The sequence "emdangl" rearranges to "mangled" (an appropriately fitting word scramble solution).
There are 7 letters in the sequence "emdangl", so there are 7! = 7*6*5*4*3*2*1 = 5040 different permutations of the seven letters. The exclamation mark is shorthand to represent factorial notation. Factorials are the idea of multiplying from that integer counting down until you get to 1. The reason why this works is because we have 7 letters to pick from for the first slot, then 6 for the next, and so on until all seven slots are filled out.
Since there is one solution ("mangled") out of 5040 total permutations, this means the probability of getting the solution just by random chance/guessing is 1/5040
Use a calculator shows that 1/5040 = 0.0001984 approximately.
The word 'emdangl' can be arranged in 5040 ways. The probability of randomly selecting one arrangement is 1/5040.
Explanation:The word 'emdangl' has 7 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of distinct objects, which is n-factorial (n!). For this word, there are 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways to arrange the letters.
Now, let's determine the probability of randomly selecting one arrangement of the given letters. Since there is only one correct unscrambling, the probability is 1 out of the total number of arrangements, which is 1/5040.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ2
Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams of part thereof. What could be the weight in grams of a package for which the charge is $1.55?
Answer:
1050 g < weight ≤ 1150 g
Step-by-step explanation:
Let w represent the weight of the package in grams. The the number of 100-gram increments after the first 250 grams is given by ...
⌈(w-250)/100⌉ . . . . . . . where ⌈ ⌉ signifies the ceiling function
and the charges for a package exceeding 250 grams will be ...
0.65 + 0.10⌈(w -250)/100⌉ = 1.55
0.10⌈(w -250)/100⌉ = 0.90 . . . . . . . . subtract 0.65
⌈(w -250)/100⌉ = 9 . . . . . . . . . . . . . . . divide by 0.10
8 < (w-250)/100 ≤ 9 . . . . . . . . . . . . . . meaning of ceiling function
800 < w -250 ≤ 900 . . . . . . . . . . . . . multiply by 100
1050 < w ≤ 1150 . . . . . . . . . . . . . . . . . add 250
The weight in grams could be greater than 1050 and at most 1150 for a charge of $1.55.
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00. Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20 for the 15% gratuity." How should Antoine respond to Tess's method?
Answer:
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.
This in real becomes :
[tex]0.15\times46=6.90[/tex] dollars
But, Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20
So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of [tex]4.6+2.3=6.9[/tex] dollars which is the real amount.
Answer:
Ntoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00.
This in real becomes :
dollars
But, Tess says, "It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20
So, Tess is wrong. Rather she should have done 10% of $46 giving $4.6 and then half of 4.6 that is 2.3 dollars. Getting a total of dollars which is the real amount.
Step-by-step explanation:
trust me
I need help with this problem.
Problem: Same y intercept as x+4y=16, through (4,5)
Y intercept is when x=0 so 4y=16, y=4, y intercept (0,4)
Slope of line through (0,4) and (4,5) is change in y over change in x,
m = (5 - 4)/(4 - 0) = 1/4
Answer: slope 1/4
Check:
The new line is y = (1/4) x + 4
because the y intercept is still (0,4)
Let's check it's through (4,5)
(1/4) (4) + 4 = 5 check
As a part of a project for his statistics class, Marcus wanted to find out the percentage of American households that still have a landline phone.
*There wasn’t a question for this so I thought I would post it. The answer is C. 463 households!*
How many households is 463 households
Answer:
C
Step-by-step explanation:
Just got it right.
The equation below is equivalent to which of the following quadratic equations?
(1/(a+x))+(1/(b+x))=(1/(c+x))
a. ax^2+bc+c=0
b. x^2+2cx+bc+ac-ab=0
c. 2x^2+(b+c-a)x+b(c+a)=0
d. (x^2/a^2)+(b^2/c^2)=((b+c)/(a+c))
an explanation would be appreciated! :)
Answer:
b. x^2 +2cx +bc+ac-ab = 0
Step-by-step explanation:
It's a matter of what I would describe as tedious algebra. You have to multiply by the least common denominator, then simplify to standard form.
