The number of unique permutations that may be made from all of the letters in each word 210.
What is permutations?The number of alternative arrangements of such an object in different orders or sequences is referred to as its permutation. These are typically computed using factorials, as denoted by the symbol. Only natural numbers are utilized in factorials.
Assume we wish to find the number of various permutations of n objects, where p items are one type, q items are another, r items are yet another, and so on.
According to the given data:For the word 'UNUSUAL' there are 7 letters. Then there are 7! possibilities.
We have to divide this by the number of possibilities where letters would replace the same letters.
there are letter U repeated 3 time so 3!
= [tex]\frac{7!}{3!}[/tex]
= 210
the number of unique permutations that may be made from all of the letters in each word 210.
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On a plane trip to Hawaii, the baggage weight projected was 2,182 1/4 lbs. The actual weight of all bags totaled 2,095 1/3 lbs. By how much was the projected weight overstated?
The projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.
What is an expression?
Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that : the baggage weight projected was 2,182 1/4 lbs and the actual weight of all bags totaled 2,095 1/3 lbs.
Now, to find out by how much was the projected weight overstated we subtract weight projected with actual weight of baggage :
weight overstated = weight projected - actual weight
weight overstated = 2,182 1/4 lbs - 2,095 1/3 lbs
weight overstated = 87 - 1/12 lbs
weight overstated = 86(11/12) lbs
Therefore, the projected weight of baggage overstated on a plane trip to Hawaii is 86(11/12) lbs.
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Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
The equation in slope-intercept form is y = x - 6.
What is in slope-intercept form?
Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line p is
y = 8x + 2
Comparing with the slope intercept form, slope = 8
If two lines are parallel, it means that they have the same slope. Therefore, the slope of line q passing through ( -1 , -2 ) is 8
To determine the y intercept, we would substitute m = 8, x = - 1 and
y = -2 into y = mx + c. It becomes
-2 = 8 × - 1 + c
-2 = - 8 + c
c = - 8 + 2 = -6
The equation becomes
y = x - 6
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Babies are weighed at birth to monitor their progress. Martin weighs 0.6 kg less than Daniel who weighs 0.4 kg less than Kevin. Martin weighs x kilograms and the total weight of the three boys is 10.3 kg. Form an equation in x, solve it and state the weight of each baby
The weight of each baby based on the information will be:
Martin = 2.9 kg
Daniel = 3.5kg
Kevin = 3.9 kg
How to illustrate the information?Martin = x
Daniel = x + 0.6
Kevin = x + 1
Total weight = 10.3 kg
Therefore, this will be solved as:
x + x + 0.6 + x + 1 = 10.3
3x + 1.6 = 10.3
3x = 10.3 - 1.6
3x = 8.7
Divide
x = 8.7 / 4
x = 2.9
Therefore, the weights will be:
Martin = x = 2.9 kg
Daniel = x + 0.6 = 2.9 + 0.6 = 3.5kg
Kevin = x + 1 = 2.9 + 1 = 3.9 kg
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Simple Math Range and domain help Part 4
The distance in feet that a ball rolls down an incline is modeled by s(t) = −2t^2 − 2 , where t is seconds after the ball begins rolling. Find its instantaneous velocity at t = 4 seconds.
v(4) = ____
Answer:
-16
Step-by-step explanation:
pretty sure its the right answer, we did this a week ago in class so it may be wrong.
so first u gotta find the derivative of s(t) to get the vel equation. the derivative of s(t):
s(t)'= -4t, which is the vel equation
s(t)'=v(t)
v(4)=-4(4)
which equals -16
The instantaneous velocity of the ball at t = 4 seconds is -16 feet per second.
To find the instantaneous velocity of the ball at t = 4 seconds, we need to calculate the derivative of the given function s(t) with respect to t, and then evaluate it at t = 4.
