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Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish in a certain bay after the first year.Write the explicit equation for f(n) that represents the number of lionfish in the bay after n years.
Answers
Answer:
f(n) = 8000(1.67)ⁿ⁻¹
Explanation:
The equation for exponential growth has the following form:
[tex]f(x)=a(1+r)^x[/tex]Where a is the initial amount, r is the growth rate and x is the variable.
In this case, we know the amount after the first year and the growth rate and the variable is the number of years. So, replacing a by 8,000 and r by 0.67 and x by (n-1) because we will not include the 1st year, we get:
[tex]f(n)=8000(1+0.67)^{n-1}[/tex]Therefore, the explicit equation for f(n) is:
[tex]f(n)=8000(1.67)^{n-1}[/tex]A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $11.90 per pound with a Arabian Mocha coffee blend that normally sells for $13.10 per pound to create 10 pounds of a coffee that can sell for $12.86 per pound. How many pounds of each kind of coffee should they mix? A) Write an equation using the information as it is given above that can be solved to answer the question. Use z as your variable to represent the quantity of Queen City coffee blend. Equation: 11.92 + 13.1. – 131 = 128.6 Х
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The linear equations are x + y = 10 and (11.90)x + (13.10)y = (12.86)(10) and the value of x and y are 2 and 8 respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A coffee distributor needs to mix a(n) Queen City coffee blend that normally sells for $11.90 per pound.
Let x and y be the quantity of Queen City coffee (lbs) and the quantity of Arabian Mocha coffee (lbs)
From the data given;
The equations can be framed:
x + y = 10
(11.90)x + (13.10)y = (12.86)(10)
After solving the substitution method:
x = 2
y = 8
Thus, the linear equations are x + y = 10 and (11.90)x + (13.10)y = (12.86)(10) and the value of x and y are 2 and 8 respectively.
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Lesson 4: Proportional Relationships a 2. A recip Equations the qu a. Let's write equations describing proportional relationships. b. 4.1: Number Talk: Division Find each quotient mentally. C. 645 - 100 645:50 48.6 - 30 48.6 + x
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Move the decimal point of 645 two units left ( You are dividing by 100)
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[tex]\frac{645}{50}=\frac{129}{10}=12.9[/tex]Simplify 645/50 as 129/10, now move the decimal point of 129 one unit left (You are dividing by 10).
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[tex]\frac{48.6}{30}=\frac{243}{\frac{5}{30}}=\frac{243}{150}=\frac{81}{50}[/tex]Express 48.6 as 243/5, then use division of fractions to get 243/150, then simplify 243/150 as 81/50
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[tex]\frac{48.6}{x}=\frac{\frac{243}{5}}{x}=\frac{243}{5x}[/tex]Express 48.6 as 243/5, then use division of fractions to get 243/5x
Which relation is a function?
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Use the vertical line test.
hello I am needing help how to solve the attached photo
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For this question, we can see our function has two variables ("x" and "y"). So all we h=need to do is to substitute the different values of "x" to get the corresponding values of "y". So, let's calculate as follows:
Once we got all y-values we can finish our table as follows:
And that is our final answer.
1 A Great Way to Make Money POW ID: 965 High School, Discrete Math, Discrete Math Print Problem As your sixteenth birthday approaches you are looking for ways to make money so you can buy a used car. Currently, you earn $10 a week for doing chores around the house. Your father realizes that you are trying to save up, and offers you the following deal. You can either be paid the $10, or you can pull two bills from a brown paper bag. In the bag there are two $1 bills, two $5 bills, and a $10 bill. For example, you might pull out a $1 bill followed by a $5 bill, and earn only $6. Or you might pull out the $10 bill followed by a $5 bill and earn $15. If you were given this option every week, what would be better for you to do in the long run? Is pulling two bills from the paper bag a great way to make money?
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The problem is about probability, so we need to know actually what is the probability of win more than $10 with the bag option, and see what is better in the long run. So we first are going to find
[tex]P(x>10)[/tex]Where x is "the resultin money of pulling two bills from the paper bag", now
[tex]undefined[/tex]HELP!!!
In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.
54°
58°
122°
126°
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The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.
What is a triangle?
A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
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If $360 is invested at an interest rate of 4% per year and is compounded quarterly, how much will the investment be worth in 18 years?Use the compound interest formula A = P(1 + r over n)nt.