After multiplying the equation by (x+a)(x+b)(x+c) and subtracting the right side, you have ...
(x +b)(x +c) +(x +a)(x +c) -(x +a)(x +b) = 0
Expanding each factor pair gives ...
(x² +(b+c)x +bc) +(x² +(a+c)x +ac) -(x² +(a+b)x +ab) = 0
Collecting terms gives ...
x²(1 +1 -1) +x(b+c +a+c -a -b) +(bc +ac -ab) = 0
x² +2cx +bc +ac -ab = 0 . . . . . matches selection B
In a parade, 36 members of the color guard are to march in front of 120 members of the high school marching band. Both groups are to have the same number of students in each row. What is the greatest number of students that could be in each row? How many rows will each group have?
The greatest number of students that could be in each row is 12, which is the greatest common divisor of 36 and 120. The color guard will have 3 rows, and the high school marching band will have 10 rows.
Explanation:To determine the greatest number of students that could be in each row and the number of rows each group will have, we need to find the greatest common divisor (GCD) of the two numbers representing the members in each group, 36 and 120. The greatest common divisor is the largest number that divides both numbers without leaving a remainder. Calculate this by listing the factors of each number or using the Euclidean algorithm.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The greatest common divisor is the largest factor both numbers share, which is 12. Therefore, the greatest number of students per row is 12.
Now, to find the number of rows for each group, divide the total number of members in each group by the number of students per row:
Color guard: 36 members \/ 12 members per row = 3 rowsMarching band: 120 members \/ 12 members per row = 10 rowsSo, there will be 3 rows of color guard members and 10 rows of marching band members.
Write an expression for "the quotient of 2 and 4."
Answer:
2÷ 4
Step-by-step explanation:
Quotient means division
2÷ 4
Bryan hits a golf ball whose path is given by the function f(d) = -0.01d2 + 3d, where d is the distance the ball travelled in feet and f(d) is the height of the ball. The height of the golf ball when it was hit was feet and the ball reached a maximum height of feet.
Answer:
0 ft225 ftStep-by-step explanation:
h(0) = -.01·0² +3·0 = 0 . . . . . the height when the ball was hit
The function can be factored as ...
f(d) = -0.01d(d -300)
This has zeros at d=0 and d=300, so the maximum will be halfway between, at d=150.
f(150) = -0.01·150(150 -300) = -1.5(-150) = 225
The height of the ball when hit was 0 feet, and the ball reached a maximum height of 225 feet.
Bryan hits a golf ball whose path is given by the function f(d) = -0.01d2 + 3d, where d is the distance the ball travelled in feet and f(d) is the height of the ball. The height of the golf ball when it was hit was feet and the ball reached a maximum height of feet.
Module 8 Pre-Cal DBA Help? (!!!!!!!IMPORTANT!!!!!!!)
I have a DBA tomorrow, 7-20-19 and I have to tell my teacher 3 things I learned. I havent learned a single thing and I dont understand most of it.
The module consists of Parabolas, Ellipses, Hyperbolas, Parametric Equations. and Polar Coordinates. What are a few things that I can say I learned about these specific topics?
Answer:
Heres the truth.
Step-by-step explanation:
If you haven't learned anything and you need to do a DBA. Just tell your teacher this, "Even though I've completed the Module... I still don't fully understand the concepts throughout the module. Is there anyway you can help me go over, review, and workout specific things that i understand and don't understand?"
It's best to actually do the work instead of submiting questions for others to answer on here. You should ask for help from a teacher, or go to the online tutoring.
Assume that by continuing your education, you increased your yearly earning potential from $21,484 to $39,746. If the additional education costs $18,000, in about how many years will it pay for itself?
Answer:
By continuing my education I increased my earning potential from $21,484 to $39,746 a year. That's a difference of $18262 a year.
If the additional education costs $18,000, then in one year it will pay for itself.
Answer:
The answer is 1 year.
