To determine the length of the rectangular flower garden, we need to derive equations from the given measurements and relations. The given measurements are the area, and the relation of the width and the length. From these, we generate the equation needed. We do as follows:
Area = Length x Width
where length = x ft
width = x - 3 ft
area = 54 ft^2
54 ft^2 = x ft (x -3) ft
54 ft^2 = x^2 - 3x ft^2
Solving for the value of x, we will have two values which are
x = -6 ft ( NOTE: this value can't be the answer since we cannot have a negative value for the length)
x = 9 ft = length
I really need help solving this practice from my prep guide in trigonometry
Given: Different angles in degrees and in terms of pi. The different angles are:
[tex]\begin{gathered} a)714^0 \\ b)\frac{23\pi}{5} \\ c)120^0 \\ d)\frac{31\pi}{6} \end{gathered}[/tex]To Determine: The equivalence of the given angles
The equivalent of degree and pi is given as
[tex]\begin{gathered} 2\pi=360^0 \\ \pi=\frac{360^0}{2} \\ \pi=180^0 \\ 360^0=2\pi \\ 1^0=\frac{2\pi}{360^0} \\ 1^0=\frac{1}{180}\pi \end{gathered}[/tex][tex]\begin{gathered} a)714^0 \\ 1^0=\frac{1}{180}\pi \\ 714^0=\frac{714^0}{180^0}\pi \\ 714^0=3\frac{29}{30}\pi \\ 714^0=\frac{119\pi^{}}{30} \end{gathered}[/tex][tex]\begin{gathered} b)\frac{23\pi}{5} \\ 1\pi=180^0 \\ \frac{23\pi}{5}=\frac{23}{5}\times180^0 \\ \frac{23\pi}{5}=828^0 \end{gathered}[/tex][tex]\begin{gathered} c)120^0 \\ 1^0=\frac{\pi}{180} \\ 120^0=120\times\frac{\pi}{180} \\ 120^0=\frac{2\pi}{3} \end{gathered}[/tex][tex]\begin{gathered} d)\frac{31\pi}{6} \\ 1\pi=180^0 \\ \frac{31\pi}{6}=\frac{31}{6}\times180^0 \\ \frac{31\pi}{6}=930^0 \end{gathered}[/tex]ALTERNATIVELY
A revolution is 360 degree
[tex]\begin{gathered} a)714^0 \\ \text{Multiples of 360 degre}e \\ 2\times360^0=720^0 \\ \text{equivalent of 714 degre}e\text{ would be} \\ 720^0-714^0=6^0 \end{gathered}[/tex][tex]undefined[/tex][tex]\begin{gathered} a)714^0=\frac{119\pi}{30} \\ b)\frac{23\pi}{5}=828^0 \\ c)120^0=\frac{2\pi}{3} \\ d)\frac{31\pi}{6}=930^0 \end{gathered}[/tex]what is the slope of the line represented by y = -5 + 2?
Question:
Find the slope of
[tex]y=-5x+2[/tex]Answer:
Remember that when we have the equation of a line in the form
[tex]y=mx+b[/tex]The slope of the line is the number that accompanies x (A.K.A Coefficient)
Therefore, the slope of the line is -5
Write the equation of a line, in slope-intercept form, that has a slope of m= -2 and y-interceptof b = -8.Y=
Explanation
We are given the following:
[tex]\begin{gathered} slope(m)=-2 \\ y\text{ }intercept(b)=-8 \end{gathered}[/tex]We are required to determine the equation of the line in the slope-intercept form.
We know that the equation of a line in slope-intercept form is given as:
[tex]\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y\text{ }intercept \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} y=mx+b \\ where \\ m=-2\text{ }and\text{ }b=-8 \\ y=-2x+(-8) \\ y=-2x-8 \end{gathered}[/tex]Hence, the answer is:
[tex]y=-2x-8[/tex]Find the equation of the line connecting the points (2,0) and (3,15). Write your final answer in slope-intercept form.
The first step to find the equation of the line is to find its slope. To do it, we need to use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where y2 and y1 are the y coordinates of 2 given points on the line, and x2 and x1 are the x coordinates of the same points. m is the slope.
Replace for the given values and find the slope:
[tex]m=\frac{15-0}{3-2}=\frac{15}{1}=15[/tex]Now, use one of the given points and the slope in the point slope formula:
[tex]y-y1=m(x-x1)[/tex]Replace for the known values:
[tex]\begin{gathered} y-0=15(x-2) \\ y=15x-30 \end{gathered}[/tex]The equation of the line is y=15x-30
Show instructionsQuestion 1 (1 point)Does the point (0,5) satisfy the equation y = x + 5?TrueFalse
The equation is
[tex]y=x+5[/tex]The point given is:
[tex](x,y)=(0,5)[/tex]The x coordinate given is 0 and the y coordinate given is 5.
