Answer:
13 square units
Step-by-step explanation:
We need to find the distance between the points using the
Pythagorean Theorem, a² + b² = c²
(3,6) and (6,5); 6 - 3 = 3 and 6 - 5 = 1
3² + 1² = c²
9 + 1 = c²
c = √10
(6,5) and (5,1); 6 - 5 = 1 and 5 - 1 = 4
1² + 4² = c²
1 + 16 = c²
c = √17
√17 + √10 = 13.038
Which linear inequality is represented by the graph
Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]
Step-by-step explanation:
Determine the equation form of the inequalityGiven function form
Point-Slope form : y = mx + b
m = slopeb = y-interceptGiven the information from the graph
Since the graph crosses (0, 2), b = 2
Find the slope
Choose any two points from the graph
(x₁, y₁) = (0, 2)
(x₂, y₂) = (2, 3)
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (3 - 2) / (2 - 0)
Slope = 1 / 2
m = 1 / 2
Therefore, the equation form of the inequality is y = (1/2)x + 2
Determine whether it is ≤ or ≥Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.
The shaded region is below the solid line, therefore, it is ≤
Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]
To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.
y ≤ (1/2) x + 2
0 ≤ (1/2) 0 + 2
0 ≤ 2 TRUE
Hope this helps!! :)
Please let me know if you have any questions
I reallly badly need help
Answer:
You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
Step-by-step explanation:
The above is a cyclic quadrilateral.
What is a cyclic quadrilateral?A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.
To find either x or y, we should note:
The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.
Therefore,
2x + 2x + 4= 180
4x = 180 - 4
4x = 176
x = 44°
To find y
3y + 8 + y = 180°
4y = 180 - 8
4y = 172
y = 43°
Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
P^2=mx/t-t^2x make x the subject
Answer:
[tex]x=\frac{P^2t}{(m-t^3)}[/tex]
Step-by-step explanation:
[tex]P^2=\frac{mx}{t} -t^2x\\\\P^2+t^2x=\frac{mx}{t}\\\\t(P^2+t^2x)=mx\\\\P^2t+t^3x=mx\\\\P^2t=mx -t^3x\\\\P^2t=x(m-t^3)\\\\\frac{P^2t}{(m-t^3)} =\frac{x(m-t^3)}{(m-t^3)} \\\\\frac{P^2t}{(m-t^3)}=x[/tex]
Given that it was less than 80º on a given day, what is the probability that it also rained that day? 0.3 0.35 0.65 0.7
The probability that it also rained that day is to be considered as the 0.30 and the same is to be considered.
What is probability?The extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
The probability that the temperature is lower than 80°F and it rained can be measured by determining the number at the intersection of a temperature that less than 80°F and rain.
So, This number is 0.30.
Hence, we can say that it was less than 80°F on a given day, the probability that it also rained that day is 0.30.
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The above question is incomplete.
The conditional relative frequency table was generated using data that compared the outside temperature each day to whether it rained that day. A 4-column table with 3 rows titled weather. The first column has no label with entries 80 degrees F, less than 80 degrees F, total. The second column is labeled rain with entries 0.35, 0.3, nearly equal to 0.33. The third column is labeled no rain with entries 0.65, 0.7, nearly equal to 0.67. The fourth column is labeled total with entries 1.0, 1.0, 1.0. Given that it was less than 80 degrees F on a given day, what is the probability that it also rained that day?
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Answer: Its 0.3 so the first one
Step-by-step explanation:
Im 101% sure
Archeologists discovered a relic dating to the year 107 B.C. How old would this relic have been at the turn of the 20th century?
Step-by-step explanation:
The turn of the 20th century = 1900
So it is 1900 + 107 years ago, hence, 2007
Q11) kelly puts $350 in a savings account. the savings account accrues interest at a flat rate of 1.05% a month. how much will the account be worth in 7 months ?
The account be worth in 7 months is 375.725 .
What is the amount in simple interest?Amount (A) is the total money paid back at the end of the time period for which it was borrowed. The total amount formula in case of simple interest can also be written as: A = P(1 + RT)
Here, A = Total amount after the given time period.
Given that,
P = $350, R = 1.05%, T = 7 month
The simple interest equation uses "t" as years, but is just cycles, using an APR rate.
now, if we never mind "t" as years and just use it as an interest cycle, then we can say the rate is 1.05% and the period is 7 cycles.
A = P(1 + RT)
= 350(1+1.05%×7)
= 350(1+0.0105×7)
= 350(1+0.0735)
= 350×1.0735
A = $375.725
Hence, The account be worth in 7 months is 375.725 .
