Sample mean = 3.43
sample standard deviation = 2.07
Explanation:
Given: 2, 3, 2, 5, 7, 1, 4
Total numbers = 7
1) Sample mean is calculated by finding the average of the data set
[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]2) We have sample standard deviation and population standard deviation.
SInce the question asked for sample mean, we will be calculating sample standard deviation.
Standard deviation is calculated as:
[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]
Instructions: Find the area of the circle. Round your answer to the nearest tenth.
Given:
The Radius of the circle: 2.5 inch
To find:
The area of the circle
Step-by-step solution:
We know that:
The Area of the circle = π(r)²
The Area of the circle = π(2.5)²
The Area of the circle = 3.14 × (2.5)²
The Area of the circle =
How many degrees was ABCDE rotated? (submit your answer as a number)
If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)
Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,
For the original figure, the coordinate is (1, 3)
For the ratated figure, the coordinate of A' is (- 1, - 3)
This corresponds to what was we stated earlier
Thus, it was rotated 180 degrees in the counterclockwise direction
Enzo counted the number of sunny days each of his favorite towns had in the year 2013 and graphed theresults.Light LandBright VillagePlaceShiny TownSun City -050100150200250300Number of Sunny Days
From the graph, we can see that the town that had most sunny days was Shiny Twon.
So, between this town and Sun City, we have Bright Viallge, that had a number of sunny days between Sun City and Shiny Town.
So the answer is Bright Village.
Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
We will have the following:
[tex]\sin (2\theta)=-\frac{1}{2}\Rightarrow2\theta=2\pi n_1+\frac{7\pi}{6}[/tex][tex]\Rightarrow\theta=\pi n_1+\frac{7\pi}{12}[/tex]Now, we will solve for the following:
[tex]\Rightarrow\pi n_1+\frac{7\pi}{12}\le2\pi\Rightarrow\pi n_1\le\frac{17\pi}{12}[/tex][tex]\Rightarrow n_1\le\frac{17}{12}[/tex]This value in degrees is:
[tex]\frac{17}{12}\text{radians}=81.169\text{degrees}[/tex]So, the solution is located in the interval:
[tex]\lbrack0,81\rbrack[/tex]4. Find the slope of the two points: (-3,-2) & (5, -8)
Enter Numerical value ONLY. NO Decimals
Try Again!
5. Find the slope of the two points: (6, 10) and (-2, 10) *
Enter Numerical value ONLY. NO Decimals
Your answer
This is a required question
Answer:
The slope of (-3, -2) and (5, -8) is -3/4
The slope of (6, 10) and (-2, 10 ) is 0
Step-by-step explanation:
[tex]\frac{-8 - (-2)}{5 - (-3)} = \frac{-6}{8} = -\frac{3}{4}[/tex]
and
[tex]\frac{10 - 10}{-2 - 6} = \frac{0}{-8} = 0[/tex]
the variables x and y vary inversely. use x=-2 and y=3 to write and equation relating x and y. then find y when x=-1
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define the variation that occurs in the Question.
Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
STEP 2: Interpret the statements in the question tab
[tex]\begin{gathered} x\text{ varies inversely as y} \\ x\propto\frac{1}{y} \end{gathered}[/tex]STEP 3: Get the constant of variation
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \text{Introducing the constant, we have;} \\ x=k\times\frac{1}{y},x=\frac{k}{y} \\ By\text{ cross multiplication,} \\ x=ky \\ \text{Divide both sides by y} \\ \frac{x}{y}=k \end{gathered}[/tex]STEP 4: Use the given values to get the equation relating x and y
[tex]\begin{gathered} \frac{x}{y}=k,x=-2,y=3 \\ By\text{ substitution,} \\ \frac{-2}{3}=k \\ k=\frac{-2}{3} \\ \\ \text{The equation relating x and y will be:} \\ x=-\frac{2}{3}y \\ x=\frac{-2y}{3} \end{gathered}[/tex]Hence, the equation relating x and y is:
[tex]x=\frac{-2y}{3}[/tex]STEP 5: Find y when x=-1
[tex]\begin{gathered} x=ky \\ \text{Divide both sides by k to get the value of y} \\ y=\frac{x}{k} \\ x=-1,k=-\frac{2}{3} \\ By\text{ substitution,} \\ y=\frac{-1}{\frac{-2}{3}} \\ y=-1\div-\frac{2}{3} \\ y=-1\times\frac{-3}{2}=\frac{-1\times-3}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Hence, the value of y when x=-1 is 3/2
A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer: 75
Step-by-step explanation:
So first, we need to divide 125 by 5
125÷5=25
Next we need to multiply 3 by 25.