We put the respective point and see if the equation holds true or not.
Thus,
[tex]undefined[/tex]• 5th 3230 [] What would be the slope of a line perpendicular to the line graphed above? -2 2 1/2 -1/2 Zoom in Double Jeop 3:39
When two lines are perpendicular to each other, their slopes would be a negative inverse of each other. This simply means the slope of a line perpendicular to the one in the question should be equal to the negative inverse of the one we have here. Let us begin by calculating the slope of this line.
When you are given two endpoints, the slope is derived as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]When the coordinates are (0, 3) and (-1.5, 0)
That is, when x = 0 then y = 3 (observe the point where the line touches the vertical axis), and when x = -1.5, then y = 0 (observe the point where the line touches the horizontal axis)
Therefore, the coordinates (0, 3) and (-1.5, 0) are now your (x1, y1) and (x2, y2)
[tex]\begin{gathered} m=\frac{0-3}{-1.5-0} \\ m=\frac{-3}{-1.5} \\ m=2 \end{gathered}[/tex]Therefore the slope of a line perpendicular to the one on the graph is -1/2.
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Given 4 h + 6 = 30
4 h = 30 - 6
4 h = 24
Divide both sides by 4, we have:
h = 24 /4
h = 6
Find the equation of a line parallel to y=x+6 that passes through the point (8,7)(8,7).
The equation of the line which is parallel to the line y = x + 6, and which passes through the point (8, 7) is; y = x - 1
What are parallel lines in geometry?Parallel lines are lines do not intersect and which while on the same plane, have the same slope.
The given line to which the required line is parallel to is y = x + 6
The point through which the required line passes = (8, 7)
The slope of the given line, y = x + 6, is 1,
The slope of parallel lines are equal, which gives;
The slope of the required line is 1
The equation of the required line in point and slope form is therefore;
y - 7 = 1×(x - 8) = x - 8
y = x - 8 + 7 = x - 1
The equation of the required line in slope–intercept form is; y = x - 1
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A student council president wants to learn about the preferred theme for the upcoming spring dance. Select all the samples that are representative of the population.
The idea of being representative of the population is actually reflecting the characteristics (features) we want to study of the whole population.
In this case, the samples that better represent the whole population are B and D. Why? Because they give us the possibility of taking a student of every grade. The other options, excluding the "bus option" and the first option, fail doing that. Finally, these options (bus option and lunch option) are related to the council president.
Can't help me??
x/4 - 9 = 7
solve the equation... use transposing method
The Answer Is x = 64.
Explanation.x/4 - 9 = 7
x/4 = 7 + 9
x/4 = 16
x = 16 × 4
x = 64
_________________
Class: High School
Lesson: Equation
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
Answer:
x = 64
Step-by-step explanation:
x/4 - 9 =7
Step 1: Add 9 to both sides
x/4 - 9 + 9 = 7 + 9
x/4 = 16
Step 2: Multiply right side by 4
x/4= 16 x 4
x = 64
Step 3: Prove your x-value
64/4 = 16 - 9 = 7
64/4 - 9 = 7
So x = 64
PS: Please make brainliest.
There are 10 males and 18 females in the Data Management class. How many different committees of 5 students can be formed if there must be 3 males and 2 femalesA: 18360B: 2600C: 98280D: 15630
Answer:
A: 18360
Explanation:
The number of ways of combinations to select x people from a group of n people is calculated as
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]Since we need to form committees with 3 males and 2 females, we need to select 3 people from the 10 males and 2 people from the 18 females, so
[tex]10C3\times18C2=\frac{10!}{3!(10-3)!}\times\frac{18!}{2!(18-2)!}=120\times153=18360[/tex]Therefore, there are 18360 ways to form a committee.
So, the answer is
A: 18360
You are given the equation 12 = 3x + 4 with no solution set. Part A: Determine two values that make the equation false. Part B: Explain why your integer solutions are false. Show all work.
[tex]12=3x+4 \\ \\ 8=3x \\ \\ x=8/3[/tex]
So, two integer values are 1 and 2 since they are not the solution to the equation.
In the equation y = 2x, y represents the perimeter of a square.What does x represent?Ahalf the length of each sideBthe length of each sideСtwice the length of each sideDtwice the number of sides
Given:
An equation that represents the perimeter of a square:
[tex]y=2x[/tex]To find:
What x represents.