Given that s(t) = -2t² - 2, we can find the velocity function v(t) by taking the derivative of s(t):
v(t) = d/dt (-2t² - 2)
v(t) = -4t
Now, we can find the instantaneous velocity at t = 4 by substituting t = 4 into the velocity function:
v(4) = -4(4)
v(4) = -16
This means that at that specific moment, the ball is moving downward with a velocity of 16 feet per second. The negative sign indicates the direction of motion.
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For each function, find f(-2), f(0), and f(3)
The values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
How to Find the value of a Function?Given the function, f(x) = 3x, to find the values of f(-2), f(0), and f(3), solve as shown below.
Find f(-2) by substituting x = -2 into the function, f(x) = 3x:
f(-2) = 3(-2)
f(-2) = -6
The value of f(-2) for the given function is: -6
Find f(0) by substituting x = 0 into the function, f(x) = 3x:
f(0) = 3(0)
f(0) = 0
The value of f(0) for the given function is: 0
Find f(3) by substituting x = 3 into the function, f(x) = 3x:
f(3) = 3(3)
f(3) = 9
The value of f(3) for the given function is: 9
Thus, the values of the functions are:
f(-2) = -6
f(0) = 0
f(3) = 9
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ANSWER PLEASEEEEEEEEEEEEEEEEEE
Answer: x∈[-4,3) y∈(-5,5)
Step-by-step explanation:
[tex]Domain:x\in[-4,3)\\Range\ of\ y:\ y\in(-5,5)[/tex]
And please show the work plsss help
Answer:
7
Step-by-step explanation:
3 goes into 21 7 times leaving no remainder which means: 3 x 7 = 21
Trymaine is 7 years older than Sunny. In 3 years the sum of their ages will be 39. How old is Trymaine now?
Trymaine is 20 years old and Sunny is 13 years old.
GIven, Trymaine is 7 years older than Sunny.
In 3 years the sum of their ages will be 39.
Let the age of Trymaine be a and age of Sunny be b.
we have,
a = b ₊ 7
a ₊ 3 ₊ b ₊ 3 = 39
a ₊ b = 39 ₋ 6
a ₊ b = 33 .... eq(2)
therefore a = b ₊ 7
a ₋ b = 7 ....eq(1)
solve eq (1) and eq(2)
2a = 40
a = 20
and a ₋ b = 7
20 ₋ b = 7
₋b = 7 ₋ 20
₋b = ₋13
b = 13
hence Trymaine is 20 years old , whereas Sunny is 13 years old.
hence we get the ages of Trymaine and Sunny as 20 and 13 respectively.
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- Six inches more than 3 times the height, h
Answer:
3h+6 inches
Step-by-step explanation:
The bills for the month of July have come in. The electric bill is $276.93, the water bill is $69.24, the cell phone bill is $102.56, and the cable bill is $73.69. Rounding each bill to the nearest dollar, estimate what the total household bills are for the month of July.
Answer:
Step-by-step explanation:
Round each number individually,
276.93 Rounded up -> 277
69.24 Rounded Down -> 69
102.56 Rounded up -> 103
73.69 Rounded up -> 74
Total = 523
Anything 0.50 to 0.99 gets rounded up
Anything 0.01 to 0.49 gets rounded down
When to the nearest dollar
State of the following Conjecture is true or false
Given X is not a negative number
Conjecture X is a positive number
True or false?
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
Given X is not a negative number and conjecture X is a positive number.
What is a conjecture?A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases.
Given X is not a negative number
Conjecture X is a positive number
If X is 0, which is neither positive nor negative.
So, the statement is false.
The given conjecture X is a positive number is not always correct. Therefore, the given conjecture is false.
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Suppose a trucking company's costs for hauling consumer goods varies jointly with the number of trucks running and the hours each truck is used. When the company runs full fleet of 16 trucks at 8 hours each, the cost is $20,500. In an effort to cut costs, the owner of the trucking company wants to know what the cost would be when running only half of the fleet for 6 hours each?
The cost of running only half of the fleet for 6 hours each would be $7687.2 .
