To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
If f(x)=x²+5 and g(x)=3x, find
a. (f+ g)(x)
b. (f -g)(x)
c. (f . g)(x)
d. (f/g)(x)
a. (f + g)(x)= _____
(Simplify your answer.)
The value of the functions are:
a. (f + g)(x) = x² + 3x + 5
b. (f - g)(x) = x² - 3x + 5
c. (f * g)(x) = 3x³ + 15x
d. (f/g)(x) = (x² + 5)/(3x)
How to Solve Functions?If we are given an expression of functions, we need to plug in each of the given functions into the equation and solve as you would simplify an algebraic expression.
We have the functions:
f(x) = x² + 5
g(x) = 3x
a. (f + g)(x) means we are going to add the functions f(x) and g(x):
(f + g)(x) = x² + 5 + 3x = x² + 3x + 5
b. (f - g)(x) means we are going to find the difference of the functions f(x) and g(x):
(f - g)(x) = x² + 5 - 3x = x² - 3x + 5
c. (f * g)(x) means we are to find the product of the two functions f(x) and g(x):
(f * g)(x) = (x² + 5)(3x) = 3x³ + 15x
d. (f/g)(x) means we are to find the quotient of the two functions f(x) and g(x):
(f/g)(x) = (x² + 5)/(3x)
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determine each quotient 5 divided by 1/105 divided by 3/105 divided by 9/10
Solution
- To divide by a fraction, you simply invert the fraction and instead multiply by the inverted fraction.
- Thus, we have:
[tex]\begin{gathered} \text{ 5 divided by }\frac{1}{10}: \\ \\ 5\div\frac{1}{10}=5\times\frac{10}{1}=50 \\ \\ \text{ } \\ \text{ 5 divided by }\frac{3}{10}: \\ \\ 5\div\frac{3}{10}=5\times\frac{10}{3}=\frac{50}{3} \\ \\ \\ \\ \text{ 5 divided by }\frac{9}{10}: \\ \\ 5\div\frac{9}{10}=5\times\frac{10}{9}=\frac{50}{9} \end{gathered}[/tex]a rectangle solid measures 8cm long by 2cm wide by 2cm high. what is the surface-to-area-to-volume ratio?
The ratio of surface to area to volume of the given rectangle is 5 : 4 : 8
Length of the rectangle , l = 8 cm
Breadth of the rectangle , b = 2 cm
Height of the rectangle , h = 2 cm
Perimeter of the rectangle is
P = 2 (l +b)
= 2(8 + 2)
= 2 (10)
= 20 cm
Therefore , the perimeter of the rectangle is 20 cm
Area of the rectangle is
A = l x b
A = 8 x 2
A = 16 cm²
Therefore , area of the rectangle is 16 cm²
Volume of the rectangle is
V = l x b x h
V = 8 x 2 x 2
V = 8 x 4
V = 32 cm³
Therefore, volume of the rectangle is 32 cm³
Ratio of surface to area to volume = 20 : 16 : 32
= 5 : 4 : 8
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Find the exact value of cos 4pi/3 in simplest form with a rational denominator?
The given expression is
[tex]cos\frac{4\pi}{3}[/tex]Since the angle is greater than pi, then it lies in the 3rd quadrant
Since in the 3rd quadrant the value of cosine is negative, then we will use the expression
[tex]cos\frac{4\pi}{3}=cos(\pi+\frac{\pi}{3})=-cos\frac{\pi}{3}[/tex]Since the value of cos(pi/3) = 1/2, then
[tex]\begin{gathered} cos\frac{\pi}{3}=\frac{1}{2} \\ \\ cos\frac{4\pi}{3}=-cos\frac{\pi}{3}=-\frac{1}{2} \end{gathered}[/tex]The answer is -1/2
2.85-6.2 divided by 2 square
Answer:
142.5 i think that answer
GIVEN: AD is angle bisector of
Given:
AD is angle bisector of angle BAC.
AB = AC.
The objective is to prove BD = DC.
Step 1:
Statement: AD is angle bisector of angle BAC.
Reason: Given.
Step 2:
Statement:
[tex]\angle BAD=\angle\text{DAC}[/tex]Reason: Definition of angle bisector.
Step 3:
Statement:
[tex]AB\cong AC[/tex]Reason: Given
Step 4:
Statement: AD = AD.
Reason: Reflexive.
Step 5:
Statement:
[tex]\Delta BAD\text{ }\cong\text{ }\Delta CAD[/tex]Reason: By SAS criteria.
Step 6:
Statement:
[tex]BD\cong DC[/tex]Reason: By Corresponding parts of congruent triangles (CPCT).
Hence, the required results are obtained.
Michael has 2 1/2 cups of orange juice in a jar he pours the juice into glasses that each hold 3/4 cups how many glasses can he fill?