Solution:
It is known that the perimeter of the square is equal to four times the side of the square.
Let the side of the square be s. So,
[tex]\begin{gathered} y=P \\ 2x=4s \\ x=\frac{4s}{2} \\ x=2s \end{gathered}[/tex]Therefore, x represents twice the length of each side.
A woman is floating in a
boat that is 175 feet from
the base of a cliff. The cliff
is 250 feet tall. What is the
angle of elevation from
the boat to the top of the
cliff?
The angle of depression between the cliff and the boat is 55.0
What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object of from the horizontal line. It's basically used to get the of distance of the two objects where the angles and an of object's distance from the ground are known to us.
A boat is moving 175 feet from the base and a women is in the boat.the height of the cliff is 259 feet tall. Here we have to find the angle between the cliff and the boat.
As per the given question
We have a right angled traingle where base is 175 ft and height is 250 ft.
Thus,
We know that tan theta =opposite/adjacent
250/175
So theta=tan^-1(250/175)
So theta = 55.0
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In how many ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table?241220
The number of people to be seated around the table, n=5.
Now, n=5 people can be seated in a circle in (n-1)! ways.
[tex](n-1)!=(5-1)=4!\text{ =4}\times3\times2\times1=24[/tex]Therefore, Joe, Mary, Steve, Tina and Brenda can be seated around the round table in 24 ways.
what are the equations of the asysyoptes of the rational function
To find the asymptotes, we have to solve the following.
[tex]x^2-4x+3=0[/tex]We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.
[tex](x-3)(x-1)=0[/tex]So, the solutions are x = 3 and x = 1.
Hence, the asymptotes x = 1 and y = 1/2.The graph below shows the function.
Which probem situation can be represented by the equation below?3x +3 <11F Joe and Hannah together got less than 11 questions correct on their quizzes. Joe got 3 more questions correct than Hannah. What is x, the number of quiz questions Hannah got 3 correct?G A coin collection of dimes and quarters has less than 11 coins. The collection has more than 3 times as many quarters as dimes. How many dimes, x, is in the collection?H Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?J The length of a rectangle is 3 inches more than the width, x. Three times the length is less than 11. What is the width of the rectangle?
Let x be correct questions of Joe and y be correct quiz question of Joe. The in equality for Joe and Hannah together questions is,
[tex]x+y<11[/tex]Joe got 3 more questions correct than Hannah, means equaltion is,
[tex]y=x+3[/tex]So inequality obtained is,
[tex]\begin{gathered} x+x+3<11 \\ 2x+3<11 \end{gathered}[/tex]Thus option F is incorrect.
Let x be number of dimes and y be number of quarters. So inequality for collection of coins is,
[tex]x+y<11[/tex]The number of quarters are,
[tex]y=3x[/tex]So resultant inequality is,
[tex]\begin{gathered} x+3x<11 \\ 4x<11 \end{gathered}[/tex]Thus option G is incorrect.
Let larger number be y. So sum of numbers is less than 11, means
[tex]x+y<11[/tex]The equation of larger number in terms of smaller number is,
[tex]y=2x+3[/tex]Substitute the value of y in the inequality to obtain the desired inequality.
[tex]\begin{gathered} x+2x+3<11 \\ 3x+3<11 \end{gathered}[/tex]Thus inequality obtained is 3x + 3 < 11.
Thus option H is correct.
Correct option : Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?
What is the slope of a line perpendicular to the line whose equation is15x + 12y = -108. Fully reduce your answer.Answer:Submit Answer
GIven:
The equation of a line is 15x+12y=-108.
The objective is to find the slope of the perpencidular line.
It is known that the equation of straight line is,
[tex]y=mx+c[/tex]Here, m represents the slope of the equation and c represents the y intercept of the equation.
Let's find the slope of the given equation by rearranging the eqation.
[tex]\begin{gathered} 15x+12y=-108 \\ 12y=-108-15x \\ y=-\frac{15x}{12}-\frac{108}{12} \\ y=-\frac{5}{4}x-9 \end{gathered}[/tex]By comparing the obtained equation with equation of striaght line, the value of slope is,
[tex]m_1=-\frac{5}{4}[/tex]THe relationship between slopes of a perpendicular lines is,
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{5}{4}\cdot m_2=-1 \\ m_2=-1\cdot(-\frac{4}{5}) \\ m_2=\frac{4}{5}^{} \end{gathered}[/tex]Hence, the value of slope of perpendicular line to the given line is 4/5.
Which of the following describes point D?
