cannot attend, 6 from the east cannot attend, and 12 from the west cannot attend. how many people should you expect to attend the meeting?
Given the graph below, which of the following statements is true?
○The graph represents a one-to-one function because every x-value is paired with only one y-value.
○The graph represents a one-to-one function because it is defined for all x-values.
○The graph does not represent a one-to-one function because it does not pass through the origin.
○The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
The answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
What is the one-to-one function?
The one-to-one function is a special function that maps every element of the range to exactly one element of its domain i.e, the outputs never repeat. As an example, the function g(x) = x - 4 is a one-to-one function since it produces a different answer for every input.
To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.
To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.
Of course, it passes the vertical line test, so it's a function.
Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places.
We, therefore eliminate choices A and B.
We can eliminate choice C because nowhere is it requires a function to pass through the origin for it to be one-to-one.
Hence, the answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
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Answer:
D for Edge
Step-by-step explanation:
y
the 140 employees in a factory are either right handed or left handed
The frequency table is given below.
The probability that a person chosen is a left-handed female is 31/140.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total number of employees = 140
Male:
Number of male = 65
Right-handed.
= Total number of right-handed - Female right handed
90 - 44 = 46
Left-handed.
= 65 - 46
= 19
Female:
Number of females.
= Total employees - Number of males
= 140 - 65
= 75
Right-handed.
= 75 - 31
= 44
Left-handed.
= 31
Now,
The frequency table.
RH = 46
LH = 19
Male = 65
140
Female = 75
RH = 44
LH = 31
Now,
The probability that a person is a left-handed female.
= Number of left-handed females / Total number of employees
31/140
Thus,
The frequency table is given above.
The probability that a person is a left-handed female is 31/140.
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Is figure B a scale factor of figure A What is x
Answer:
Step-by-step explanation:
Step 1:
Make a proportion:
10/5 = 22/x
Step 2:
Cross multiply:
10x=22*5
10x=110
Step 3:
Divide by 10 to isolate x:
x=11
Which line is parallel to the line y=12x+5
hEEEELLLLLPPPPPP
Select all of the terms that apply to the shape.
hexagon
convex
irregular polygon
octagon
decagon
concave
heptagon
pentagon
regular polygon
nonagon
the shape is a arow pointing up and downn
Pentagon, irregular polygon and convex polygon are the names that apply to the given form.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
A pentagon is a polygon with five sides, and if these sides are uneven, it is an irregular pentagon, also known as an irregular polygon.
A convex polygon is one with all of its internal angles smaller than 180°.
As a result, the terms for the given form are pentagon, irregular polygon, and convex polygon.
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The question seems incomplete, the missing figure has been attached below
Francesca had 32 cups of flour. She used 2/8 of the flour for a recipe. How much flour did Francesca use? Write an equation to model your work.
Answer:
8 cups of flour
Step-by-step explanation:
If you want an equation it will be:
[tex]\frac{2}{8} * \frac{32}{1} = \frac{64}{8} = 8[/tex]
So Francessa used 8 cups of flour
A transformation is applied to a figure to create a new figure. Which transformation does not preserve congruence?
The transformation that does not preserve congruence is translation
The term called transformation is defined as the process of changing the position of an object on an xy-plane.
Here we have know that the transformation is applied to a figure to create a new figure.
And here we also know that the only transformation that does not preserve congruence is a translation 7 units down
So the transformation of figure and the reflection preserve the congruence since it only create a mirror image of the figure.
And the term called dilation also preserve congruence since it only enlarges the given figure.
Here we want to know that concept of translation a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
Based on this definition we have conclude that the solution is translation.
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Please answer this edpuzzle! PLEASE! Whoever answers it first, I will mark you brainliest.
The simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
How to simplify the algebraic expression?The algebraic expression for this problem is defined as follows:
9x + 2y + 3 - 4x + 8.
To simplify the expression, we combine the like terms, which are the terms that have the same unknown variable, hence:
9x - 4x = 5x.2y.3 + 8 = 11.Hence the simplified algebraic expression for this problem is given as follows:
5x + 2y + 11.
Meaning that the third option is the correct option.
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i need to verify that this is true. (1-sinx)(1+cscx)=cscx-sinx
We can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.
What is equation?An equation is a mathematical expression containing symbols, constants, and/or numbers that combine to create an equation that states the equality of two mathematical expressions. Equations are used to describe relationships between different quantities and can be used to model real-world phenomena. Equations can also be used to solve problems and make predictions about a system.
To verify that this equation is true, we can use algebraic manipulation. First, we need to expand the left side of the equation. We can do this by multiplying (1-sinx) by (1+cscx). This gives us the equation (1-sinx)(1+cscx) = 1+cscx-sinx-sinxcscx.
Next, we need to simplify the right side of the equation. We can do this by combining the two terms with a minus sign. This gives us cscx-sinx.
Finally, we can compare the two equations. We see that both equations are equal, so the original equation is true.
Therefore, we can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.