25×3=75
The printer can print 75 pages in 125 seconds.
Please provide deep explanation, so i can understand and learn. Thank you
Assume the height of the box is x.
5 reams of paper have 5 x 500 = 2500 sheets of paper.
This means that each sheet of paper has a thickness of x/2500.
Two sheets of paper have a thickness of 2 times x/2500.
Simplifying the fraction:
[tex]2\cdot\frac{x}{2500}=\frac{x}{1250}[/tex]Two sheets of paper have a thickness of 1/1250th of the height of the box.
Assume the height is x = 20 cm, then two sheets are 20/1250 = 0.016 cm thick.
11) -3(1 + 6r) = 14 - r 12) 660+6)-5=1+6v 13) -4k + 2(5k - 6) = -3k - 39 14) -16 + 5n=-71-
-3(1+6r) = 14 -r
-3-18r = 14 - r
-3-14 = -r +18r
-17 = 17r
17r/17 = -17/17
r = -1
Frankenstein was in charge of bringing punch to the Halloween party. He brought 36 liters of his famous eyeball punch. How many gallons was this?
Answer: 9.5112
Step-by-step explanation:
There are 0.2642 gallons in a liter. So, in 36 liters, there are [tex]36(0.2642)=9.5112 \text{ gal }[/tex]
In an experiment, the probability that event B occurs is , and the probability that event A occurs given that event B occurs is 3 7) What is the probability that events A and B both occur? Simplify any fractions.
We have to use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A|B) is the probability that A occurs given that B occurs, P(B) is the probability that B occurs, and P(A∩B) is the probability that both events A and B occur.
In this case, since we are asked for the probability that events A and B both occur, we need to solve the equation for P(A∩B):
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]And the information we have about the problem is:
[tex]\begin{gathered} P(A|B)=\frac{3}{7} \\ P(B)=\frac{2}{9} \end{gathered}[/tex]We substitute this into the formula for P(A∩B):
[tex]P\mleft(A\cap B\mright)=\frac{3}{7}\cdot\frac{2}{9}[/tex]Solving the multiplication of fractions:
[tex]\begin{gathered} P\mleft(A\cap B\mright)=\frac{3\cdot2}{7\cdot9} \\ P\mleft(A\cap B\mright)=\frac{6}{63} \end{gathered}[/tex]And finally, we simplify the fraction by dividing both numbers in the fraction by 3:
[tex]P\mleft(A\cap B\mright)=\frac{2}{21}[/tex]Answer: 2/21
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
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Identify the domain, vertical asymptotes and horizontal asymptotes of the following rational function: f(x)= \frac{3x-4}{x^3-16x} Domain is all real numbers except x\neq Answer , Answer and AnswerVertical asymptote at x= Answer , Answer and AnswerHorizontal asymptote at y= Answer
Answer
Domain is all real numbers except x ≠ 0, -4, and 4
Vertical asymptote at x = 0, -4, and 4
Explanation
Given function:
[tex]f(x)=\frac{3x-4}{x^3-16x}[/tex]Note: The domain of a function is a set of input or argument values for which the function is real and defined.
For the function to be real; the denominator must not be equal zero, i.e.
[tex]\begin{gathered} x^3-16x\ne0 \\ x(x^2-16)\ne0 \\ x(x-4)(x+4)\ne0 \\ x\ne0,x-4\ne0,\text{ and }x+4\ne0 \\ \therefore x\ne0,x\ne4,\text{ and }x\ne-4 \end{gathered}[/tex]Hence, the domain is all real numbers except x ≠ 0, -4, and 4.
Note: A vertical asymptote with a rational function occurs when there is division by zero.
Hence, the vertical asymptote at x = 0, -4, and 4
What is f(2) - f(0) answer choices:A) 1B) 2C) 3D) 4
The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:
[tex]\begin{gathered} (0,f(0))=(0,1)\rightarrow f(0)=1 \\ (2,f(2))=(2,4)\rightarrow f(2)=4 \end{gathered}[/tex]Then we get:
[tex]f(2)-f(0)=4-1=3[/tex]AnswerThen the answer is option C.