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Find two power series solutions of the given differential equation about the ordinary point x = 0. y'' + xy = 0
Answer:
First we write y and its derivatives as power series:
y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2
Next, plug into differential equation:
(x+2)y′′+xy′−y=0
(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0
x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0
Move constants inside of summations:
∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0
∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0
Change limits so that the exponents for x are the same in each summation:
∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0
Pull out any terms from sums, so that each sum starts at same lower limit (n=1)
∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0
Combine all sums into a single sum:
4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0
Now we must set each coefficient, including constant term =0 :
4a2−a0=0⟹4a2=a0
2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0
We would usually let a0 and a1 be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since a0=4a2 , I’ll choose a1 and a2 as the two arbitrary constants. We can still express all other constants in terms of a1 and/or a2 .
an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)
a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2
a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2
a5=−(4⋅3)a4+2a32(5⋅4)=15!a2
a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2
We see a pattern emerging here:
an=(−1)(n+1)n−4n!a2
This can be proven by mathematical induction. In fact, this is true for all n≥0 , except for n=1 , since a1 is an arbitrary constant independent of a0 (and therefore independent of a2 ).
Plugging back into original power series for y , we get:
y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯
y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯
y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)
Notice that the expression following constant a2 is =4+ a power series (starting at n=2 ). However, if we had the appropriate x -term, we would have a power series starting at n=0 . Since the other independent solution is simply y1=x, then we can let a1=c1−3c2, a2=c2 , and we get:
y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)
y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)
y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)
y=c1x+c2∑n=0∞(−1)n+1n−4n!xn
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HELP! 25 points!
question is in the file!
please answer asap
Answer:
Option C: x = 6
Step-by-step explanation:
Hi There!
7 + 5 (x - 3) = 22
=> 7 + 5x - 15 = 22
=> 5x = 22 - 7 + 15
=> 5x = 30
=> x = 30/5
=> x = 6
x = 6 makes the statement true.
Thank you,
Eddie
What is the following quotient?6-3(^3√6)/3/9
O 2(3√3)-3√/18
O 2(³√/3)-3(³/2)
O 3(3/3)-3√/18
O 3(³√/3)-3(3√/2)
Applying properties of exponents, the quotient is given as follows:
[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]
What is the quotient?The expression is given by:
[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}[/tex]
The 3 can be inserted into the cube root, as follows:
[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}[/tex]
Applying the subtraction, we have that the expression is:
[tex]\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}[/tex]
The denominator can be simplified as follows:
[tex]\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}[/tex]
Then:
[tex]\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}[/tex]
Hence the quotient is given by:
[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]
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Help pls!!
Use 3.14 for pi.
To find the area, we take into account that your data is:
r = 6 cmπ = 3.14To calculate the area of the circle, we use the following formula:
Area: π * r²
We substitute the data in the formula, and we begin to solve.
A = 3.14 * (6 cm)²taking the square root
A = 3.14 * 36 cm²Multiply the two numbers
A = 113.04 cm²Therefore, the area of the circle is 113.04 cm². The correct alternative is option "A".
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In the question, it is given that a circle has a radius of 6 cm , we have to find the Area.
To Find the area of the circle , we must know this formula:
[tex] \quad\quad\quad \longrightarrow\underline{\boxed{\color{violet}{A=\pi*r^2}}}[/tex]
Now, we will substitute the values in the formula:
[tex]\rightarrow\sf{A=\pi*r^2} \: \: \: \: \: \: \: ( \red{\pi = 3.14})[/tex]
[tex]\rightarrow\sf{A = 3.14 * 6^2}[/tex]
[tex]\rightarrow\sf{A = 3.14 * 36}[/tex]
[tex]\rightarrow\sf{A = 113.0}[/tex]
The area of circle is 113.0 approx .
[tex] \color{blueviolet}{ \mathfrak{llNotYourll}}[/tex]
At Eva’s restaurant, 2/3 of the dishes on the menu are vegetarian. Of the vegetarian dishes, 1/10 are pasta dishes. What fraction of the dishes on the menu are vegetarian pasta?
Answer:
1/15 of the dishes on the menu are vegetarian pasta.
Step-by-step explanation:
1/10 of 2/3 of all dishes are vegetarian pasta.
1/10 of 2/3 of all = 1/10 * 2/3 * 1 = 2/30 = 1/15
simplify -3/2 * 9/6
A. -4
B. -1
C. 4
D. 1
Answer:
-2.25
Step-by-step explanation:
Determine and state the coordinates of the center and the length of the radius of the
circle whose equation is x2 + y2 + 6x = 6y + 63
we can see that the center is (-3, 3) and the radius is 9 units.