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Answer:
The formula for compound interest is given below as
[tex]\begin{gathered} A=P\left(1+\frac{r}{n}\right?^{nt} \\ P=money\text{ invested=\$360} \\ r=rate=4\% \\ n=number\text{ of times compounded=4} \\ t=time=18years \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A=P\left(1+\frac{r}{n}\right?^{nt} \\ A=360\left(1+\frac{4}{400}\right?^{4\times18} \\ A=360\left(1.01\right)^{72} \\ A=360\times2.0471 \\ A=736.96 \end{gathered}[/tex]Hence,
The total amount accrued, principal plus interest, with compound interest on a principal of $360.00 at a rate of 4% per year compounded 4 times per year over 18 years is $736.96.
The graph of a function f is shown below.Find f(3). f(3)=
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when x is 3, y is 1
look 3 units to the right, and then see where the line crosses
find the slope of the line that contains the two points shown below simplify as much as possible and do not convert to a decimal if you get a fraction
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Let:
[tex]\begin{gathered} (x1,y1)=(-5,-3) \\ (x2,y2)=(5,5) \end{gathered}[/tex]The slope is given by:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-(-3)}{5-(-5)}=\frac{8}{10}=\frac{4}{5}[/tex]Four times the quotient of a number and 9 plus 14, how do I right it as an expression?
Answers
The expression is written as (4n/9) + 14
What is an expression?
An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. Many writers differentiate between an expression and a formula, with the former referring to a mathematical item and the latter referring to a statement about mathematical things. For instance, is a formula. However, in modern mathematics, and particularly in computer algebra, formulae are considered as expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.
The expression is written as (4n/9) + 14
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i need help with this question.use the function u= c + 4 to find the value of u when c = 1
Answers
Answer:
5
Explanation:
Given the below function;
[tex]u=c+4[/tex]To find u when c = 1, all we have to do is substitute the value of c into the above equation and solve for u;
[tex]\begin{gathered} u=1+4 \\ u=5 \end{gathered}[/tex]fia needs 3/4 cup of sugar but only has a a 1/3 cup and a 1/8 cup which one should she use and why
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Fia needs 3/4 cub of sugar
She has only a 1/3 cup and a 1/8 cup
To find which cup should she use :
Divide 3/4 by 1/3 and divide 3/4 by 1/8
The operation which give integer number is the true choice
So,
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\cdot\frac{3}{1}=\frac{9}{4}=2\frac{1}{4} \\ \\ \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\cdot\frac{8}{1}=\frac{24}{4}=6 \end{gathered}[/tex]So, it should be use a 1/8 cup, so 6 times of a 1/8 cup will give 3/4 cup of sugar.
So, the answer is : a 1/8 cup
VAn item costs $310 before tax, and the sales tax is $6.20.Find the sales tax rate. Write your answer as a percentage.0%X5?
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Given:
The cost of the item is
[tex]\text{ \$}310.[/tex]The sales tax is
[tex]\text{ \$}6.20[/tex]Required:
We have to find the Sale tax rate and write the answer in percentage.
Explanation:
The formula for the sales tax rate is
[tex](\frac{\text{ sales tax}}{\text{ cost}}\times100)\%.[/tex]Therefore, The required sales tax rate is
[tex](\frac{6.20}{310}\times100)\%=(\frac{620}{310})\%=2\%.[/tex]Final answer:
Hence the final answer is
[tex]2\%.[/tex]Can you please help me solve the equation in the picture?
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Hello! First, let's write the equation:
Find the equation of the line with Slope = −3-3 and passing through (2,−13)(2,-13) . Write your equation in the form y=mx+by=mx+b .
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Given that the slope of the line is:
[tex]m=-3[/tex]And knowing that the line passes through this point:
[tex]\mleft(2,-13\mright)[/tex]You need to remember that the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
In order to find the value of "b", you can substitute the slope and the coordinates of the point on the line, into the equation:
[tex]-13=(-3)(2)+b[/tex]Now you can solve for "b":
[tex]\begin{gathered} -13=-6+b \\ -13+6=b \\ b=-7 \end{gathered}[/tex]Knowing "m" and "b", you can write the following equation of the line in Slope-Intercept Form:
[tex]y=-3x-7[/tex]Hence, the answer is:
[tex]y=-3x-7[/tex]A cyclist rides his bike at a speed of 24miles per hour what is this speed in miles per minute how many miles will the cyclist travel in 5minutes ?