Three different transformation are performed on the shaded triangle. Each transformation results in on of three images. Match each image to the transformation applied on the shaded triangle
We are given a triangle and three possible transformations performed on it. The first transformation shows that the triangle has no change in orientation, therefore, this transformation is a translation only.
For image 2 we notice that the orientation of the triangle changes. If we draw a horizontal line in the middle of the shaded triangle and image 2 we notice that these two images are related by a reflection, also after this reflection the image was translated therefore, for image two we have reflection across a horizontal line followed by a translation.
For image 3 we can draw a vertical line in the middle of the shaded triangle and image 3 and we do a reflection across this vertical line since there is a change in the orientation of the figure.
if angle 2 = 106 degrees, what is the measurement of angle 6 ? ( better explanation in picture )
angle 2 and angle 6 are corresponding angles.
Since the lines crossed by the trnasversal are parallel, corresponding angles are congruent. (equal)
angle 6 = 106°
Tristan tried his luck with the lottery. He can win $85 if he can correctly choose the 3 numbers drawn. If order matters and there are 13 numbers in the drawing, how many different ways could the winning numbers be drawn?
The ways to select the winning numbers is 286
How to determine the ways the winning numbers could be drawn?From the question, we have
Total numbers, n = 13Numbers to select, r = 3The winning numbers could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 13 and r = 3
Substitute the known values in the above equation
Total = ¹³C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 13!/10!3!
Evaluate
Total = 286
Hence, the number of ways is 286
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Find the union of E and L.Find the intersection of E and L.Write your answers using set notation (in roster form).
For the intersection operation we have to look what elements both sets have in common, in this case both E and L has the number 8. Then the second answer is:
[tex]E\cap L=\lbrace8\rbrace[/tex]Now, the union operation adds the all elements into a single set without repetition, in this case the first answer is:
[tex]E\cup L=\lbrace-2,1,2,3,6,7,8\rbrace[/tex]The amount of freight transported by rail in the u.s was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then.a. write a function representing the amount of freight, in billions of ton-miles, transported annually. ( 1960 = year 0 )b. graph the functionc. in what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (1,000 billion)?
The amount of freight transported by rail was 580 billion ton-miles in 1960.
The amount increased at a rate of 2.32% per year.
a. The growth in freight transport with respect to the passing years can be expressed as exponential growth. The general form of this equation is
[tex]y=a(1+r)^x[/tex]Where
y represents the final number after "x" periods of time
a represents the initial number at x=0
r represents the growth rate, expressed as a decimal value
x represents the number of time intervals that have passed
For this example, the initial amount is a=580 billion
The growth rate is r=2.32/100=0.0232
You can determine the equation as follows:
[tex]y=580(1+0.0232)^x[/tex]b. This function is of exponential increase, its domain is all real numbers and its range is all positive real numbers, you can symbolize it as y > 0, it's increasing, and it has a horizontal asymptote as x approaches -∞
To graph it, you have to determine at least two points of the graph, I will determine 3
For x=-100
[tex]\begin{gathered} y=580(1+0.0232)^{-100} \\ y=58.53 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} y=580(1+0.0232)^0 \\ y=580 \end{gathered}[/tex]For x=10
[tex]\begin{gathered} y=580(1+0.0232)^{10} \\ y=729.51 \end{gathered}[/tex]The points are
(-100,58.53)
(0,580)
(10,729.51)
Plot the points and then draw an increasing line from -∞ to +∞
c. To determine the time when the freight transported will exceed 1000 billion tom-miles, you can use the graph, just determine the value of x, for which y=1000
This value is approximate x=23.57
This means that counting from 1960 will take 23 and a half years to reach over a trillion ton-miles transported.
Add the number of years to the initial year to determine the date:
[tex]1960+23=1983[/tex]By 1983 the number of ton-miles transported will exceed the trillion.
In the similaritytransformation of AABCto ADFE, AABC was dilated bya scale factor of 1/2, reflected4 across the x-axis, and movedthrough the translation [? ].
We have to identify the translation.
We can see that the green triangle represents the transformation of triangle ABC after a dilation with a scale factor of 1/2 and a reflection across the x-axis.
We can then find the translation in each axis from the image as:
Triangle is DEF is translated 3 units to the left (and none in the vertical axis).
We can express this translation as this rule:
[tex](x+3,y+0)[/tex]Answer: (x+3, y+0)
According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 70 received emails.