How to find the center and radius of the circle?The general circle equation, for a circle with a center (a, b) and radius R is given by:
(x - a)^2 + (y - b)^2 = R^2
Here we have the equation:
x^2 + y^2 + 6x = 6y + 63
Let's complete squares:
x^2 + y^2 + 6x - 6y = 63
(x^2 + 6x) + (y^2 - 6y) = 63
(x^2 + 2*3x) + (y^2 - 2*3y) = 63
Now we can add and subtract 9, (two times) so we get:
(x^2 + 2*3x + 9) - 9 + (x^2 - 2*3x + 9) - 9 = 63
(x + 3)^2 + (y - 3)^2 = 63 + 9 + 9 = 81 = 9^2
(x + 3)^2 + (y - 3)^2 = 9^2
Comparing with the general circle equation, we can see that the center is (-3, 3) and the radius is 9 units.
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Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.
Answer:
x = 12
Step-by-step explanation:
sqrt(x+4) - 3 = 1
First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.
sqrt(x+4) = 1 + 3
sqrt(x+4) = 4
To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.
(sqrt(x+4))^2 = 4^2
x + 4 = 16
subtract 4 to finish up.
x = 12
Check:
sqrt(12 + 4) - 3 = 1
sqrt16 - 3 = 1
4 - 3 = 1
1 = 1 Check!
A 5-pound box of raspberries costs $27.20. What is the price per ounce?
$
Answer:
$0.34 per ounce
Step-by-step explanation:
A 5 pound box can be changed to ounces. There are 16 ounces in a pound. So we have 5 groups of 16.
5 × 16 is 80 ounces.
There are 80 ounces in 5lbs.
To get a price per ounces, divide.
dollars/ounces
= 27.20/80
= 0.34 dollars/oz.
This is 34cents per ounce.
Given w = 10, what is the answer to w + (w – 12 ÷ 22 • 3) • 7? (1 point) 73 66 23 17
Answer:
68.54
Step-by-step explanation:
w + (w – 12 ÷ 22 • 3) • 7
10 + (10 – 12 ÷ 22 • 3) • 7
Parentheses first
(10 – 12 ÷ 22 • 3)
(10 – 36 ÷ 22)
(10 – 1.636)
(8.364)
-------
10 + (8.364) • 7
10 + 58.54
68.54
The value of the expression will be equal to 66.54. The correct option is B.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is w + (w – 12 ÷ 2^ 2• 3) • 7 and the value of w is 10.
By substituting the value of w equal to 10 the value of the expression is,
E = w + (w – 12 ÷ 22 • 3) • 7
E = 10 + (10 – 12 ÷ 22 • 3) • 7
Solve the Parentheses first.
P = (10 – 12 ÷ 22 • 3)
P = (10 – 36 ÷ 22)
P = (10 – 1.636)
P = (8.364)
Solve further to get the final value.
E = 10 + (8.364) • 7
E = 10 + 56.54
E = 66.54.
Therefore, the value of the expression will be equal to 66.54.
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The length and breadth of a rectangular park 25m and 12m. find the distance covered by a boy who takes 4 rounds of the garderean. also find its a
Answer:296 m
I’m assuming “breadth” is width and garderean is just the park.
(25+25+12+12) times 4.
A is never defined
Which response best identifies why a surgical mask should not be used as a respiratory to protect against the inhalation of biohazards or bioaerosols
The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery.
What is a surgical mask used for?
A surgical mask exists primarily utilized to protect patients and healthcare employees from people who may contain a respiratory infection or to protect sterilized or disinfected medical devices and supplies. The nurse should dispose of the mask. This exists because the safety mechanisms of the mask may be compromised and therefore pose a risk to the patient that exists undergoing surgery. It exists still suggested that medical personnel err on the side of warning when it arrives to the managing of equipment, whether it be a significant piece of equipment or even a small one like a surgical mask.
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Prove that 1 + cos theta - sin^2 theta
divided by sin theta [ 1 + cos theta]
is equal to cot theta
Answer:
CotO
Step-by-step explanation:
The process is int the picture
Hurry show your work
24- 4 to rhe power of 2 x 3+15
the expression is simplified to give - 39
How to simply the expression
Given the expression;
= 24- 4 to the power of 2 x 3+15
= 24 - (4^2 × 3 ) + 15
First, expand the bracket
= 24 - ( 16 × 3) + 15
Find the product of the bracket
= 24 - 48 + 15
From our knowledge of BODMAS, we add before we subtract
Now, let's add first
= 24 - 63
The, subtract
= - 39
The expression is simplified to - 39
Thus, the expression is simplified to give - 39
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“Eighteen is equal to the product of a number (n) and 9.”