The company runs full fleet of 16 trucks at 8 hours each.
Which means total hours of running on full fleet = 128 Hours
So, The cost of running 128 hours = $20,500
Then, cost of running 1 hour = $20,500 ÷ 128
= $160.15
Now we will determine the cost of running trucks on half fleet for 6 hours each.
As we already know that
Full fleet = 16 Trucks
Then, Half fleet = 8 Trucks
Total hours of trucks running on half fleet = 8 × 6
= 48
The cost of running 48 hours = 48 × $160.15
= $7687.2
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Help
Please help
I appreciate it
Step-by-step explanation:
f(g(x)) means g(x) is embedded in f(x) as the argument or input value for f(x).
therefore,
f(g)x)) = 4(x² - 1) - 7 = 4x² - 4 - 7 = 4x² - 11
c. is the right answer
g(f(x)) is now the other way around. now f(x) is the only value for g(x) :
g(f(x)) = (4x - 7)² - 1 = 16x² - 56x + 49 - 1 = 16x² - 56x + 48
a. is the right answer
ce
Part 1 of 2
Shureka Washburn has scores of 61, 77, 65, and 81 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam counts as two tests
b. Explain the meaning of the answer to part (a).
a. The solution set is {x (Type an inequality.)
The value of x is 74
Surekha Washburn has scores of 61, 65, 77, and 81 on her algebra tests.
a. Use an inequality to find the scores she must make on the final exam to pass the course with an average of 72 or higher, given that the final exam
counts as two tests.
let score on final exam is x
two test are 2x
then we get the value of x
[tex]\frac{61 + 65 + 77 + 81 + 2x}{6}[/tex] = 72
[tex]\frac{284 + 2x}{6}[/tex] = 72
284 + 2x =432
2x = 432 - 284
x = [tex]\frac{148}{2}[/tex]
x = 74
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Average Formula in Maths
The formula to find the average of given numbers or values is very easy. We just have to add all the numbers and then divide the result by the number of values given. Hence, the average formula in Maths is given as follows:
Average = Sum of Values/ Number of values
Suppose, we have given with n number of values such as x1, x2, x3 ,….., x n. The average or the mean of the given data will be equal to:
Average = (x1+x2+x3+…+x n)/n
How to Calculate Average?
We can easily calculate the average for a given set of values. We just have to add all the values and divide the outcome by the number of given values.
Average can be calculated using three simple steps. They are:
Step 1: Sum of Numbers:
The first step in finding the average of numbers is to find the sum of all the given numbers.
Step 2: Number of Observations:
Next, we have to count how many numbers are in the given dataset.
Step 3: Average Calculation:
The final step in calculating the average is to divide the sum by the number of observations.
Now, let us consider an example to calculate the average.
If there are a group of numbers say, 20, 21, 23, 22, 21, 20, 23. Then find the average of these values.
By average formula, we know,
Average = (Sum of values)/No. of values
= (20+21+23+22+21+20+23)/7
= 150/7
=21.42
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What is -10= -10 + 7m showing work?
Answer:
m = 0
Step-by-step explanation:
- 10 = - 10 + 7m ( add 10 to both sides )
0 = 7m ( divide both sides by 7 )
0 = m
Find the constant of variation k for the direct variation. 4x = –6y
The constant of variation k for the direct variation in 4x = –6y will be 1.5.
What is direct variation?It should be noted that a direct variation simply means the mathematical relationship that exists between two variables which can be expressed by an equation such that a variable is equal to another one.
Therefore, the constant of variation k for the direct variation in 4x = –6y will be:
4x = –6y
Divide through by 4
4x / 4 = -6y / 4
x = -1.5y
Therefore, the constant of variation is 1.5.
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will mark brainliest 15 points
Based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex]
What is the Product Rule of Exponents?The product rule of exponents says that if two quantities that are multiplied together have the same base, we will add their exponents together to get the product.