(a)
What is the expected number of these emails that are tracked?
(b)
What are the variance and standard deviation for the number of these emails that are tracked? (Round your answers to three decimal places.)
Var(x)
=
=
Using the binomial distribution, the measures are given as follows:
a) Expected value: 28.
b) Variance of 16.8 and standard deviation of 4.099.
What is the binomial distribution formula?The formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.Hence, in the context of this problem, the values of these parameters are given as follows:
p = 0.4, n = 70.
The expected value of the distribution is calculated as follows:
E(X) = np.
Hence:
E(X) = 70 x 0.4 = 28.
The variance of the distribution is calculated as follows:
V(X) = np(1 - p) = 70 x 0.4 x 0.6 = 16.8.
The standard deviation of the distribution is calculated as follows:
sqrt(V(X)) = sqrt(16.8) = 4.099.
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h(r) = (r +1)(r+8)1) What are the zeros of the function?Write the smaller r first, and the larger second.smaller r =larger s 2) What is the vertex of the parabola
For the zeros of the function, we have to solve h(r)=0, therefore:
[tex]\begin{gathered} h(r)=(r+1)(r+8) \\ h(r)=0 \\ \Rightarrow(r+1)(r+8)=0 \\ \Rightarrow r=-1\text{ or } \\ r=-8 \end{gathered}[/tex]then, the smaller r is -8 and the larger is -1.
Now, to find the vertex of the parabola, we can find the x-coordinate of the vertex from the general rule:
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \text{ x-coordinate: -b/2a} \end{gathered}[/tex]In this case, we have the following:
[tex]\begin{gathered} h(r)=(r+1)(r+8)=r^2+8r+r+8=r^2+9r+8 \\ \Rightarrow a=1,b=9 \\ \Rightarrow-\frac{b}{2a}=-\frac{9}{2(1)}=-\frac{9}{2} \end{gathered}[/tex]now that we have the x-coordinate of the vertex, we just evaluate the function on that point to find the y-coordinate of the vertex:
[tex]h(-\frac{9}{2})=(-\frac{9}{2}+1)(-\frac{9}{2}+8)=(-\frac{7}{2})(\frac{7}{2})=-\frac{49}{4}[/tex]therefore, the vertex of the parabola is the point (-9/2,-49/4)
Which of the following measurements form a right triangle? Select all that apply.
We are asked to find which of the measurements form a right triangle.
A right triangle is a triangle that has an angle of 90°, and also we can use the Pythagorean theorem in them.
The Pythagorean theorem tells us that the sum of the two legs of the triangle squared is equal to the hypotenuse squared:
[tex]a^2+b^2=c^2[/tex]Where a and b are the legs of the triangle and c is the Hypotenuse. Also, in the right triangle, the hypotenuse is the longest side of the triangle.
We will use the Pythagorean theorem formula on all of the options using the first two given measures as a and b, and check that we the third measure as the value of c.
Option A. 7in, 24in, and 25 in.
We define:
[tex]\begin{gathered} a=7 \\ b=24 \end{gathered}[/tex]And apply the Pythagorean theorem:
[tex]7^2+24^2=c^2[/tex]And we solve for c. If the result for x is 25, the triangle will be a right triangle, if not, this will not be an answer.
-Solving for c:
[tex]\begin{gathered} 49+576=c^2 \\ 625=c^2 \end{gathered}[/tex]Taking the square root of both sides we find c:
[tex]\begin{gathered} \sqrt[]{625}=c \\ 25=c \end{gathered}[/tex]Since we get the third measure as the value of c option A is a right triangle.
Option B. 18ft, 23ft, and 29 ft.
we do the same as did with option A. First, define a and b:
[tex]\begin{gathered} a=18 \\ b=23 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]18^2+23^2=c^2[/tex]And solve for c:
[tex]\begin{gathered} 324+529=c^2 \\ 853=c^2 \\ \sqrt[]{853}=c \\ 29.2=c \end{gathered}[/tex]We get 29.2 instead of just 29, thus option B is NOT a right triangle.
Option C. 10in, 24in, and 26 in.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=24 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]10^2+24^2=c^2[/tex]Solve for c:
[tex]\begin{gathered} 100+576=c^2 \\ 676=c^2 \\ \sqrt[]{676}=c \\ 26=c \end{gathered}[/tex]We get 26 which is the third measure given, thus, option C is a right triangle.
