11. In how many different ways can the letters of the word MATH be rearranged to form a four-letter code word (i.e. it doesn't have to be a word in English)?
Answers
The number of letters in the word MATH IS
[tex]=4[/tex]To rearrange a letter with n letters to form a four-letter code will be
[tex]\begin{gathered} n! \\ \text{Where n=4} \end{gathered}[/tex]Hence,
The number of ways of rearranging the words will be
[tex]\begin{gathered} =4! \\ =4\times3\times2\times1 \\ =24\text{ ways} \end{gathered}[/tex]This problem is a bit different. Instead of choosing one item from each of several different
categories, we are repeatedly choosing items from the same category (the category is: the
letters of the word MATH) and each time we choose an item we do not replace it, so there is
one fewer choice at the next stage: we have 4 choices for the first letter (say we choose A),
then 3 choices for the second (M, T, and H; say we choose H), then 2 choices for the next
letter (M and T; say we choose M) and only one choice at the last stage (T). Thus, there are
4 · 3 · 2 · 1 = 24 ways to spell a code word with the letters MATH.
Hence,
The final answer = 24 ways
Related Questions
Every rhombus is a square 
Answers
Answer: False!
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Rhombus as a quadrilateral with equal sides. The angles may or may not be right-angled.
However, a square is a quadrilateral with equal sides and all angles are right angles.
Hence, every square is a rhombus but the opposite is not true.
Answer the questions below.
Answers
Michael bought 1/2 pound of Swiss cheese. He used 1/4 pound for
a sandwich. How much was left?
Answers
Answer:
1/4
Step-by-step explanation:
1/2 - 1/4 = 2/4 - 2/4 = 1/4
HELPPPPPPPPP PLEASEEEEEEEEEE
Answers
which set could not represent the lengths of the slides of a triangle?
Answers
hello
to solve this question, we asume it's a right angled triangle and we use pythagorean theorem
pythagorean thorem states that the square of the longest side which is the hypothenus of a triangles is equal to the sum of the square of the two other sides which are the opposite and adjacent
according to pythagorean
[tex]x^2=y^2+z^2[/tex]now we go through the options
from the first option (3, 4, 5)
the longest side here is 5
let's check if this is true
[tex]\begin{gathered} x^2=y^2+z^2 \\ 5^2=4^2+3^2 \\ 25=16+9 \\ 25=25 \end{gathered}[/tex]option 1 is represents a triangle
let's check option 2
(2, 5, 9)
longest side = 9
[tex]\begin{gathered} 9^2=2^2+5^2 \\ 81=4+25 \\ 81\ne29 \end{gathered}[/tex]option 2 does not represents a triangle and it's the right option here
The students in my class watch less than 2 hours television at night. how can I decide what data to collect to test this statement, How can I design a suitable data collection instrument?
Answers
Solution
For this case we need to select a sample of students from the class
We can ask to each student how much time spend on average watching tv at night
From the results we can take the average and the standard deviation and we can use a t-test to test the statement
For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.A. yes; y=2xB. yes; y=3xC. yes; y=4xD. no; y does not vary directly with x.
Answers
We are given a table with values of "x" and associated values of "y". Let's remember that direct variation implies that each value of "y" will be related with its corresponding value of "x" according to the following relationship:
[tex]y=kx[/tex]Where "k" is the constant of proportionality. If the table shown has direct variation the same constant should apply for each value. Let's take the first value of the table, that is, x = 3 and y = 6. Substituting we get:
[tex]6=k(3)[/tex]Dividing both sides by 3 we get:
[tex]\frac{6}{3}=k[/tex]Solving the operations:
[tex]2=k[/tex]Now we substitute in the relationship:
[tex]y=2x[/tex]Now, for the second value of "x", that is x = 6:
[tex]\begin{gathered} y=2(6) \\ y=12 \end{gathered}[/tex]Since we did not get the corresponding value of "y" in the table, this means that the constant of proportionality doesn't work for this value, and therefore, "y" does not vary directly with "x".