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If the speed of the cyclist is 24 miles/hour
In miles per minutes, 60 minutes = 1 hour
To convert into miles per minutes,
[tex]\text{Speed in miles per mins=}\frac{24}{60}=0.4\text{ miles/min}[/tex]Speed in miles/min is 0.4 miles/min
If the cyclist travels for 5 minutes, distance travelled in miles will be,
[tex]\begin{gathered} dis\tan ce=\text{speed}\times\text{time} \\ \text{Where sp}eed=0.4\text{ miles/min} \\ \text{time}=5\min \\ \text{distance}=0.4\text{ miles/min}\times5\min =2\text{ miles} \end{gathered}[/tex]Distance travelled in miles is 2 miles
What is a possible step when solving for x? Sey. 51x + 2x = 37
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Solving for x, the value of x is 37/53
Algebraic expression: what is it?An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. As an illustration, the algebraic expression 3x2 2xy + c
Given,
51x + 2x = 37
To resolve the x equation
51x + 2x = 37
Including the xs
53x = 37
53 divided between the two sides
53x/53 = 37/53
x = 37/53
As a result, by solving for x in the subsequent steps, we obtain:
x = 37/53
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The original blueprint for the Morenos' livingroom has a scale of 2 inches = 5 feet. The familywants to use a new blueprint that shows thelength of the living room to be 15 inches. Ifthe width of the living room on the originalblueprint is 6 inches and the length is 9.6 inches,what are the scale and the width of the newblueprint?
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Step 1
The original blueprint of the family has a scale of 2inches=5feet
The family wants to use a new blueprint that shows the length of the living room to be 15 inches.
Step 2
The width of the living room is
[tex]\frac{6}{2}\times5=15feet[/tex]Hence, the length of the living room is
[tex]\frac{9.6}{2}\times5=24feet[/tex]So the new scale is;
[tex]\begin{gathered} \frac{15}{24}=\frac{5}{8} \\ ie\text{ 5inches=8f}eet \end{gathered}[/tex]The width of the new print is;
[tex]\begin{gathered} \frac{6}{2}\times5=15feet \\ \frac{15}{8}\times5=9.375inches \end{gathered}[/tex]Hence the scale of the new print is; 5inches = 8feet
Width of new blue print=9.375inches
Which expression can be used to find the difference of the polynomials?
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[10m + (-7m)] is the formula that can be used to find the difference between the polynomials (10m - 6) and (7m - 4). + [(-6) + 4].
[10m + (-7m)] + [(-6) + 4]
With more calculation
= 10m - 7m - 6 + 4
so we do
= 3m - 2 …. (2)
As (1) and (2) are equivalent
The polynomial's differences can be calculated using the equation [10m + (-7m)] + [(-6) + 4].
In order to find the difference between the polynomials, one can utilize the formula [10m + (-7m)] + [(-6) + 4].
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At a school concert the total value of tickets sold was $3990. Student tickets sold for $8 and adult tickets sold for $11. The number of adult tickets sold was 6 less than 4 times the number of student tickets. Find the number of student tickets sold.
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The number of student tickets sold is 78.
Given,
The number of student tickets sold = x
The number of adult tickets sold = 4x - 6
Total value of tickets sold = $3990
Value of one student ticket = $8
Value of one adult ticket = $11
Now, we have to find the number of student tickets sold:
Here,
The expression :8x + 11(4x - 6) = 3990
Solve the expression:
8x + 44x - 66 = 3990
52x - 66 = 3990
Add 66 to both sides
52x - 66 + 66 = 3990 + 66
We get,
52x = 4056
Divide 52 on both sides
52x / 52 = 4056/52
That is,
x = 78
Therefore,
The number of student tickets sold is 78.
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community gym charges a $50 membership fee and a $60 monthly fee. Workout gym charges a $225 fee and a $5 monthly fee. After how many months will the total amount paid to both gyms be the same?
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Step 1 : Let's review the information given to us to answer the problem correctly:
Community Gym = $50 (Membership fee) + $ 60 (Monthly fee)
Workout Gym = $ 225 (Membership fee) + $ 5 (Monthly fee)
Step 2: Let's write the equation to answer the question, as follows:
Let x to represent the number of months that the total amount paid to both gyms will be the same
Community Gym = Workout Gym
Therefore,
50 + 60x = 225 + 5x
Like terms:
60x - 5x = 225 - 50
55x = 175
Dividing by 55 at both sides:
55x/55 = 175/55
x = 3.18 months
0.18 * 30 = 5.4 days
Step 3: Interpretation of the answer
Approximately after 3 months and 5 days and a half the total amount paid to both gyms will be the same
Describe the similarity transformation that maps the preimage to the image. I need help with question 4
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The coordinates of the vertices of the original shape are given to be:
[tex]\begin{gathered} L\Rightarrow(6,6) \\ M\Rightarrow(0,4) \\ N\Rightarrow(0,6) \end{gathered}[/tex]The transformed shape coordinates are given to be:
[tex]\begin{gathered} L^{\prime}\Rightarrow(7,2) \\ M^{\prime}\Rightarrow(4,1) \\ N^{\prime}\Rightarrow(4,2) \end{gathered}[/tex]On observation, the shapes show a dilation and a shift in position.
