Answer:
Step-by-step explanation:
The number of ways to arrange the letters in "HEDGEHOG" is 8!/(2!3!). The exclamation mark (!) means factorial, which is the product of all positive integers up to that number. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we have two H's and three E's, so we have to divide the total number of arrangements by the number of arrangements of H's and the number of arrangements of E's to avoid overcounting.
The total number of arrangements of the eight letters is 8!:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
The number of arrangements of H's is 2!:
2! = 2 x 1 = 2
The number of arrangements of E's is 3!:
3! = 3 x 2 x 1 = 6
So the number of arrangements of the letters in "HEDGEHOG" that avoid overcounting is:
40320 / (2 x 6) = 40320 / 12 = 3360.
Therefore, there are 3360 ways to arrange the letters in "HEDGEHOG".
why is this graph not a function?
The graph is not a function because it fails the vertical line test
How to determine why it is a not functionFrom the question, we have the following parameters that can be used in our computation:
The graph (added as an attachment)
The given graph when represented as an equation, is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
This is so because they do not pass the vertical line test
Hence, the graph is not a function
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help please!!!!!!!!!!
Answer:
5x(8-1)=(5x10)-(5x4)
Which of the following is the midsegment for A ACE?
A. AC
B. BC
C. DB
D. CE
Explanation:
Points B and D are midpoints of segments AC and CE respectively. This is because of the tickmarks indicating congruent segment pieces (AB = BC and CD = DE)
Joining the midpoints together forms a midsegment. The midsegment is half as long as the side parallel to it. This means BD is half as long as AE. Flip things around to say that AE is twice as long as BD.
What is (−2) ( 3 4/7 ) ? step by step
Answer:-50/7 or -7.143
Step-by-step explanation:
you have to turn the 3 4/7 into an improper fraction by this:
3x7=21
21+4=25
which makes it 25/7
(25/7)x(-2) = -50/7 or -7.143
A rectangular garden 12 feet by 16 feet has a stone path along the perimeter with the same width, w. The area of the garden and path is 420 square feet.
The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420
This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:
(12+2w)(16+2w) = 420
Expanding and simplifying, we get:
4w² + 56w - 204 = 0
Dividing by 4, we get:
w² + 14w - 51 = 0
Factoring, we get:
(w+17)(w-3) = 0
Since the width of the path cannot be negative, the only valid solution is w = 3.
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Complete question is in the image attached
Please help me!! Quiz due 11:59pm - Match each scatterplot shown below with one of the four specified correlations
Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.
If x and y vary inversely, we can write their relationship then the function that models the inverse variation is y = 80/x.
What is Function?
In mathematics, a function is a rule or mapping that associates each input value (also called the independent variable) with a unique output value (also called the dependent variable). Functions are often represented using an equation, formula, or a graph, and are used to model real-world phenomena and solve problems in various fields such as science, engineering, economics, and more.
They can take different forms and have different properties, such as being linear, quadratic, exponential, periodic, or more complex. Some common notation used to represent functions includes f(x), y = f(x), or simply y.
If x and y vary inversely, we can write their relationship as:
x * y = k
where k is a constant of proportionality. We can use the given initial values of x and y to solve for k:
10 * 8 = k
k = 80
Therefore, the function that models the inverse variation is:
x * y = 80
or
y = 80/x
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ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
48ft²
Step-by-step explanation:
Visualize the trapezoid as consisting of a rectangle with two triangles on either side. To find its total area, find the area of each and add them up.
Note that the formula for the area of a square is (base*height) and the formula for the area of a triangle is (0.5*base*height). The bottom of the trapezoid is 15ft and the top is 9ft, which makes the combined bases of the two triangles 15-9=6ft, meaning each triangle's base is 3ft.
Area of left triangle = 0.5*3*4 = 6ft²
Area of square = 4*9 = 36ft²
Area of right triangle = 0.5*3*4 = 6ft²
Therefore the total area is: 6ft² + 36ft² + 6ft² = 48ft²
Answer:
48ft?