Mischa dives from a platform that is 5 meters above water. Her dive takes her 1.7 meters below the surface of the water. How
far does Mischa's dive take her?
Answers
Conditional equations - Mischa's dives take her 6.5 meter
What are conditional equations?
An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation.
Explain the airthematic mathematical operations.
it deals with the study and use of numbers in all other branches of mathematics. Basic operations include +,-, x, and /.
We frequently employ these fundamental mathematical operations in our daily lives: +, -,x, and, /. For every such area of our lives, we apply mathematical operations, whether it be to figure out the annual budget or distribute things evenly to a lot of people.
Mischa dives from a platform that is 5 meters above the water.
Her dive take her 1.7 meters below the surface of the water.
The total distance of Mischa's dive take her will be,
5+1.7meters
=6.7 meter
thus Mischa's dives take her 6.5 meters far.
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A food company sells its corn flakes in two different sizes: the regular box and the family value box. For the family value box, the length of the box has been increased by 30%, the height has been increased by 25%, and the width remains the same.By what percentage does the volume of the box increase from the regular box to the value box? Round your answer to the nearest percent.
Answers
Hay, this is the solution:
Length of the box = increased 30%
Height = Increased 25%
Width = Remains the same
Volume of the value box = 1.3 * 1.25 * 1
Volume of the value box = 1.625
Volume of the regular box = 1 * 1 * 1
Volume of the regular box = 1
Percentage of increase = 1.625/1 - 1
Percentage of increase = 0.625
Percentage of increase = 62.5 = 63% (Rounded to the nearest p
An expresion is shown. - 2 3 /4 + 3 2/3 What is the value of the expression?
Answers
,By following these steps, we can find the value of this expression:
[tex]-2\times\frac{3}{4}+3\times\frac{2}{3}[/tex]first we multiply both -2 and 3 by their corresponding fractions, we do this by just multiplying the numbers with the numerator of the fraction, like this:
[tex]\frac{-2\times3}{4}+\frac{3\times2}{3}=\frac{-6}{4}+\frac{6}{3}=-\frac{6}{4}+\frac{6}{3}[/tex]Now simplify the fractions:
[tex]-\frac{6}{4}+\frac{6}{3}=-\frac{3}{2}+2[/tex]To sum fractions, we have to make sure that the denominators are the same, this is not the case, we can make their denominators the same by dividing and multiplying the two by two, like this:
[tex]-\frac{3}{2}+2=-\frac{3}{2}+\frac{2\times2}{2}=-\frac{3}{2}+\frac{4}{2}[/tex]Now, we just have to sum up the numerators, like this:
[tex]-\frac{3}{2}+\frac{4}{2}=\frac{-3+4}{2}=\frac{1}{2}[/tex]Then, the value of this expression is:
[tex]\frac{1}{2}[/tex]how do you start square roots in mathmaticals?
Answers
Answer:
a square root is basically any number multiplied by itself to get another number. there are 2 types, perfect and non perfect, perfect is when the number being multiplied by itself is an a whole number, while the non perfect is when the number that is being multiplied by itself is a decimal or fraction
Step-by-step explanation:
Mr. Cumme has 8 3/4 yards of material for her class. he needs to use 1/3 of the material to make an example. How many yards of material will he need to make the example?
Answers
Given:
Mr. Cumme has 8 3/4 yards of material for her class.
he needs to use 1/3 of the material to make an example.
To find the number of yards of material that he will need, we will multiply 1/3 by 8 3/4 to get the answer.
[tex]\frac{1}{3}\times8\frac{3}{4}=\frac{1}{3}\times\frac{35}{4}=\frac{35}{12}=2\frac{11}{12}[/tex]So, the answer will be 2 11/12 yards.
I need help trying to find side c and to see if my other answers are correct?