Given the following:
a^4 * a^6
Applying the product rule of exponents, we will have:
a^4 * a^6 = a[tex]^{(4 + 6)}[/tex]
a^4 * a^6 = [tex]a^{10}[/tex].
Therefore, based on the product rule of exponents, a^4 * a^6 = [tex]a^{10}[/tex].
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Identify the coefficient of 6x3
Answer:
you to get my number 3 whole thing together
PLEASE HELP
A weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean. Using Bernoulli's principle, what do we know about the ocean and the coast?
A. The air over the ocean has more volume than the air over the coast
B. The air over the ocean has more mass than the air over the coast
C. There is less air pressure over the ocean than over the coast
D. The air over the ocean has less mass than the air over the coast
E. There is more air pressure over the ocean than over the coast
F. The air over the ocean has less volume than the air over the coast
Using Bernoulli's principle, the thing that we know about the ocean and the coast is that E. There is more air pressure over the ocean than over the coast.
What is Bernoulli's principle?According to Bernoulli's principle, which governs fluid dynamics, a fluid's speed increases concurrently with a reduction in pressure or potential energy.
The Bernoulli principle establishes a connection between a fluid's elevation and speed and its pressure. In water, air, or any other fluid with a very low viscosity, these characteristics can be approximated using Bernoulli's equation.
Since the weatherwoman is on the news explaining that there will be high winds on the central coast coming in from the ocean, it implies that there is more air pressure over the ocean than over the coast.
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what is the quotation of -80 and -16
Based on the given task content, the quotient of - 80 and - 16 is 5
What is quotient?Quotient refers to the number resulting from the division of one number by another. Such as: the quotient of 12 divided by 4 is 3.
The divisor
The number or expression that another is to be divided by.
In "42 ÷ 3" the divisor is the 3.
The dividend
These refers to numbers or expressions that is to be divided by another.
In "42 ÷ 3" the dividend is the 42.
Quotient of -80 and -16= - 80 / - 16
= 5
Therefore, the quotient of -80 and -16 is 5
Complete question:
what is the quotient of -80 and -16
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Can I get help with this math problem lol
Answer:
m = 2
Step-by-step explanation:
Find LCM.
[tex]7,\:14\\14=7\cdot \:2\\=2\cdot \:7\\=7\cdot \:2\\=14\\[/tex]
Multiply
[tex]\frac{2m}{7}\cdot \:14+\frac{3m}{14}\cdot \:14=1\cdot \:14[/tex]
Simplify(AA)
[tex]\frac{2m}{7}\cdot \:14\\=\frac{2m\cdot \:14}{7}\\=\frac{28m}{7}\\=4m[/tex]
Simplify(AB)
[tex]\frac{3m}{14}\cdot \:14\\=\frac{3m\cdot \:14}{14}\\=3m[/tex]
Simplify(AC)
[tex]1\cdot \:14\\= 14[/tex]
Divide
[tex]=7m = 14\\\frac{7m}{7}=\boxed{\frac{14}{7}}\\= 2[/tex]
A scientist needs 10 liters of a 20% acid solution for an-experiment, but she has only a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters of the 5% and the 40% solutions should she mix to get the solution she needs?
The liters of the 5% and the 40% solutions is
x= 4.3L
This is further explained below.
How many liters of the 5% and the 40% solutions should she mix to get the solution she needs?You have been tasked with creating a solution with a concentration of 20% in a volume of 10 liters by combining solutions of 5% and 40%. It seems as if there may be more than one response to this question. If you assume that the combined volume of the 5% and 40% solutions equals 10L, then you may calculate the required volume of solution. The formula ought to go as follows:
10 L= 40% solution volume+ 5% solution volume
10 L= x + 5% solution volume
5% solution volume= 10l-x
In conclusion, The formula for calculating volume would look like this then:
Volume 0.2*concentration 0.2= volume 0.4*concentration 0.4 + volume 0.05*concentration 0.05
10 * 0.2= x *0.4 + (10- x) *0.05
10l * 0.20= x * 35% + 10*0.05
x *35 = 10l * 20 - 10 *5= 10 *15
x = 10l *15/35
x= 4.28 L
x= 4.3L
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15. Write a two-column proof.