Step-by-step explanation:
You increased your yearly earning potential from $21,484 to $39,746.
The difference is : [tex]39746-21484=18262[/tex] dollars
This difference is in a year.
So, if the additional education costs $18,000, then in about 1 year it will pay for itself.
Hence, the answer is 1 year.
Kelly is willing to pay $5.20 for a gallon of gasoline. The price of gasoline at her local gas station is $3.80. If she purchases ten gallons of gasoline, then Kelly's consumer surplus is A. $3.80. B. $52. C. $14. D. $1.40.
QUESTION IS GIVEN IN PICTURE NEED HELP!!!
Answer:
The slopes of f(x) and g(x) are the same.Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
========================================
We have:
[tex]f(x)=3x+6\to m_f=3[/tex]
From the table:
[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]
[tex]m_f=m_g=3[/tex]
Answer:
1st one
Step-by-step explanation:
Because of Theorem 5.47 any function that is continuous on (0, 1) but unbounded cannot be uniformly continuous there. Give an example of a continuous function on (0, 1) that is bounded, but not uniformly continuous.
Answer:
[tex]f: (0,1) \to \mathbb{R}[/tex]
[tex]f(x) = \sin(1/x)[/tex]
Step-by-step explanation:
f is continuous because is the composition of two continuous functions:
[tex]g(x) = \sin(x)[/tex] (it is continuous in the real numbers)
[tex]h(x) = 1/x[/tex] (it is continuous in the domain (0,1))
It is bounded because [tex]-1 \leq \sin(\theta) \leq 1[/tex]
And it is not uniformly continuous because we can take [tex]\varepsilon = 1[/tex] in the definition. Let [tex] \delta > 0[/tex] we will prove that there exist a pair [tex]x,y\in \mathbb{R}[/tex] such that [tex]|x-y|< \delta[/tex] and [tex]|f(x) -f(y)|> \varepsilon = 1[/tex].
Now, by the archimedean property we know that there exists a natural number N such that
[tex] \frac{1}{N} < 2\pi \delta[/tex]
[tex]\Rightarrow \frac{1}{2\pi N} < \delta[/tex].
Let's take [tex]x = \frac{1}{2\pi N + \pi/2}[/tex] and [tex]y = \frac{1}{2\pi N + 3\pi/2}[/tex]. We can see that
[tex]|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}<\frac{1}{2\pi N} <\delta[/tex]
And also:
[tex]|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon[/tex]
And we conclude the proof.
If RT = 6 and RS = 9, then RX =
A - sqrt(54)
B - 13.5
C - 7.2
D - 4
Answer:
Option D RX=4 units
Step-by-step explanation:
we know that
In the right triangle RTS
The cosine of angle TRS is equal to
cos(TRS)=RT/RS
substitute
cos(TRS)=6/9 -----> equation A
In the right triangle RTX
The cosine of angle TRX is equal to
cos(TRX)=RX/RT
substitute
cos(TRX)=RX/6 -----> equation B
∠TRS=∠TRX -----> is the same angle
Match equation A and equation B
6/9=RX/6
RX=6*6/9=4 units
Consider the quadratic function f(x)=8x2−7x+6. What is the constant of the function?
−7
6
7
8
Answer:
6
Step-by-step explanation:
The 8 is the leading coefficient, the -7 is the linear term, and the 6 is the constant.
Answer:
the constant term is 6.
Second option is correct.
Step-by-step explanation:
The quadratic function is [tex]f(x)=8x^2-7x+6[/tex]
The general form of a quadratic function is [tex]y=ax^2+bx+c[/tex]
Here c is the constant term and a can't be zero.
On comparing the given equation with the general form, we get
a = 8
b = -7
c = 6
Therefore, the constant term is 6.
Second option is correct.
A research group wants to find the opinions’ of city residents on the construction of a new downtown parking garage. What is the population of the survey
downtown shoppers
downtown visitors
downtown workers
city residents
Answer:
downtown workers
Step-by-step explanation:
The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.