The image has a scale factor of 1/2, meaning it is reduced by 1/2. Therefore, the original coordinates will be reduced to give:
[tex]\begin{gathered} L^{\doubleprime}\Rightarrow\frac{1}{2}(6,6)=(3,3) \\ M^{\doubleprime}\Rightarrow\frac{1}{2}(0,4)=(0,2) \\ N^{\doubleprime}\Rightarrow(0,6)\Rightarrow(0,3) \end{gathered}[/tex]The translation of the initial image can be gotten by subtracting the corresponding coordinates:
[tex]\begin{gathered} L^{\prime}-L^{\doubleprime}=(7-3,2-3)=4,-1 \\ M^{\prime}-M^{\doubleprime}=(4-0,1-2)=4,-1 \\ N^{\prime}-N^{\doubleprime}=(4-0,2-3)=4,-1 \end{gathered}[/tex]All the differences are the same. This means that the image moves to the right by 4 units and down by 1 unit.
The dilation rule with a scale factor of k is given to be:
[tex](x,y)\to(kx,ky)[/tex]The translation rule for a units to the right and b units down is given to be:
[tex](x,y)\to(x+a,y-b)[/tex]Combining both rules, we have:
[tex](x,y)\to(kx+a,ky-b)[/tex]Given:
[tex]\begin{gathered} k=\frac{1}{2} \\ a=4 \\ b=1 \end{gathered}[/tex]Therefore, the transformation is given to be:
[tex]\Rightarrow(\frac{1}{2}x+4,\frac{1}{2}y-1)[/tex]Hey, I’m really having trouble with this question and could use some help.
Answers
From the given graph, we have 2 points with coordinates:
[tex]\begin{gathered} (x_1,y_1)=(1,2) \\ \text{and} \\ (x_2,y_2)=(4,1) \end{gathered}[/tex]The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]With the given points, we can find the slope m as follows:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{then} \\ m=\frac{1-2}{4-1} \end{gathered}[/tex]which gives
[tex]m=\frac{-1}{3}=-\frac{1}{3}[/tex]Then, our line equation has the form
[tex]y=-\frac{1}{3}x+b[/tex]Now, we can find the y-intercept b by substituting one of the two given points. For instance, if we substitute point (1,2) into the last result, we get
[tex]2=-\frac{1}{3}(1)+b[/tex]which gives
[tex]\begin{gathered} 2=-\frac{1}{3}+b \\ \text{then} \\ 2+\frac{1}{3}=b \\ \frac{7}{3}=b \end{gathered}[/tex]then, the line equations is
[tex]y=-\frac{1}{3}x+\frac{7}{3}[/tex]a) The linear function is
[tex]f(x)=-\frac{1}{3}x+\frac{7}{3}[/tex]b) What is f(6)?
In this case, we have that x=6. Then, by replacing this value into our function, we get
[tex]f(6)=-\frac{1}{3}(6)+\frac{7}{3}[/tex]which gives
[tex]\begin{gathered} f(6)=-\frac{6}{3}+\frac{7}{3} \\ f(6)=\frac{-6+7}{3} \\ f(6)=\frac{1}{3} \end{gathered}[/tex]therefore, the answer for part b is
[tex]\frac{1}{3}[/tex]Please help would really appreciate!!!!
Answers
A) f(-1) + f(3) = 0
B) f(-1) - f(3) = 0
How the functions are calculated?
[tex]f(x)=2x^{2} -4x-6[/tex]
f(-1) = 2(1) -4(-1) -6
=2+4-6
=6- 6
=0
f(3) = 2(9)- 4(3) - 6
=18- 12- 6
=18 - 18
= 0
A) f(-1) + f(3) = 0 + 0 = 0
B) f(-1) - f(3) = 0 - 0 = 0
What are functions?
A relationship between a group of inputs and one output each is referred to as a function. It is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.y = f (x) is how functions are typically represented .To learn more about functions, refer:
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I need help with this question part a and b
Answers
Answer:
• (a)f[g(x)]=(3x-84)/4
,• (b)7.5
Explanation:
A function that converts shoe sizes in France to those in England is:
[tex]g(x)=\frac{3x-94}{4}[/tex]A function that converts shoe sizes in England to those in the United States is:
[tex]f(x)=x+\frac{5}{2}[/tex]Part A
To find a function that converts shoe sizes in France to those in the United States, we evaluate the composition, g(f(x)).