Answers
we have that
B=5 degrees
C=125 degrees
b=200 units
step 1
Find out the measure of angle A
Remember that
the sum of the interior angles in any triangle must be equal to 180 degrees
so
A+B+C=180
substitute given values
A+5+125=180
A=180-130
A=50 degrees
step 2
Applying the law of sines
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]Find out the value of a
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]substitute given values
[tex]\frac{\sin 50^o}{a}=\frac{\sin 5^o}{200}[/tex]solve for a
[tex]a=\frac{200\cdot\sin 50^o}{\sin 5^o}[/tex]a=1,757.9 units
step 3
Find out the value of c
[tex]\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]substitute given values
[tex]\frac{\sin 5^o}{200}=\frac{\sin 125^o}{c}[/tex][tex]c=\frac{200\cdot\sin 125^o}{\sin 5^o}[/tex]c=1,879.7 unitsFind the sum of the first 9 terms of the following sequence. Round to the nearesthundredth if necessary.40,-16,32/5
Answers
SOLUTION
The following sequence is a geometric series and we have been provided with the formula
[tex]S_n=\frac{a_1-a^{}_1r^n}{1-r}[/tex]Here a1 is the first term = 40,
r is the common ratio = -0.4 (to get r, divide the second term by the first term)
n = number of terms = 9. Now let's solve
[tex]\begin{gathered} S_n=\frac{a_1-a^{}_1r^n}{1-r} \\ \\ S_9=\frac{40_{}-40\times(-0.4)^9}{1-(-0.4)} \\ \\ S_9=\frac{40_{}-(-0.0105)^{}}{1+0.4} \\ \\ S_9=\frac{40_{}+0.0105^{}}{1+0.4} \\ \\ S_9=\frac{40.0105^{}}{1.4} \\ \\ S_9=28.5789 \end{gathered}[/tex]The sum to the nearest hundredth becomes = 28.58
The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard
deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?
(A) 61.6 minutes
(B) 78.4 minutes
(C) 79.8 minutes
(D) 80.4 minutes
Answers
Write the equation of the line in point-slope form that has a slope of 2/3 and a y-intercept of (0,-2)
y-2= 2/3 (x-0)
y-0= 2/3 (x-2)
y-0=2/3 (x+2)
y+2=2/3 (x-0)
Answers
Answer:
y + 2 = 2/3(x - 0)
Step-by-step explanation:
The general form of an equation of line with slope m, passing through point (x1, y1) is:
y - y1 = m(x - x1)
substituting values:
y - (-2) = 2/3(x - 0)
simplify
y + 2 = 2/3(x - 0)
Answer:
where
m(Gradient or slope) =2/3
y1=-2
x1=0
An artist is building a pedestal out of wood that
will be used to display a piece of sculpture. She
plans to cover the pedestal with tile.
10 cm
6 cm
10 cm
16 cm
30 cm
How much tile will it take to cover the pedestal,
including the bottom?
Answers
The area of tiles taken to cover the pedestal, including the bottom is 1176 cm².
What is the Total Surface Area of a Triangular Prism?A triangular prism's surface area is also referred to as its total surface area. A triangular prism's total surface area is the sum of the areas of all its faces. A triangular prism consists of two triangular faces and three rectangular faces.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh
where,
b is the base triangle's bottom edge, h is its height, L is its length, and S1, S2, and S3 are the three edges (sides) of the base triangle (bh).
[2 (1/2 bh)] = bh is the area of the two triangular faces
Given:
From the figure, we can say that the pedestal is in form of a triangular prism.
To find the area of the tile that it takes to cover the pedestal, including the bottom we have to determine the surface area of the pedestal.
So from the figure,
The side lengths of the triangular base are:
S1 = S2 = 10 cm
S3 = 16 cm
Base of prism = 16 cm
Height of prism = 6 cm
Length of prism = 30 cm
Surface area = (S1 +S2 + S3)L + bh
= (10+10+16)30 + 16×6
= 1176 cm²
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A bell rings every 20 minutes. A horn blows every 30 minutes. If Htel Htel heard the two sounds at 8:00AM, at what time will be hear the sounds together again.