GIVEN: m/GFI = 128°
PROVE: m/EFI = 40°
According to the given a two-column proof bellow the EFI = 40°
What is two-column proof?A two-column geometric proof is made up of a set of claims and the reasons why we know they are true. The statements are stated in the left column, while the reasons for making them are mentioned with in right column.
According to the given data:Given:
GFI = 128°where
9x - 2 = 128°
EFI = 40° And
4x = 40
So,
GFI = 128°where
9x - 2 + 4x = 128°
13x = 130
x = 10
putting the value x = 10 in EFI = 40° And 4x = 40:
So,
4x = 40
4(10) = 40
40 = 40
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How do you
Work this equation 5/16 + (-7/16)=
Answer:
-1/8
Step-by-step explanation:
So to start you already have the denominator equal, which helps a lot. So you do whatever operation is on top which in this case would be 5 + -7. Which you end up with -2/16. Then you simplify and end up with -1/8. Hope this helps. Have a great night. :)
A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.
Calculate the centripetal acceleration of the child
Calculate the net horizontal force exerted on the child
a: The centripetal acceleration of the child = 1.60 m/s².
b: The net horizontal force exerted on the child = 40N.
What is defined as the centripetal acceleration?The acceleration of such a body traveling in a circular path is known as centripetal acceleration. Since velocity is a vector quantity (it has a magnitude, a speed, as well as a direction), when a body moves on a circular path, its direction changes and consequently its velocity changes, resulting in acceleration.The parameters provided;
merry-go-round radius, r = 1.70 m child's speed, v = 1.65 m/s child's mass = 25 kg.Part a: The child's centripetal acceleration is calculated as follows:
a = v²/r
Put the values;
a = 1.65²/1.7
a = 1.60 m/s²
Thus, the child's centripetal acceleration is 1.60 m/s².
Part b: The child's net horizontal force is calculated as follows:
F = ma
F = 25×1.60
F = 40 N
Thus, child's net horizontal force is 40 N.
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The complete question is-
A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.65 m/s.
a. Calculate the centripetal acceleration of the child
b. Calculate the net horizontal force exerted on the child
Mass of child = 25 kg.
7.2 HELPPPPPPP
1.Find the missing length indicated. Leave your answer in simplest radical form.
2.Find the missing length indicated. Leave your answer in simplest radical form.
3.Find the missing length indicated. Leave your answer in simplest radical form.
4.Find the missing length indicated. Leave your answer in simplest radical form.
In simplest radical form, the values are,
(1) The missing length = 48
(2) The missing length = 48
(3) The missing length = 140
(4) The missing length = 25
(1) : In triangle,
ΔADB ≅ ΔABC
∠A = ∠A
∠ABC = ∠ABD
So, ΔADB ≅ ΔABC
AD/AB = AB/AC
AD = 64 AND AC = 100 substitute in this equation,
64/AB = AB/100
AB * AB = 64*100
[tex]AB^{2}[/tex] = 6400
AB = [tex]\sqrt{6400}[/tex]
AB = 80
Because,
∠ADB = 90°
So,
[tex]AD^{2} +BD^{2} =AB^{2}[/tex]
[tex]BD^{2} = AB^{2} -AD^{2}[/tex]
BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]
BD = [tex]\sqrt{6400-4096}[/tex]
BD = [tex]\sqrt{2304}[/tex]
BD = 48
Therefore,