Visualize the trapezoid as consisting of
a rectangle with two triangles on either
side. To find its total area, find the area of
each and add them up.
SOMEONE PLEASE HELP...............
A plane that passes through three edges of a cube produces a triangular cross section as shown.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
A cross section of a cube that is a regular hexagon can only be obtained if the plane passes through the cube at a 60-degree angle with respect to its edges. If a plane is placed in this manner, it will intersect six of the cube's edges at their midpoints, producing a regular hexagon cross section.
What are True Statements about a Plane that Pass Through a Cube?The plane that passes through three edges of a cube to produce a regular hexagonal cross section must intersect the edges of the cube at 60 degree angles. This can be achieved if the plane is aligned with the diagonal of one of the faces of the cube, passing through the opposite vertices of the face.
This configuration of the plane will result in a regular hexagonal cross section of the cube as each vertex of the hexagon will correspond to one of the vertices of the cube, and each side of the hexagon will intersect two edges of the cube at 60 degree angles.
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Interpret the scatter plot based on the shape of the distribution.
Answer: Looks like a positive correlation with an outlier in the lower left.
Step-by-step explanation:
I need to know why the medians differ relative to the data set and the best measure of center?
Explanation:
In this case the median value is more representative of the 'center' of the population. The median is a better measure when the data set is skewed, has fat tails as compared to a normal didtribution, or has outliers. Otherwise you should use the arithmetic mean.
The smiths took out a $130,000, 30 year mortgage at an APR of 3.4%. The monthly payment was $576.53. What will be their total interest charges after 30 years?
The total interest charges after 30 years with an APR of 3.4 % is given by the equation A = $ 77,550.80
What is Annual Percentage Yield?The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.
Given data ,
Let the total interest charges after 30 years be represented as A
Now , the equation will be
The APR percentage = 3.4 %
The amount taken as loan = $ 130,000
The number of years = 30 years
The monthly payment = $ 576.53
The number of payments n = 30 x 12 = 360 payments
So , the total amount paid in 30 years = monthly payment x number of payments
Substituting the values in the equation , we get
The total amount paid in 30 years = 360 x 576.53
The total amount paid in 30 years = $ 207,550.80
Now , the total interest charges after 30 years A = total amount paid in 30 years - amount taken as loan
Substituting the values in the equation , we get
The total interest charges after 30 years A = $ 207,550.80 - $ 130,000
On simplifying the equation , we get
The total interest charges after 30 years A = $ 77,550.80
Hence , the interest charges after 30 years is $ 77,550.80
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LMNO is a parallelogram. If NM = x + 37 and OL = 5x + 9 find the value of x.
The value for the variable x in the parallelogram is equal to 7.
How to evaluate for the variable x in the parallelogramThe parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.
We shall evaluate for variable x as follows:
5x + 9 = x + 37
5x - x = 37 - 9 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7
Therefore, the value for the variable x in the parallelogram is equal to 7.
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The value of the variable x is 7
How to determine the valueIt is important to note that the opposite sides of a parallelogram are congruent or equal in length.
Then, for the parallelogram LMNO
NM is parallel to OL
Now, substitute the values, we get;
NM = OL
x + 37 = 5x + 9
collect like terms
x - 5x = 9 - 37
subtract the like terms
-4x = -28
Make 'x' the subject
x = 7
Hence, the value is 7
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9. Evan and Yong used this shape
, representing the unit fraction, to draw 1 whole.
Shania thinks both of them did it correctly. Do you agree with her? Explain your answer.
From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .
What is a unit fraction ?
A unit fraction is a fraction whose numerator (top number) is equal to 1. For example, 1/2, 1/3, 1/4, and so on are all unit fractions. Unit fractions are commonly used to represent parts of a whole, and they can also be used to perform certain mathematical operations such as addition and multiplication.
Given ,
Evan and Yong used the given shape representing the unit fraction, to draw 1 whole.
so,
from the given figure ,
in the evan diagram we can say it was mentioned correct, as we need to write down that in 1/3 where as in the Yong's case we can say that it does not come to 1/3 as a final resultant.
Therefore, From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .
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Out of a random sample of 300 voters, it was found that 172 voters are in favor of Issue #1.
Out of a total of 75,000 voters, how many do you predict will vote against Issue #1?
It is predicted that ___
voters are against Issue #1.
A- 30,000
B- 32,000
C- 43,000
D- 60,000
Answer:
B)32000
Step-by-step explanation:
Out of 300, 172 are in favor, and 142/300 is simplfieid as 43/75
43/75 is equal to 43,000/75000
Subtract 75000 by 43000
The difference is 32,000.
32,000 voters are against the Issue.
If possible factor. Find LCD. Multiply both sides by LCD. Solve show all work.
The lowest common denominator of the fraction is 6
What is LCDThe lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.
The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.
In the fraction given;
x / 3 + x / 2 = 20
The lowest common denominator is 6
Using 6, we can divide through each of the fraction.
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Find the equation of the line with slope 7 which goes through the point (−2,−9).
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ 7}(x-\stackrel{x_1}{(-2)}) \implies y +9= 7 (x +2) \\\\\\ y+9=7x+14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]
I need the modulus of: I 9+40i I
I = absolute value
The required modulus is 41 .
Complex Numbers:A real and imaginary number combo with the formula a + bi , where
a and b are real numbers, and
i is the "unit imaginary number" √(−1)
a and b may also have zero values.
We are aware that complex numbers are made up of both actual and fictitious numbers.
The imaginary part, y, is multiplied by I the square root of -1, and the real part, x.
Modulus of x+iy = [tex]\sqrt{x^2 +y^2}[/tex]
Here, 9 and 40 are substituted for x and y.
i.e. 9+40i
We square the coefficients, add them, and then find the square root to obtain the modulus.
|9+40i| =[tex]\sqrt{9^2 +40^2} =\sqrt{81+1600} =\sqrt{1681}[/tex][tex]=41[/tex]
By long division method we find that
|9+40i| =41
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The cost for shipping a package that weighs x pounds from Boise
to Los Angeles is shown at the right. How much more does
Shipping Central charge than Globe Delivery?
Shipping Central charges $0.51 more than Globe Delivery for any given weight of the package.
How to calculate this?The cost for shipping a package that weighs x pounds from Boise to Los Angeles is shown below.
Company Cost ($)
Shipping Central 3x+3.50
Globe Delivery 2x + 2.99
To determine the amount more Shipping Central charges than Globe Delivery, you can subtract the cost function for Globe Delivery from the cost function for Shipping Central.
The difference between the two cost functions is:
3x + 3.50 - (2x + 2.99) = x + 0.51 = $0.51 + x
This means that, for any given weight of the package, Shipping Central charges $0.51 more than Globe Delivery.
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The length of each side of an equilateral triangle having an area of square root of 243sq.cm is
Answer:
[tex]\textrm{Each side = 23.6893 cm}\\\\\\\textrm{Rounded to 2 decimal places = 23.69 cm}\\\\\textrm{Rounded to 1 decimal place = 23.7 cm}[/tex]
You can choose the level of precision as desired from the above
Step-by-step explanation:
The area of an equilateral triangle of side a
is
[tex]A = \dfrac{(a^2 \sqrt{3})}{4}[/tex]
We are given A = 243
Plugging in values we get
[tex]243 = \dfrac{a^2\sqrt{3}}{4}[/tex]
Switch sides so [tex]a^2[/tex] term is on the left
[tex]\dfrac{a^2\sqrt{3}}{4} = 243[/tex]
Multiply by 4 both sides to get rid of the denominator:
[tex]\dfrac{a^2\sqrt{3}}{4} \times 4 = 243 \times 4\\\\a^2\sqrt{3} = 972\\\\[/tex]
Divide by [tex]\sqrt{3}[/tex] both sides:
[tex]a^2 = \dfrac{972}{\sqrt{3}}\\\\a^2 = 561.18446\\\\a = \pm \sqrt{561.18446}\\\\[/tex]
Taking only positive square root:
[tex]a = \sqrt{561.18446}\\\\a = 23.6893\\\\[/tex]
Que es el crecimiento exponencial?