Answers
Answer:
Htel Htel will hear the sounds again at 9:00 AM
Suppose f(x) = 3x² – 48. Solve f(x) = 0
Answers
ANSWER:
x = 4 and x = -4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)\: =\: 3x^{2}\: -\: 48[/tex]We solve the values of x for when the function is equal to 0, as follows:
[tex]\begin{gathered} \: 3x^{2}\: -\: 48=0 \\ \: 3x^{2}\: -=48 \\ x^2=\frac{48}{3} \\ x=\sqrt[]{16} \\ x=\pm4 \end{gathered}[/tex]if EB=7, find the value of CD
Answers
Both lines AB and CD are secant lines beacuse in two points they are touching the circunference. There is a Theorem which says the following
[tex]PB\cdot PA=PD\cdot PC[/tex]Since the distance from the center of the circle to each secant line is the same (5 units), we could assume that the both secant lines are similar. saying:
[tex]PB=PD;\text{ }PA=PC\Rightarrow AB=CD[/tex]Then the lenght of CD is:
[tex]CD=2\cdot EB=2(7)=14[/tex]Complete the table given the following function:
f(x) = −2x^2 + 1
Answers
Answer:
if f(-4) = -31
then
f(-2) = -7
f(0) = 1
f(1) = -1
f(3) = -17
Step-by-step explanation:
You have to replace the x of the f(x) equation with said number in the left column. Then plug it into your calculator and your golden :]
f(x) = -2x²+1
= -2(-4)²+1
= -32+1
= -31x = -2f(x) = -2x²+1
= -2(-2)²+1
= -2(4)+1
= -8+1
= -7x = 0f(x) = -2x²+1
= -2(0)²+1
= -2(0)+1
= 0+1
= 1x = 1f(x) = -2x²+1
= -2(1)²+1
= -2(1)+1
= -2+1
= -1x = 3f(x) = -2x²+1
= -2(3)²+1
= -2(9)+1
= -18+1
= -17A rectangular auditorium seats 1749 people the number of seats in each row exceed the number of rows by 20 find the number of seats in each row
Answers
Let x = the number of seats
Let y = the number of rows.
Since the auditorium is rectangular and it has 1,749 people, then we can say that:
[tex]x\times y=1749[/tex]Then, if the number of seats "x" exceeds the number of rows "y" by 20, then we can say that:
[tex]\begin{gathered} seat=row+20 \\ x=y+20 \end{gathered}[/tex]Now we have two equations. To solve for x, let's use the substitution method.
1. Rewrite the equation 2 x = y + 20 into y = x - 20.
2. Replace the value of "y" in equation 1 by x - 20.
[tex]\begin{gathered} xy=1749 \\ x(x-20)=1749 \end{gathered}[/tex]2. Multiply x and x - 20.
[tex]x^2-20x=1749[/tex]3. Transfer the constant term 1749 on the left side of the equation. When transferring over the equal sign, the operation will change. From +1749, it becomes -1749.
[tex]x^2-20x-1749=0[/tex]4. To solve this quadratic equation, let's find the factors of -1749 that sums to -20.
a. 3 and -583 = -580
b. 11 and -159 = -148
c. 33 and -53 = -20
As we can see above, the factors of -1749 that sums to -20 are 33 and -53. Hence, the quadratic equation above can be factored to:
[tex](x+33)(x-53)=0[/tex]5. Equate each factor to zero and solve for x.
[tex]\begin{gathered} x+33=0 \\ x=-33 \end{gathered}[/tex][tex]\begin{gathered} x-53=0 \\ x=53 \end{gathered}[/tex]Since the value of x cannot be negative, then the value of x is 53.
Therefore, the number of seats in each row is 53. In addition, there are 33 rows in the auditorium.