Answer:
n=2
Step-by-step explanation:
Create an equation.
9n=18
Divide 9 from both sides.
9n/9=18/9
n=2
Hope this helps!
6. For what value of p, the binary number 110P/2 represents 25?
Step-by-step explanation:
25 as binary number is
11001
1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 1 = 25
25×2 = 50 = 11001 × 2 = 110010
multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.
and so, we see
110P = 110010
P = 010
FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.
so, the problem should have looked like
110P/10 = 11001
110P = 11001×10 = 110010
P = 010
Answer:
01
Step-by-step explanation:
From decimal to binary;
25/2==> 1 (remainder)
12/2===>0
6/2==>0
3/2===>1
1
=11001
Checking the answer;
11001
=1*2^4+1*2^3+0*2*2+0*1+1*2^0
=1*16+1*8+0+0+1*1
=16+8+0+0+2
=25
Write the given second order equation as its equivalent system of first order equations
The second-order equation as its equivalent system of first-order equations is
[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]
An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.
Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.
In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.
Taking v = u, we have:
u" + 4u' + 6u = 4sin(3t)
--> v' + 4v + 6u = 4sin(3t)
So the system of equations is:
u' = 0u + 1v
v' = -6u - 4v + 4sin(3t)
So we can write it as:
u(1) = 7.5
v(1) = u'(1) = 9
So the initial condition matrix is:
[tex]\left[\begin{array}{ccc}u(1)\\\\v(1)\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}7.5\\\\9\end{array}\right][/tex]
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2. A ribbon is 5 long. A piece of length 3 4/5 is cut from it. What is the length of the remaining piece?
Answer:
Given,The ribbon is 5m long.
The length of the piece = 3 ^ 4 / 5 m.
To find,The length of the remaining piece.
Solution,We can simply solve this mathematical problem by using the following mathematical process.
First of all, we have to convert the length of the cut piece into simple decimal value.
Length of cut piece =3^ 4 / 5 = (3 * 5 + 4) / 5 = 19/5 = 3.8m
Length of the remaining ribbon = Intital length cut length = 5 - 3.8 = 1.2m = 12/10 - m = 6/5 * m = 1 1/5 m
(The final value is also expressed in fractional form)Hence, the length of the remaining piece is 15m.Answer: 1 1/5
Step-by-step explanation:
5 - 3 = 2 - 4/5 = 1 1/5
-4 = p + 7 using sum in verbal expression form
Find the probability of rolling a sum less than 5 or a sum greater than 7 when a pair of dice is rolled.
Answer:
Step-by-step explanation:
Solution
There are 36 possible ways to combine two dice. The ones you are interested in, are in the table below
Numbers less that 5 are with their probabilities
Number Probability How done.
2 1/36 1 + 1
3 2/36 2 + 1 1 + 2
4 3/36 2 + 2 1 +3 3 + 1
Total 6/36 1/6
Greater than 7
Number Probability How done
8 5/36 6+2 2+6 5 +3 3+5 4 + 4
9 4/36 6+3 3 + 6 5+4 4+ 5
10 3/36 6+4 4 +6 5 + 5
11 2/36 5+6 6 + 5
12 1 /36 6 + 6
Total 15/36
Answer
15/36 + 1/6 = 15/36 + 6/36 = 21/36
Final Answer: 7/12
the point in the graph of the equation 2x+5y=20, where x coordinate is 5/2, is
Answer: (5/2, 3)
Step-by-step explanation:
Substituting in x=5/2,
[tex]2(5/2)+5y=20\\\\5+5y=20\\\\5y=15\\\\y=3[/tex]
So, the point is (5/2, 3)
find the value of n: [tex]\frac{10n}{-5} = -4[/tex]
Answer:
n = 2
Step-by-step explanation:
cross multiply
-5 times -4 = 20
10n = 20
n = 2
[tex]\bf{Move \ the \ negative \ symbol \ to \ the \ left. }[/tex]
[tex]\boldsymbol{\sf{-\dfrac{10n}{5}=-4 \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\boldsymbol{\sf{-2n=-4 }}[/tex]
[tex]\bf{Divide \ both \ sides \ by \ -2. }[/tex]
[tex]\boldsymbol{\sf{n=\dfrac{-4}{-2} }}[/tex]
[tex]\bf{Two \ negatives \ make \ a \ positive. }[/tex]
[tex]\boldsymbol{\sf{n=\dfrac{4}{2} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\blue{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \underline{n=2}}}}}[/tex]
5) For the fraction 3/25, (a) write a percent and (b) write a decimal.
Is the function y = 3x4 - 1 linear or nonlinear?