Thus, option "downtown workers" is correct.
The population of the survey would be the city residents.
Explanation:The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.
Learn more about Population of the survey#SPJ12
The A-1 Car Rental Agency charges $23 per day plus $.10 per mile. The EZ Rental Agency charges $30 per day and $.05 per mile. If x is miles and y is total cost, write the ordered pair (x,y) that shows at what point the two companies charge the same amount.
Answer:
(140, 37)
Step-by-step explanation:
If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same. The number of miles will also be the same at this cost. That means we need cost functions for each. x is the number of miles that is driven, our independent variable. If A-1 charges .10 per mile, the expression is .1x. If the flat fee is 23, regardless of how many miles you drive, you can expect to pay
y = .1x + 23
If EZ charges .05 per mile, the expression is .05x. If the flat fee is 30, regardless of how many miles you drive, you can expect to pay
y = .05x + 30
If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.
.1x + 23 = .05x + 30 and
.05x = 7 so
x = 140 miles.
In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.
y = .1(140) + 23
y = 14 + 23
y = 37
The coordinate pair is (140 miles, $37)
This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.
How do you solve for n^3 + 3n^2 + n - 33 = 0?
Answer:
one real root: n ≈ 2.38450287889
Step-by-step explanation:
My favorite solution method for higher-degree polynomials is to use a graphing calculator.
Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).
You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.
__
Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...
y = (n +2.692)² + 6.591
Hence, the complex roots will be near -2.692±i√6.591.
_____
There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...
n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889
Hashem was studying for his upcoming math test. On Monday, he studied for 2 over 3 of an hour. On Tuesday, he studied for 5 over 6 the amount of time he studied on Monday. What fraction of an hour did Hashem study on Tuesday? _____ of an hour
Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos(1.05h)+37 . Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Answer:
Period=6
Step-by-step explanation:
Given:
t=1cos(1.05h)+37
Using acos(bx-c)+d to find the period of the given function
amplitude= a
period= 2π/Bb
phase shift=c (positive is to the left)
vertical shift=d
comparing with t=1cos(1.05h)+37, we get
a=1
b=1.05
c=0
d=37
period= 2π/b
=2π/1.05
=5.983
=6
Period of function is 6, after every 6 hours the refrigerator sensor will reach its maximum temperature and the cycle will move towards reducing temperature i.e it'll reach the minimum temperature then again the cycle will move upwards raising the temperature to maximum and so one period will be completed!
Answer:
6
Step-by-step explanation:
Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos(1.05h)+37. Therefore, the period of the function is 6.
At a school dance, the ratio of boys to girls is 7 to 5. What fraction of students at the dance consists of girls? (You must use the fraction form of a ratio
Answer:
5/12
Step-by-step explanation:
The fraction that is girls is the ratio of girls to the total of boys and girls:
girls/(boys+girls) = 5/(7+5) = 5/12
What is the determinant of
15
18
154
Answer:
The determinant is 15.
Step-by-step explanation:
You need to calculate the determinant of the given matrix.
1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right][/tex]
2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right][/tex]
3. Expand along the row 2: (See attached picture).
We get that the answer is 15. The determinant is 15.
Answer:
The answer is 15
Step-by-step explanation:
A cylindrical pail that has the base area of 9 pi inches squared and a height of 10 inches. One friend bought a pyramid mold with a square base with edge length of 4 inches and height of 7 inches. The other friend bought a cone with a radius of 2.5 inches and the height of six inches. What is the volume of these three objects?
Answer:
cylinder — 90π in³pyramid — 37 1/3 in³cone — 12.5π in³Step-by-step explanation:
The volume of a cylinder is given by ...
V = Bh . . . . . where B is the base area and h is the height
The volume of a pyramid or cone is given by ...
V = (1/3)Bh . . . . . where B is the base area and h is the height
The area of a square of side length s is ...
A = s²
The area of a circle of radius r is ...
A = πr²
___
Using these formulas, the volumes of these objects are ...
cylinder: (9π in²)(10 in) = 90π in³
square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³
cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid
Answer:
12.5
Step-by-step explanation:
I really need help with this question!