[tex]\begin{gathered} f(x)=x+\frac{5}{2} \\ f[g(x)]=g(x)+\frac{5}{2}=\frac{3x-94}{4}+\frac{5}{2}\frac{=3x-94+10}{4} \\ \implies f[g(x)]=\frac{3x-84}{4} \end{gathered}[/tex]A function that converts shoe sizes in France to those in the U.S is:
[tex]f[g(x)]=\frac{3x-84}{4}[/tex]Part B
Given a size 38 shoe in France:
[tex]f[g(38)]=\frac{3(38)-84}{4}=\frac{114-84}{4}=\frac{30}{4}=7.5[/tex]A size 38 shoe in France is of size 7.5 in the United States.
The two-way table shows the number of students that do or do not do chores at home and whether they receive an allowance or not. Allowance No Allowance Do Chores 13 3 Do Not Do Chores 5 4 a. How many total students do chores? b. What is the relative frequency of students that do chores and get an allowance to the number of students that do chores? Round to the nearest hundredth if necessary.
Answers
Given the table showing the number of students who do or do not perform chores, and who do or do not receive an allowance, we can add the numbers along the rows and columns, as shown in the diagram below:
Now, that we have summed the numbers along the vertical and horizontal directions, we can now proceed to answer the questions asked.
a.) The total number of students who do chores is equal to the horizontal sum of the numbers in the 'DO CHORES' row. This value is 16
Thus, 16 students do chores
b) The relative frequency of the students that do chores and get an allowance to the number of students that do chores is simply the ratio of the value in the cell that represents an intersection of the first 'DO CHORES' row, and the first 'ALLOWANCE' column, to the value that represents the sum of all the students that do chores ( i.e, the value at the end of the first row).
Thus, this is equal to = 13/16
Therefore, 13/16 is the relative frequency of the students that do chores and get an allowance to the number of students that do chores
c) The relative frequency of the students that do not do chores nor get an allowance to the total number of students, is simply the ratio of the value in the cell that represents an intersection of the second 'DO NOT DO CHORES' row, and the second 'NO ALLOWANCE' column, to the sum of the values in the last row or the last column.
Thus, this is equal to = 4/( 18 + 7) OR 4/(16 + 9) both of which is still 4/25
Therefore, 4/25 is the relative frequency of the students that do not do chores nor get an allowance to the total number of students.
d) The students who do not do chores are a total of 9
Of this 9, the number of students that do receive their allowance fall under the 'ALLOWANCE' column, and is equal to 5.
Therefore, expressed as a percentage of those who do not do their chores, the students who do not get an allowance are = (5/9) * 100 = 55% ( to the nearest whole number)
Thus 55% of students who do not do chores do not get an allowance
convert 3.2 yards to feet
Answers
1 yard is equivalent to 3 feet. Then to convert 3.2 yards to feet we can use the next proportion,
[tex]\frac{1\text{ yard}}{3.2\text{ yard}}=\frac{3\text{ ft}}{x\text{ ft}}[/tex]Solving for x,
[tex]\begin{gathered} 1\cdot x=3\cdot3.2 \\ x=9.6 \end{gathered}[/tex]3.2 yards is equivalent to 9.6 feet
Factor completely 12m^2-3
Answers
Answer:
3 ( 2m-1)(2m+1)
Step-by-step explanation:
12m^2-3
Factor out the 3
3( 4m^2 -1)
3 ( ( 2m)^2 - 1^2)
Using the difference of squares ( a^2 - b^2) = ( a-b) (a+b)
3 ( 2m-1)(2m+1)
12m^2 - 3 = 3(4m^2 - 1)
but the bracket contains the difference between two squares
= 3(2m - 1)(2m + 1)
Explain why a V-shaped graph does not represent a linear function.
Answers
A V-shaped graph belongs to an absolute value function or a piecewise function, never to a linear function (these are graphed only with a single line).
Why a V-shaped graph does not represent a linear function?This is really trivial question.
A linear function has a graph that is a straight line.A V-shaped graph is not a straight line, is a V.So the answer is really trivial, as you can see.
But let's explain it a little bit more.
The only functions that have V-shaped graphs are piecewise functions (formed of two linear equations) or absolute value equations, neither of these are exactly linear (but they are made of "linear like parts").
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