The concept of exponential growth function is discussed below.
What is exponential function?An exponential function is of the form -
y = A(B)ˣ
Given is to explain exponential growth.
Exponential growth of a quantity happens if the rate of instantaneous change is directly proportional to the quantity itself. The general exponential function is -
y = A(B)ˣ
More specifically -
[tex]$f(x)=a(1+r)^{x}[/tex]
where -
f(x) = exponential growth function
{a} = initial amount
{r} = growth rate
{x} = number of time intervals
Therefore, the concept of exponential growth function is discussed above.
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{Question in english -
What is exponential growth?}
You randomly draw once from this deck of cards.
4 6
1 6 9 4
8
1
1
2 6 7
What is the probability of not drawing an even number? Write your
answer as a fraction.
9
5
Answer:why not
Step-by-step explanation:that sa prrety nice ask
Answer: 5/8
Step-by-step explanation:
The probability of not drawing an even number can be calculated by finding the number of odd numbers in the deck and dividing by the total number of cards. In this deck, there are 5 odd numbers: 1, 1, 1, 7, and 9. The total number of cards is 8. Therefore, the probability of not drawing an even number is 5/8. The answer is written as a fraction as 5/8.
Grant is thinking of two numbers. He says one of the numbers is twice the other number and the sum of the number is 42. What are the numbers?
On solving the provided question, we can say that by linear equation If The Grant is thinking of two numbers, they are 13 and 26.
What is a linear equation?A linear equatiοn is one that has the form y = mx+b in algebra. B is the slοpe, and m is the y-intercept. It's usual to refer tο the previous clause as a "linear equation with twο variables" because y and x are variables. The twο-variable linear equations knοwn as bivariate linear equations.
There are several instances οf linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred tο as being linear when an equation has the fοrm y = mx+b, where m stands for the slοpe and b for the y-intercept. When an equatiοn has the formula y = mx+b, with m denοting the slope and b the y-intercept, it is referred tο as being linear.
x be the first number and y be the secοnd number:
x = 2y
x + y = 39
Plug x = 2y in the other equation:
2y + y = 39
3y = 39
y = 13
x = 26
If The Grant is thinking of two numbers, they are 13 and 26. He claims that the total of the two numbers is 39 and that one of the numbers is double the other.
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A survey is taken at a movie theater in Wayside. The first 100 people who entered the theater were asked about their favorite type of movie. What is true about this situation?
The population is the first 100 people at the theater, and the sample is the total number of people who go to the movie theater.
The population is the total number of people who go to the movie theater, and the sample is the first 100 people at the theater.
The population is the number of people who go to the movie theater, and the sample is the number of people in the town of Wayside.
The population is the number of people in the town of Wayside, and the sample is the number of people who go to the movie theater.
What is true about the population and sample of the survey is that;'
The population is the total number of people who go to the movie theater, and the sample is the first 100 people at the theater.
How to Identify the Population and sample of the data?In statistics, the population is defined as the entire group that you want to draw conclusions about. However, the sample is defined as the specific group that you will collect data from. The size of the sample is always less than the total size of the population. In research, a population doesn't always refer to people.
Now, we are told that a survey is taken at a movie theater in Wayside. The first 100 people who entered the theater were asked about their favorite type of movie.
Thus, the sample will be 100 people surveyed as they are part of the entire people at the movie theater.
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PT=y, TR=3x + 1, QT=3y, TS = 4x + 13
find x and y
The values of x and y for the parallelogram PQRS are respectively, 2 & 7
What are the properties of parallelogram ?Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.
Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.