Answer:
(0,4)
Step-by-step explanation:
Hi! :)
I am Pretty sure this is what it is, if this is not what you are needing please let me know.
Can you help me with this true and false problem?
FALSE.
Explanations:Given the linear relations 2x - 3y = 4 and y = -2/3 x + 5
Both equations are equations of a line. For the lines to be perpendicular, the product of their slope is -1
The standard equation of a line in slope-intercept form is expressed as
[tex]y=mx+b[/tex]m is the slope of the line
For the line 2x - 3y = 4, rewrite in standard form
[tex]\begin{gathered} 2x-3y=4 \\ -3y=-2x+4 \\ y=\frac{-2}{-3}x-\frac{4}{3} \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Compare with the general equation
[tex]\begin{gathered} mx=\frac{2}{3}x \\ m=\frac{2}{3} \end{gathered}[/tex]The slope of the line 2x - 3y = 4 is 2/3
For the line y = -2/3 x + 5
[tex]\begin{gathered} mx=-\frac{2}{3}x \\ m=-\frac{2}{3} \end{gathered}[/tex]The slope of the line y = -2/3 x + 5 is -2/3
Take the product of their slope to determine whether they are perpendicular
[tex]\begin{gathered} \text{Product = }\frac{2}{3}\times-\frac{2}{3} \\ \text{Product = -}\frac{4}{9} \end{gathered}[/tex]Since the product of their slope is not -1, hence the linear relations do not represent lines that are perpendicular. Hence the correct answer is FALSE
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.f(x)=sqrt(x)+2g(x)=x^2+7f(g(x))= ?g(f(x))= ?
Answer:
[tex]\begin{gathered} \begin{equation*} f(g(x))=\sqrt{x^2+7}+2 \end{equation*} \\ \begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*} \end{gathered}[/tex]Explanation:
Given the functions f(x) and g(x) below:
[tex]\begin{gathered} f(x)=\sqrt{x}+2 \\ g\mleft(x\mright)=x^2+7 \end{gathered}[/tex]Part A
We want to find the simplified form of f(g(x)).
[tex]f(x)=\sqrt{x}+2[/tex]Replace x with g(x):
[tex]f(g(x))=\sqrt{g(x)}+2[/tex]Finally, enter the expression for g(x) and simplify if possible:
[tex]\implies f\mleft(g\mleft(x\mright)\mright)=\sqrt{x^2+7}+2[/tex]Part B
We want to find the simplified form of g(f(x)). To do this, begin with g(x):
[tex]g\mleft(x\mright)=x^2+7[/tex]Replace x with f(x):
[tex]g(f(x))=[f(x)]^2+7[/tex]Finally, enter the expression for f(x) and simplify if possible:
[tex]\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=(\sqrt{x}+2)^2+7 \\ =(\sqrt{x}+2)(\sqrt{x}+2)+7 \\ =x+2\sqrt{x}+2\sqrt{x}+4+7 \\ \implies g(f(x))=x+4\sqrt{x}+11 \end{gathered}[/tex]Therefore:
[tex]\begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*}[/tex]3. A student solved an order of operations problem asshown.(2 - 4)2 – 5(6 - 3) + 13(-2)2 - 30 - 3 + 134 - 33 + 13-16What error did this student make? Explain in completesentences. What should the correct answer be?
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
Parentheses first
[tex]\begin{gathered} (2-4)=-2 \\ (6-3)=3 \\ \end{gathered}[/tex]substitute
[tex]\begin{gathered} (-2)2-5(3)+13 \\ -4-15+13 \\ -4-2 \\ -6 \\ \end{gathered}[/tex]The student error was misapplication of the comutative property
solve for y. 2x-y=12
Answer:
2x - 12 = y
Step-by-step explanation:
→ Add y to both sides
2x = 12 + y
→ Minus 12 from both sides
2x - 12 = y
hello can you help me with this math question and this a homework assignment
We know that two vectors are ortogonal if and only if:
[tex]\vec{v}\cdot\vec{w}=0[/tex]where
[tex]\vec{v}\cdot\vec{w}=v_1w_1+v_2w_2[/tex]is the dot product between the vectors.
