The number of distinct ways the letters in TALLAHASSEE can be arranged is calculated using permutations with repetitions. It involves taking the factorial of the total number of letters and dividing by the factorial of the number of times each letter repeats.
To determine the number of distinct ways the letters in TALLAHASSEE can be arranged, we must consider it as a permutation problem with repeating elements. We need to calculate the factorial of the total number of letters and then divide by the factorial of the number of times each individual letter repeats.
The word TALLAHASSEE contains 11 letters in total:
'T' occurs once.'A' occurs twice.'L' occurs twice.'H' occurs once.'S' occurs twice.'E' occurs twice.The permutation formula considering repetitions is:
Number of arrangements = Total letters factorial / (Product of each letter's factorial)
Therefore:
Number of arrangements = 11! / (2! * 2! * 2! * 2!)
This would give us the total number of distinct arrangements of the letters in TALLAHASSEE.
2.1 + (–3.7h) + 1.9h – 1.4
A town has a population of 2000 and grows at 4% every year what will be the population after 15 years to the nearest whole number
Answer:
3602
Step-by-step explanation:
The population of the town after 15 years will be approximately 3495.
Explanation:To find the population of the town after 15 years, we need to use the formula for compound interest: A = P(1 + r)^t, where A is the final amount, P is the initial amount, r is the growth rate expressed as a decimal, and t is the number of time periods. In this case, P = 2000, r = 0.04, and t = 15.
Using this formula, we can calculate the population after 15 years:
A = 2000(1 + 0.04)^15
A = 2000(1.04)^15
A ≈ 2000(1.747422)
A ≈ 3494.84
Rounding to the nearest whole number, the population after 15 years will be approximately 3495.
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Use the quadratic formula to solve for the roots of the following equation. x 2 – 4x + 13 = 0
By using the quadratic formula, the roots of the equation are,
⇒ x = 2 ± (√3/2) i
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The quadratic equation is,
⇒ x² - 4x + 13 = 0
Now, By using the quadratic formula, the roots of the equation are,
⇒ x² - 4x + 13 = 0
⇒ x = - (- 4) ± √ (- 4)² - 4×1×13 / 2
⇒ x = 4 ± √16 - 52 / 2
⇒ x = 4 ± √- 36 / 2
⇒ x = 4 ± √6 i / 2
⇒ x = 2 ± (√3/2) i
Thus, We get;
⇒ x = 2 ± (√3/2) i
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Final answer:
The roots of the quadratic equation x² - 4x + 13 = 0 are complex numbers, specifically 2 + 3i and 2 - 3i, obtained through applying the quadratic formula.
Explanation:
To solve the quadratic equation x² – 4x + 13 = 0 using the quadratic formula, we first identify a, b, and c from the equation. Here, a=1, b=-4, and c=13. The quadratic formula is ‘x' equals minus ‘b’, plus-or-minus the square root of ‘b’ squared minus four ‘a’ ‘c', all over two 'a'. Applying these values, we get:
x = – (-4) ± √((-4)² – 4(1)(13)) / (2)(1)
This simplifies to:
x = 4 ± √(16 – 52) / 2
x = 4 ± √(-36) / 2
Since the square root of -36 is 6i (where i is the imaginary unit √(-1)), the solutions are:
x = (4 ± 6i) / 2
x = 2 ± 3i
Therefore, the roots of the equation are 2 + 3i and 2 - 3i, which are complex numbers.
Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets. {jill, john, jack}, {susan, sharon}
The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
What is mean by Subsets?
A set 'A' is a subset of another set 'B' , if all the element of the set A are element of set of 'B'.
Given that;
The subsets are;
⇒ {jill, john, jack} , {Susan, sharon}
Now,
Clearly, A subsets of a set is contain all the elements of subsets.
So, We get the set;
Set = {jill, john, jack, Susan, sharon}
Thus, The smallest possible set that contains the given sets as subsets is,
⇒ {jill, john, jack, Susan, sharon}
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What is value of x?
https://static.k12.com/nextgen_media/assets/8093716-NG_GMT_SemB_08_UT_12.png
The calculated measure of the angle x is 76 degrees
How to determine the measure of the angle xFrom the question, we have the following parameters that can be used in our computation:
The figure
Also, we have
Angle with a measure of 76 degrees
By the theorem of corresponding angles, we have
x = 76
Hence, the measure of the angle x is 76 degrees
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A _____ is a type of variable that is not accounted for in a research experiment.
a. independent variable
b. dependent variable
c. confounding variable
Which set of points lies on the graph of x = -2?