Answer:
(s-6)/r
option D
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.
Now we are also given that (r,s) is on our line which means s=c(r)+6.
We need to solve this for c to put c in terms of r and s as desired.
s=cr+6
Subtract 6 on both sides:
s-6=cr
Divide both sides by r:
(s-6)/r=c
The slope in terms of r and s is:
(s-6)/r.
Can someone please help me, I need to know the missing side length (x) using trigonometric ratios.
Answer:
x=6/cos(72) is the exact answer.
[tex]x \approx 19.416[/tex].
Step-by-step explanation:
Sine
opposite
hypotenuse
Cosine
adjacent
hypotenuse
Tangent
opposite
adjacent
Soh Cah Toa is an abbreviation used to help remember the trigonometric ratios.
We see we have the angle measurement 72 degrees given at the bottom. I'm going to label my sides with respect to that angle.
The hypotenuse is x.
The adjacent is 6.
We don't have anything about the opposite side but we don't need it to find x.
So anyways we have this:
The hypotenuse is x and
the adjacent is 6.
If you look at the ratios we want to use cosine.
[tex]\cos(72)=\frac{6}{x}[/tex]
or
[tex]\frac{\cos(72)}{1}=\frac{6}{x}[/tex]
We are going to cross multiply.
x cos(72)=1 (6)
cos(72) * x=6
Now we are going to divide both sides by cos(72) giving us:
x=6/cos(72)
x=6/cos(72) is the exact answer.
Let's put it into our calculator now:
[tex]x \approx 19.416[/tex].
A simple random sample of size nequals=200200 drivers were asked if they drive a car manufactured in a certain country. of the 200200 drivers surveyed, 105105 responded that they did. determine if more than half of all drivers drive a car made in this country at the alpha equals 0.05α=0.05 level of significance. complete parts (a) through (d).
Answer:
Is there supposed to be a photo
Step-by-step explanation:
Hello, this was one of the questions in a test and above the answer choices, I couldn't find what I found to be the result. I would appreciate it if you help me.
[tex](5ab)^{\tfrac{3}{2}}=\sqrt{(5ab)^3}=\sqrt{125a^2b^3}[/tex]
Brandy watched a beetle and a spider on the sidewalk. The beetle crawled 2/5 of a yard and the spider crawled 3/20 of a yard. How much farther did the beetle crawl than the spider?
Answer:
¼ yd
Step-by-step explanation:
2/5 - 3/20
1. Find the lowest common denominator of the two fractions.
The LCD of 5 and 20 is 20.
2. Give the fractions the same LCD
2/5 - 3/20 = 8/20 - 3/20
3. Subtract the numerators
Keep the same denominator.
8/20 - 3/20 = 5/20
4. Simplify the fraction
5/20 = ¼
The beetle crawled ¼ yd further than the spider.
10. If 15 - x = 4, then x =
A. -21
B. -11
C. 1
D. 11
Answer:
D
Step-by-step explanation:
15-x=4
Subtract 15 from both sides
leaves you with
-x=-11
x=11
Hey there! :)
15 - x = 4
Subtract 15 from both sides.
-x = 4 - 15
Simplify.
-x = -11
Divide both sides by -1.
-x ÷ -1 = -11 ÷ -1
x = 11
Therefore, your answer is D. 11
~Hope I helped! :)
Spins a fair spinner numbered 1 - 5 and flips a fair coin. What is the probability of obtaining a factor of 15 and a tail?
Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.
The factors of 15 = [tex]1,\ 3,\ 5[/tex]
Then ,the probability of obtaining a factor of 15 is given by :-
[tex]P(A)=\dfrac{3}{5}[/tex]
The probability of getting a tail :-
[tex]P(B)=\dfrac{1}{2}[/tex]
Since both the events are independent , thus
The probability of obtaining a factor of 15 and a tail is given by :-
[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]
Hence, the required probability : [tex]\dfrac{3}{10}[/tex]