Given that,
The parallelogram PQRS has diagonals PR and SQ that intersects at T,
T is the midpoint of PR and T is the midpoint of SQ
If T is the midpoint of PR, then PT = TR
Given PT = y and TR = 3x+1
y = 3x+ 1 _____(i)
Also, If T is the midpoint of SQ, then ST = TQ
Given QT=3y and TS=4x+13
3y = 4x+ 13 ____(ii)
Substitute equation 1 into 2;
3y = 4x+ 13
3(3x+1) = 4x+ 13
open the parenthesis
9x+3 = 4x+13
club like terms
9x-4x = 13-3
5x = 10
x = 10/5
x = 2
Substitute x = 2 into equation 1
From 1; y = 3x+1
y = 3(2)+1
y = 6+1
y = 7
Hence, the values are x = 2 and y = 7
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The complete questions :
Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13
In ΔGHI, i = 800 cm, m m∠G=26° and m m∠H=122°. Find the length of h, to the nearest 10th of a centimeter.
Answer:
For the nearest 10th of a centimeter, the value of h is 460 cm
Step-by-step explanation:
To find length of h we can use Law of Sines . The Law states that for a triangle with sides a, b, and c and angles A, B, and C opposite to those sides, the following equation holds:
a/sin A = b/sin B = c/sin C
In ΔGHI, let h be the length of the side opposite angle H, and let i be the length of the side opposite angle I.
Now:
h/sin 122° = i/sin 26°
We can find h by cross multiplying:
h = i * sin 122° / sin 26°
=459.9
Here,
h = 459.9 cm
By taking approximation we get 460 cm
Answer:
This answer is actually 1280.3
Step-by-step explanation:
Select the correct answer.
of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit
to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
OA
OC
OD.
Answer as a fraction
Answer:
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
Step-by-step explanation:
Let the number of fit men is x.
Now,
we know
x = 12% of 200 men
x = [tex]\frac{12}{100}[/tex] ×200
x = 0.12 × 200
= 24 men.
Given,
The 60 people are fit to climb the Mount Shasta ,24 of them are men,
so there must be
60 - 24 = 36 women who are fit to climb the mountain.
The probability of a person picked at random from the group is a male or is fit to climb Mount Shasta is the sum total of the probability of picking a fit male and the probability of picking a fit female is,
P(male or fit) = P(male and fit) + P(female and fit)
P(male or fit) = P(male) × P(fit | male) + P(female) × P(fit | female)
P(male or fit) = ([tex]\frac{200}{500}[/tex]) ×([tex]\frac{24}{200}[/tex]) + ([tex]\frac{300}{500}[/tex]) × ([tex]\frac{36}{300}[/tex])
=.4 × .12 + .6 × .12
= 0.048 + 0.072
=.12
So,
P(male or fit) ≈ 0.12
As a fraction, the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 12/100.
help me with this please i need help because i dont get it <33
Answer:
C
Step-by-step explanation:
consider the coordinates of the same points on both figures
top left vertex of figure P (- 8, 8 )
top left vertex of figure Q (- 4, 4 )
note that both coordinates from Q are half the coordinates of P
then to obtain Q from P multiply each coordinate by [tex]\frac{1}{2}[/tex] , that is
(x, y ) → ([tex]\frac{1}{2}[/tex] x , [tex]\frac{1}{2}[/tex] y )
Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Answer:
(a) 24%
Step-by-step explanation:
You want the percentage of people in the Decades slice of a circle graph if it represents 96 people. The other slices represent 128, 72, 52, 24, and 28 people.
PercentThe fraction in the second category is the ratio of the number in that category to the total number. The percent is the fraction multiplied by 100%.
96/(128 +96 +72 +52 +24 +28) × 100% = 96/400 × 100% = 24%
The Decades slice of the circle would be 24%, choice A.
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An angler catches a fish that weighs 20 kg. The fish’s bones make up approximately 10% of the fish’s total weight. What is the weight of the fish meat, not including the bones, in pounds? Round to the nearest tenth if necessary.
44.0
40.0
39.6
4.4
4.0
Answer: approximately 40lbs.
Step-by-step explanation:
First, you multiply 20kg to 10%, or 0.10.
20(0.10)=2kg
Then you minus the 2kg from the initial weight
20kg
-2kg
18kg
1 kg is approximately 2.20462262 lbs., so you need to convert your kg to lbs
18kg * 2.20462262 lb/kg = 39.68320716 which is rounded up to approximately 40lbs
Hope that helps!