In this case we have the vectors:
[tex]\begin{gathered} \vec{a}=\langle-4,-3\rangle \\ \vec{b}=\langle-1,k\rangle \end{gathered}[/tex]the dot product between them is:
[tex]\begin{gathered} \vec{a}\cdot\vec{b}=(-4)(-1)+(-3)(k) \\ =4-3k \end{gathered}[/tex]and we want them to be ortogonal, so we equate the dot product to zero and solve the equation for k:
[tex]\begin{gathered} 4-3k=0 \\ 4=3k \\ k=\frac{4}{3} \end{gathered}[/tex]Therefore, for the two vector to be ortogonal k has to be 4/3.
reduce the square root of -360
reduce the square root of
[tex]\begin{gathered} \sqrt[]{-360} \\ 360=36\cdot10=6^2\cdot10 \\ \end{gathered}[/tex]There is no square root for the negative number
so, this is represent a complex number
So,
[tex]\begin{gathered} \sqrt[]{-360}=\sqrt[]{-1}\cdot\sqrt[]{360} \\ =i\cdot\sqrt[]{6^2\cdot10} \\ =i\cdot6\sqrt[]{10} \\ =6\sqrt[]{10}\cdot i \end{gathered}[/tex]What is (are) the solution(s) to the system of equations y = -x + 4 and y = -x^2 + 4 ?
Given:
[tex]\begin{gathered} y=-x+4----(1) \\ y=-x^2+4----(2) \end{gathered}[/tex]Required:
To find the solutions to the given equations.
Explanation:
Put equation 1 in 2, we get
[tex]\begin{gathered} -x+4=-x^2+4 \\ \\ -x+4+x^2-4=0 \\ \\ x^2-x=0 \\ \\ x(x-1)=0 \\ \\ x=0,1 \end{gathered}[/tex]When x=0,
[tex]\begin{gathered} y=-0+4 \\ y=4 \end{gathered}[/tex]When x=1,
[tex]\begin{gathered} y=-1+4 \\ =3 \end{gathered}[/tex]Final Answer:
The solution are
[tex]x=0,1[/tex]The solution sets are
[tex]\begin{gathered} (0,4)\text{ and} \\ (1,3) \end{gathered}[/tex]Which of the following numbers are not natural numbers?Select one:a. 1,000,000b. 5,032c. 1/4d. 25
Natural numbers are those who you use to count elements, they are by definition positive integers.
C. is not an integer, so it is not a natural number
b. 5032, a. 1000000 and d.25 are positive integers. These are natural numbers.
Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount?
The formula for simple interest is where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied.
2
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2
To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of?
Type your response here: rate= interest/$1000
Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying.
Type your response here:
Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate?
Type your response here:
Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable.
Type your response here:
Solve for the value of the unknown variable.
Type your response here:
1. One cannot figure out how much the interest rate is based on the amount charged to the credit card unless other variables are supplied.
2. We know the values of the following variables now:
The interest amountThe principal amount.3. The interest rate is 2.2% per month.
4. The period that this interest rate applies is monthly, called the MPR.
5. The annual interest rate (APR) is 26.4%.
6. The known variables about this payday loan are the interest amount, the interest rate, and the period.
7. A formula to solve for the unknown variable, principal/credit amount, is P = I / (RT), where I = interest, R = rate, and T = time period.
8. The solution for the value of the unknown variable, Principal, is $3,900.
Minimum monthly payment = interest amount = $22
Credit card bill = $1,000
Rate = interest/$1,000
Rate = $22/$1,000 = 0.022
= 2.2%
MPR = 2.2%
APR = 26.4% (2.2% x 12)
Payday Loans:The service charge for a 2-week loan = $15
Interest rate = 10%
Principal/Payloan = $3,900 ($15 / (10% x 2/52)
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Each of 6 students reported the number of movies they saw in the past year. This is what they reported:20, 16, 9, 9, 11, 20Find the mean and median number of movies that the students saw.If necessary, round your answers to the nearest tenth.
Solution:
The number of movies 6 students reported they saw in the past year is;
[tex]20,16,9,9,11,20[/tex]The mean number of movies that the students saw is;
[tex]\begin{gathered} \bar{x}=\frac{\Sigma x}{n} \\ n=6 \\ \bar{x}=\frac{20+16+9+9+11+20}{6} \\ \bar{x}=\frac{85}{6} \\ \bar{x}=14.2 \end{gathered}[/tex]The mean round to the nearest tenth is 14.2
Also, the median is the middle number of the data set after arranging either in ascending or descending order.
[tex]9,9,11,16,20,20[/tex]The median number of movies the students saw is the average or mean of the third and fourth.
[tex]\begin{gathered} \text{Median}=\frac{11+16}{2} \\ \text{Median}=\frac{27}{2} \\ \text{Median}=13.5 \end{gathered}[/tex]The median round to the nearest tenth is 13.5
If 1000 pennies are put into rolls of 50 pennies, how many rolls will be made?
Answer:
12
Step-by-step explanation:
50x2=100
100x10=1000
2+10=12