The missing length is BD = 48
(2) : In triangle,
ΔADB ≅ ΔABC
∠A = ∠A
∠ABC = ∠ABD
So, ΔADB ≅ ΔABC
AD/AB = AB/AC
AD = 64 AND AC = 100 substitute in this equation,
64/AB = AB/100
AB * AB = 64*100
[tex]AB^{2}[/tex] = 6400
AB = [tex]\sqrt{6400}[/tex]
AB = 80
Because,
∠ADB = 90°
So,
[tex]AD^{2} +BD^{2} =AB^{2}[/tex]
[tex]BD^{2} = AB^{2} -AD^{2}[/tex]
BD = [tex]\sqrt{BD^{2}-AD^{2} }[/tex]
BD = [tex]\sqrt{6400-4096}[/tex]
BD = [tex]\sqrt{2304}[/tex]
BD = 48
Therefore,
The missing length is BD = 48
(3): In triangle BDC
tanθ = BC/DC
tanθ = 60/36
θ = [tex]tan^{-1}[/tex](60/36)
θ = [tex]tan^{-1}[/tex](1.66)
θ = 53.16
And,
[tex]BD^{2} =BC^{2} +CD^{2}[/tex]
[tex](BD)^{2}[/tex] = 60*60 + 36*36
[tex](BD)^{2}[/tex] = 3600+1296
[tex](BD)^{2}[/tex] = 4896
BD = 69.97
In big triangle, ABC
cosθ = BC/AC
cosθ = 60/(36+u)
cos69.97 = 60/(36+u)
0.342 = 60/(36+u)
36+u = 60/0.342
36+u = 195.4
u = 195.4 - 36
u = 139.4
u = 140
Therefore,
The maximum length u = 140
(4) : In ΔABC and ΔDAB
∠B = ∠B (Common)
∠A = ∠D = 90°
Hence, ΔBAC ≅ ΔBDA
AB/BC = BD/AB
15/x = 9/15
x = (15*15)/9
x = 225/9
x = 25
Therefore,
The missing length x = 25
Hence,
(1) The missing length = 48
(2) The missing length = 48
(3) The missing length = 140
(4) The missing length = 25
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This is confusing me I'd appreciate some help
Answer:
d equals to -3, so in every expression we substitute d with -3.
2d(-3d)
2(-3) x (-3x-3)
-6 x 9 = -54
12d - 28
12(-3) - 28
-36-28 = -64
-3d
-3x(-3) = 9
-5d-8
-5x(-3)-8
15-8 = 7
8d+14
8x(-3) + 14
-24 + 14 = -10
hope it helps.
Solve this quadratic equation using the quadratic formula.
x² + 8x - 5
Ox=-4± √21
Oz = -4 ± √11
Oz=5±2√2
Or = 8+2√/21
According to the given statement
Quadratic equation for x2+8x−5=0 is x=-4± √21
What is Quadratic equation?Second-degree algebraic expressions of the type ax2 + bx + c = 0 are known as quadratic equations.
There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.
According to the given value;
For this equation: a=1, b=8, c=-5
1x2+8x+−5=0
Step 1: Use quadratic formula with a=1, b=8, c=-5.
x=
−b±√b2−4ac
2a
x=
−(8)±√(8)2−4(1)(−5)
2(1)
x=
−8±√84
2
x=−4+√21 or x=−4−√21
Hence,quadratic equation for x2+8x−5=0 is x=-4± √21
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: The table below shows the cost of buying and shipping boxes of shirts. The variable, b, represents the number of boxes of shirts the client ordered. Which expression best represents the cost of the shirts plus shipping?
The expression that best represents the cost of shirts plus shipping is 20b + 5.
What is the expression that represents the cost of shirts plus shipping?An expression is a statement that is made up of at least two numbers or variables and at least one mathematical operation. An expression usually does not have an equal to sign.
The first step is to determine the cost of a shirt and the cost of shipping.
a + b = 25 equation 1
a + 2b = 45 equation 2
Where:
a = cost of shipping
Subtract equation 1 from equation 2
b = 20
a = 25 - 20
a = 5
Thus, the cost of one shirt is 20. The cost of shipping is 5. The cost of shirts increases with the number of shirts bought while the cost of shipping remains constant.
The expression is: 20b + 5
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