Jeremiah scored 28 points in yesterday's basketball game. He made a total of 17 baskets. Some of the baskets were field goals (worth two points) and the rest were free throws (worth one point). How many field goals did Jeremiah make? How many free throws did he make?
Answer:
6 and 11
Step-by-step explanation:
Please help me solve for r
1. Sarah bought a mango tree that grows 4 cm each day. It was 10 cm tall when she bought it and now it is 82 cm. Write an equation to express the growth of this tree. Let "x" represent the number of days Sarah has owned the tree.
2. How many days has Sarah owned the tree?
The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter? 165 m2 2,158 m2 1,079 m2 37,699 m2
an angle bisector of a triangle divides the opposite side of the triangles into segments 6cm and 4cm long. A second side of triangle is 7.4 cm long. Find the longest and shortest possible lengths of the thrid side of the triangle
Graph y= 1/3x+3 .I just need to know the plots
Answer:
The graph shows the given straight line.
Step-by-step explanation:
We are given an equation:
[tex]y = \displaystyle\frac{1}{3}x + 3[/tex]
The attached image shows the graphical plot for the given equation.
If we compare the given equation to the
[tex]y = mx+c[/tex]
where m is the slope and c is the y-intercept of the straight line.
Comparing, we get:
[tex]m = \displaystyle\frac{1}{3}\\\\c = 3[/tex]
The line will pass by the points (-3, 2), (0, 3), and (3, 4)
Given is an equation y = x/3+3 we need to graph it,
Let's pick a few x-values and determine the y-values that go with them:
Y equals (1/3) when x = -3(-3) + 3 = -1 + 3 = 2
Y = (1/3)(0) + 3 = 0 + 3 = 3 when x = 0.
Y = (1/3)(3) + 3 = 1 + 3 = 4 for x = 3.
The points (-3, 2), (0, 3), and (3, 4) can now be plotted on the coordinate plane.
A straight line running across these locations will form the graph.
The line will have a positive slope because the value of x is positive (1/3).
Given that the y-intercept is 3, the line will cross the y-axis at (0, 3).
The plotted points (-3, 2), (0, 3), and (3, 4) lie on the line, and the line continues indefinitely in both directions.
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Please help with 2 questions.
Which algebraic expression represent the phrase “ seven more than half of a number”?
Answer:
The given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
Step-by-step explanation:
Given phrase “ seven more than half of a number”
We have to write the algebraic expression for the given phase.
Algebraic expression is the way of writing an expression in mathematical form using mathematical operations and variables.
Consider the given phrase “ seven more than half of a number”
Let the number be N,
Then half of number is [tex]\frac{1}{2}N[/tex]
and seven more means seven is added to this, the expresion becomes [tex]7+\frac{1}{2}N[/tex]
Thus, the given expression “ seven more than half of a number” can be written mathematically as [tex]7+\frac{1}{2}N[/tex]
Willem bought a jacket on sale. the price was 40% off the original price of $60. how much did he pay? answer
Hannah completed 3/4 of her homework on Saturday morning and 1/8 ofit on Saturday night. How much more homework does she need to complete?
A trowel is in the shape of a trapezoid. For what value of x is the trapezoid am isosceles trapezoid
A trapezoid becomes an isosceles trapezoid when its non-parallel sides, or legs, are of equal length. Thus, for a given length x, an isosceles trapezoid requires both legs to be x in length.
Explanation:A trapezoid is a geometric shape with one pair of parallel sides. A trapezoid becomes an isosceles trapezoid when the non-parallel sides (the legs) are equal in length. If we denote the length of the legs as x, then the trapezoid becomes an isosceles trapezoid when both legs are of equal length, meaning x equals x.
Without additional information such as the lengths of the base and height of the trapezoid or the angles within it, we cannot provide a specific numerical value for x. The key to remember here is that an isosceles trapezoid has equal length legs - so whatever value you have for one leg, the other leg must be the same for it to qualify as an isosceles trapezoid.