Option D. 10yd, 15yd, and 20yd.
Define a and b:
[tex]\begin{gathered} a=10 \\ b=15 \end{gathered}[/tex]Apply the Pythagorean theorem:
[tex]\begin{gathered} 10^2+15^2=c^2 \\ 100+225=c^2 \\ 325=c^2 \\ \sqrt[]{325}=c \\ 18.03=c \end{gathered}[/tex]We don't get 20yd as the value of c, thus, option D is NOT a right triangle.
Option E. 15mm, 18mm, and 24 mm
Define a and b:
[tex]\begin{gathered} a=15 \\ b=18 \end{gathered}[/tex]Apply the Pythagorean theorem
[tex]\begin{gathered} 15^2+18^2=c^2 \\ 225+324=c^2 \\ 549=c^2 \\ \sqrt[]{549}=c \\ 23.43=c \end{gathered}[/tex]We don't get 24 as the value of c, thus, option E is Not a right triangle.
Answer:
Option A and Option C are right triangles.
For each equation, choose the statement that describes its solution. If applicable, give the solution.
w=2
All real numbers are solutions
1) In this question, let's solve each equation, and then we can check whether there are solutions, which one would be.
2) Let's begin with the first one, top to bottom
[tex]\begin{gathered} 2(w-1)+4w=3(w-1)+7 \\ 2w-2+4w=3w-3+7 \\ 6w-2=3w+4 \\ 6w-3w=4+2 \\ 3w=6 \\ \frac{3w}{3}=\frac{6}{3} \\ w=2 \end{gathered}[/tex]Note that we distributed the factors outside the parenthesis over the terms inside.
So for the first one, we can check w=2
3) Moving on to the 2nd equation, we can state:
[tex]\begin{gathered} 6(y+1)-10=4(y-1)+2y \\ 6y+6-10=4y-4+2y \\ 6y-4y-2y=4-4 \\ 6y-6y=0 \\ 0y=0 \end{gathered}[/tex]So, there are infinite solutions for this equation, or All real numbers are solutions
the variables x and y are related proportionaly. when x=4,y=10 find y when x =18when x=18,y=_____
For variables to be related proportionally, the relationship must have a constant of proportionality. In our case we will represent the constant of proportionality as k. Therefore,
[tex]\begin{gathered} y=kx \\ \text{where} \\ k=\text{constant of proportionality} \\ 10=4k \\ k=\frac{10}{4} \\ k=\frac{5}{2} \end{gathered}[/tex]Now lets find y when x = 18
[tex]\begin{gathered} y=kx \\ y=\frac{5}{2}\times18 \\ y=\frac{90}{2} \\ y=45 \end{gathered}[/tex]What is 13.496 rounded to the nearest tenth?A.13B.13.4C.13.5D.14
1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.
2) Note this number:
We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.
3) Thus, we can round it off to:
[tex]13.5[/tex](0,1), (2,4), (4,7) (9.1)}Domain:Range:
The domain of an ordered pair are its first elements and its range are all the second elements of the ordered pair.
So, the domain ={0,2,4,9}
Range={1,4,7,1}
Joseph owns a 50 inch TV and it measures 50 inch on the diagonal. if the television is 40 inches across the bottom find the height of the TV
Let's draw the tv with the given values.
Note that we will form a right triangle with heigh of h, base of 40 and a hypotenuse of 50.
The Pythagorean Theorem is :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, a and b are the legs of the triangle.
Using the formula above. we will have :
[tex]\begin{gathered} 50^2=40^2+h^2 \\ 2500=1600+h^2 \\ h^2=2500-1600 \\ h^2=900 \\ \sqrt[]{h^2}=\sqrt[]{900} \\ h=30 \end{gathered}[/tex]The answer is 30 inches
What is the factorization of496^4-9
The given expression is
[tex]496^4-9[/tex]To factorize this, we find the square root of each term.
[tex]\begin{gathered} \sqrt[]{496^4}=496^2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]Then, we use the difference of perfect square which states
[tex]a^2-b^2=(a+b)(a-b)[/tex]So, we have
[tex]496^4-9=(496^2+3)(496^2-3)[/tex]Which region labeled in the graph below would represent the solution (the final shaded area) to the system of linear inequalities:≤12−3<−23+1
Since both inequalities include the less than symbol, <, the shaded region must be below the two lines.
The intersection (common) of the shaded regions, which are both below the two lines, is region D.