-6 x 1.5 ______ 50 ÷ (-8) which is greater
Answers
Answer: The answer is that 50 ÷ (-8) is greater
Answer:
-6 x 1.5 < 50 ÷ (-8)
-6 x 1.5 = -9
50 / -8 = -6.25
50 divided by -8 is greater than -6 times 1.5p
Step-by-step Explanation:
=D
Which expression is equivalent to (-3t - x) - (5y - 8x)?
Answers
Distribute, and combine like terms:)
Students were trying to use the sample standard deviation formula for the given
data: (8,1,3,0,3). Determine what they did wrong for each case and calculate the
correct value.
S=
Σ(x − x)2
n-1
Answers
The sample standard deviation formula is
square root {(Σ(X - mean)²) / (N - 1)}
What the student did wrong?
The square root sign was not included in their calculation
The correct value of the sample standard deviation is = 3.08
What is standard deviation?Standard deviation shows the by how much the values differs from the mean.
How to calculate the sample standard deviationThe calculation is done by forming the table and calculating the required variables as below:
X (X - mean)²
8 25
1 4
3 0
0 9
3 0
ΣX = 15
mean = ΣX/N = 15/5 = 3
Σ(X - mean)² = 38
Σ(X - mean)² / (N-1)
= 38 / 4
= 9.5
Sample standard deviation = √9.5
= 3.08
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If (-1, y) is a solution to the equation y = x + 5, determine the value of y.
HELP I WILL MARK BRAINLIEST
Answers
Answer:
4
Step-by-step explanation:
The solution to the equation means that the coordinate satisfy the equation. Given that the equation is y= x +5, we know the relationship between the y-coordinate (y) and the x-coordinate (-1) of the point.
y= x +5
Substitute the coordinates into the equation:
When x= -1, y= y,
y= -1 +5
y= 4
Thus, the value of y is 4.
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What’s the correct answer answer asap for brainlist
Answers
Answer:
the answer is C..........
The triangle is translated. B' is the translated position of B.
Draw the new triangle, then verify that they are congruent with the distance formula.
Answers
The new triangle A'B'C' shown in the attached graph has the coordinates of B' are (2, 8), A' are (1, 6), and C' (4, 6).
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
The given triangle ABC shown in the graph has:
The coordinates of B are (-7, 6),
The coordinates of A are (-8,4),
The coordinates of C are (-5, 4)
If B' is the translated position of B.
The new triangle A'B'C' shown in the attached graph has:
The coordinates of B' are (2, 8)
The coordinates of A' are (1, 6)
The coordinates of C' are (4, 6)
Length of AB = A'B' = √5
Length of BC = B'C' = 2√2
Length of CA = C'A' = 3
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PLEASE HURRY
What is the value of the expression −34 − 17 − (−22)?
Answers
Answer:
-29
Step-by-step explanation:
subtracting the negative 22 from the -17 made it positive until you subtract the 34 which made it -29
DUE IN 30 MINUTES PLEASE HELP!!!!
WITH WORK PLEASE
1. Write a piecewise defined rule from a graph
2. Write three equations and show all your steps to get full credit
Answers
For the given question,
The coordinates of the three lines are given with the end points.
Part a: The slope piece wise rule for defined graph is-
[2, 1) - as (1 - 1) is at the open interval.[1,5] - both ends with closed interval.[5,8] - both ends with the closed interval.Part b: calculate the three equations-
First find the slope for the three given lines;
slope (blue line);
coordinates - (0, -4) and (1, -1)
m = (-1 + 4)/(-1 - 0)
m = -3
Equation of line;
y + 4 = -3(x -0)
y = -3x - 4
slope (red line);
coordinates - (1, 4) and (5, 8)
m = (8 - 4)/(5 - 1)
m = 4/4
m = 1
Equation of line;
y - 4 = 1(x - 1)
y = x + 3
slope (green line);
coordinates - (5, 8) and (8, 8)
m = (8 - 8)/(8 - 5)
m = 0
Equation of line;
y - 8 = 0(x - 5)
y = 8
Thus, the three equation of line are found.
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