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kelly ran 2 miles and burned 240 calories. the next day she ran 3 miles and burned 360 calories. the next day4 miles and 480 miles. if this pattern continues, how
many calories will she burn if she runs 8 miles?
Answer:
She will burn 960 calories if she runs 8 miles
WILL GIVE BRAINLIEST, 5 STARS, AND THANK YOU
The Polygons are similar, but not necessarily drawn to scale. Find the value of x.
Jeannette earns $3.50 per hour and 4% commission on the gross amount of
her sales. How much did she earn the week she worked 35 hours and sold
$4,550 worth of merchandise?
a. $304.50
b. $182
c. $186.90
d. $122.50
HELP ASAPPP
Use the number line to find the ratio AC/CF simplify the ratio
A. 8/20
B 2/5
C 8/12
D 2/3
Answer:
The correct option is D.
Step-by-step explanation:
From the given number line it is clear that A=0, B=2, C=8, D=14, F=20 and G=22.
The length of line segment AC is
[tex]AC=C-A=8-0=8[/tex]
The length of line segment CF is
[tex]CF=F-C=20-8=12[/tex]
The ratio of line segment AC to CF is
[tex]\frac{AC}{CF}=\frac{8}{12}[/tex]
Cancel out the common factors.
[tex]\frac{AC}{CF}=\frac{2}{3}[/tex]
The simplified ratio of [tex]\frac{AC}{CF}[/tex] is 2/3.
Therefore the correct option is D.
What are the two equations created by the inequality |x–12| + 5 < 27? y1= and y2=
Answer:
y1= |x-12|
y2= 22
Which graph represents the two functions? Graph 3
Step-by-step explanation:
The school cafeteria has two meal options in the main line today: a grilled chicken sandwich or a spicy fried chicken sandwich one lunch period, 60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich. 40 of the eople who ordered the grilled chicken sandwich got a chocolate mitk to drink. If the sandwich choice and the drink choice are independent, how many of the people who ordered the spicy fried chicken sandwich got a chocolate milk?
Answer:
60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.
Step-by-step explanation:
Consider the provided information.
60 people order the grilled chicken sandwich, and 90 people order the spicy fried chicken sandwich.
40 Out of 60 people who order grilled chicken sandwich got a chocolate milk to drink.
Let say x number of people out of 90 got chocolate milk drink.
Now we need to find the people who ordered the spicy fried chicken sandwich got a chocolate milk.
The above information can be written as:
[tex]\frac{40}{60}=\frac{x}{90}[/tex]
[tex]\frac{40}{60}\times 90=x[/tex]
[tex]x=20\times 3[/tex]
[tex]x=60[/tex]
Hence, 60 of the people who ordered the spicy fried chicken sandwich got a chocolate milk.
The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is calculated as 50.
The number of people who ordered the spicy fried chicken sandwich and got a chocolate milk is to be determined.
Step-by-step explanation:
Calculate the total number of people who ordered the spicy fried chicken sandwich minus the number who got a chocolate milk with the grilled chicken (90 - 40 = 50).Therefore, 50 people who ordered the spicy fried chicken sandwich got a chocolate milk.Which equation models the problem below if c represents the number of puppies whose eyes are closed?
There are 15 puppies in a photograph, and 11 of them have their eyes open.
How many puppies have their eyes closed?
c – 11 = 15
11 – c = 15
15 + c = 11
11 + c = 15
Answer:
11+c=15
Step-by-step explanation:
4 pups have their eyes closed
Need help I dont know how to do this please help!
2. Graph the number on a number line.
10/7
Gustavo tested 1000 calculators to see if any were defective. The company claimed that the probability of a defective calculator was 1% per 1000 calculators. Gustavo found 15 defective calculators out of 1000.
What was the predicted frequency?
Predicted Frequency . . .
=(# of trials)(theoretical probability)
=(1000)(0.01)
The predicted frequency was ____
A: 1
B: 10
C: 100
D: 1000
What was the relative frequency?
Relative Frequency = Observed Frequency/Total Number of Trails
The relative frequency was _____
A: 0.15%
B: 1%
C: 1.5%
D: 15%
ITS 10
Then 1.5% thank this
Mr Savage used 3 gallons of paint to cover 1,350 square feet of wall space. At this rate, how much paint will be needed to cover 1,800 square feet
PLEASE HELP ME!!!!!!!!!
Which explains how to determine 40% of 50?