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Evaluate 0.0007 multiplied by 100
Answer:
0.07
Step-by-step explanation:
[tex]0.0007*100=0.07[/tex]
Basically, you move the 7 two places to the left since 100 has 2 zeroes.
The equation m = 40g gives the distance in miles, m, that a car can travel using g gallons of gas.
a. If the car has gone 140 miles, how much gas was used? Show your thinking.
b. Write an equation that represents the inverse function: the gallons of gas as a function of distance in miles
a)
g = m / 40
g = 140 /40
g = 3.5
b)
m = 40g
m / 40 = g
A peron i remodeling the front entrance to hi home and need to cut an arch for the top of an entranceway. The arch need to be 18 ft wide and 3 ft high. To draw the arch, he will ue tring with chalk attached at an end a a compa.
The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.
The radius of the arch is 9 feet.
The formula for calculating the radius of an arch is [tex]R = (width / 2) / sin(90°)[/tex].
Therefore, the radius of the arch is:
R = (18 ft / 2) / sin(90°) = 9 ft
To calculate the radius of the arch he needs to draw, the person can use the formula R = (width / 2) / sin(90°). In this case, the width of the arch is 18 feet, so the radius of the arch is 9 feet, calculated as R = (18 ft / 2) / sin(90°). The person will have to place the compasses 6 feet away from the point they want the arch to start, and draw the arch with a radius of 9 feet.
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Use benchmarks to estimate 11.47 + 9.02
Step-by-step explanation:
11.47 + 9.02
= 20.49 ...
[its takes so much time to solve and write here so plzzz =》]
MARK ME AS BRAINLIEST ...If 8; 2x; 2y forms an arithmetic sequence and 2x ; 2y; 36 forms a geometric sequence determine the values of x and y. Arithmetic and Geometric Series
Answer:
36
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. A geometric sequence is a sequence of numbers in which any two consecutive terms have a constant ratio.
Given that 8, 2x, 2y is an arithmetic sequence, we know that:
2x - 8 = 2y - 2x
x = y
Given that 2x, 2y, 36 is a geometric sequence, we know that:
(2y)/(2x) = 36/2y
y^2 = 36x
Now, we can use the first equation to substitute for y in the second equation, and get:
x^2 = 36x
x^2 - 36x = 0
x(x-36) = 0
So x = 0 or x = 36
However, x cannot be equal to zero because in that case the second term of the arithmetic sequence will be zero, and it will not be a valid solution. Therefore, x = 36.
So, y = x = 36.
Therefore, the values of x and y are 36.
Can someone just help explain one of the problems and I’ll try the rest? Thank you!
a) The average of daily income of a plumber from Sunday to Friday is Rs 1,300 in the last week. If he earned Rs 2,000 on Saturday, find his average of daily income of the week.
Answer: To find the average of daily income of the week, we need to find the total income of the week and divide it by the number of days in the week.
We know that the average daily income of the week is Rs 1,300 and we know that he earned Rs 2,000 on Saturday. To find the total income for the week, we can add the Saturday income to the average daily income for the 6 days.
Therefore, the total income for the week = Rs 1,300 (average daily income) x 6 (days) + Rs 2,000 (Saturday income) = Rs 7,800 + Rs 2,000 = Rs 9,800
To find the average daily income for the week, we divide the total income by the number of days in the week (7)
Average daily income = Rs 9,800 / 7 = Rs 1,400
Therefore, the average daily income of the plumber for the week is Rs 1,400.
Step-by-step explanation:
d.
What do you notice about the graph of the quadratic equation and where it crosses the
x-axis? How do these values compare to the solutions of x2 - 6x + 5 = 0? Explain.
This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation x2 - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.
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1. Gerald works 18 hours each week. He earns $10 per hour. Write an expression to find how much Gerald earns in 1 week. Write an expression to find how much Gerald earns in 4 weeks. PLS HURRY!!!
The expression for the amount earned in one week per hour is 18 x $10
The expression for the amount earned in four weeks is 18 x $10 x 4
What are the expressions?An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.
The amount earned in one week = total number of hours worked in a week x amount earned per hour
18 x $10
The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4
18 x $10 x 4
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Ms. Lambert took her family to Pimento Garden on Sunday for dinner. The total bill was $73.25, and she wanted to leave an 18% tip. How much
money should she leave for the tip? *Make sure your answer rounded to correct money form.
Answer: The answer is $13.19.
Step-by-step explanation:
1- Turn the percentage into a decimal by moving the percent sign twice to the left.
2- Multiply the bill by the decimal.
3-youll get 13.185 so you'll round up to 13.19.
hope this helps!!
PLEASEEEEEEEEEE HELPPPP
The expression for the cost of gasoline and oil will be C. 3.35c + 2.65g
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, it should be noted that Joe bought g gallons of gasoline and c cans ofg oil. The prices were givn as well.
The expression for the cost of gasoline and oil will be:
= 3.35 × c + (2.65 × g)
= 3.35c + 2.65g
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What is square root 25x²y^2/square root xy in simplest form? Assume X>o and y>0.