Number of glasses Michael can fill is [tex]3\frac{1}{3}[/tex] or 3.33 cups
How to find amount of 1 when amount of many are given ?A number is divided in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. Of course, in order to be fair, you should always pay each person the same amount.
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Given: Number of cups Michael have = 2 1/2 cups = 2 + 0.5 = 2.5 cups
To find : How many glasses he can fill .
So since each glass holds 3/4 cups = 0.75
Thus number of glasses which can be filled = 2.5 / 0.75
= 3.33 or [tex]3\frac{1}{3}[/tex]
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How do I use the graphs to evaluate the expressions
Given the graph, we cam find f(-3)+g(-2) below.
Explanation
[tex]\begin{gathered} f(-3)=-2 \\ g(-2)=0 \\ f(-3)+g(-2)=-2+0=-2 \end{gathered}[/tex]Answer: -2
Skill BuildeWatch the video and then solve the problem given below.Click here to watch the videoMargaret drove to a business appointment at 40 mph. Her average speed on the return trip was 30 mph. The return trip took 1/3 hour longer because of heavy traffic. How far did she travel to theappointment?She traveled milesEnter your answer in the answer box and then click Check Answer.All parts showing
Let's call the distance to the appointment 'd', and the time of the first travel (going to the appointment) 't'.
Now, we need to use the formula for the distance:
[tex]\text{distance}=\text{average speed }\cdot\text{ time}[/tex]For the first part of the trip, we have the distance 'd', the average speed is 40 mph and the time is 't':
[tex]d=40\cdot t[/tex]Then, for the second part of the trip (return trip), the distance is also 'd', the average speed is 30 mph, and the time is 't + 1/3', because she took 1/3 hour longer than the first trip.
So we have that:
[tex]d=30\cdot(t+\frac{1}{3})=30t+10[/tex]Now, we just need to equate both 'd':
[tex]\begin{gathered} 40t=30t+10 \\ 10t=10 \\ t=1 \end{gathered}[/tex]So the time 't' is 1 hour. Now we can use that to find the distance 'd':
[tex]d=40t=40\cdot1=40[/tex]So the distance to the appointment is 40 miles.
The table represents an absolute value function f(x).
x f(x)
−2 4
−1 3
0 2
1 1
2 0
3 1
4 2
5 3
6 4
What are the vertex and range of the function?
Vertex (0, 2), Range: {y | 0 ≤ y < ∞}
Vertex (0, 2), Range: {y | 2 ≤ y < ∞}
Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
Vertex (2, 0), Range: {y | 2 ≤ y < ∞}
From the table of the absolute value function the vertex and the range of the function is Vertex (2, 0), Range: {y | 0 ≤ y < ∞}
What is vertex of a function?the vertex represents the point where the graph crosses the axis of symmetry. This point usually occurs mid way the graph.
Examining the table shows that the coordinates of the vertex is
2 for the x coordinate0 for the y coordinateTherefore vertex ( 2, 0)
What is range ?The range is the point covered by the y coordinate. Since the ertex has the y coordinate as zero, this means that o is part of the values of the y making the third option the best choice
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Answer: Option 1
Step-by-step explanation:
just took the test
function c gives the cost,in dollars, of buying n apples. what does each expression or equation represent in this stiuation1.C(5)=4.502C(2)
1)
From the function given, the cost of 5 apples is $4.50
5 apples cost $4.50
MTR Apply Mathematics During a drought, the water level of a lake
decreases 3 inches every week. What will be the change in the water level
of the lake if the drought lasts for 7 weeks?
The level of water decreases would be 21 inches in 6 weeks if the water level of a lake decreases by 3 inches every week.
What are Arithmetic operations?The addition, subtraction, division, and multiplication of built-in functions can also be used to specify arithmetic operations. The term "arithmetic operator" refers to the operator that executes the calculation.
We have been given that a lake's water level decreases 3 inches every week when there is a drought.
We have to determine the lake's water level looks like after a seven-week drought.
As per the given condition,
Level of water decreases a week = 3 inches.
Level of water decreases in 6 weeks = 7 × 3 = 21 inches
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Use the properties of determinants to find the value of the second determinant, given the value of the first.
According to the sum property, we have:
[tex]\begin{gathered} det\begin{bmatrix}{32-s} & {16-t} & {64-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=det\begin{bmatrix}{32} & {16} & {64} \\ {0} & {0} & {0} \\ {0} & {0} & {0}\end{bmatrix}+det\begin{bmatrix}{-s} & {-t} & {-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix} \\ det\begin{bmatrix}{32} & {16} & {64} \\ {0} & {0} & {0} \\ {0} & {0} & {0}\end{bmatrix}=0 \\ det\begin{bmatrix}{-s} & {-t} & {-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-det\begin{bmatrix}{s} & {t} & {u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-3 \\ \therefore det\begin{bmatrix}32{-s} & {16-t} & {64-u} \\ {v} & {w} & {x} \\ {4} & {2} & {8}\end{bmatrix}=-3 \end{gathered}[/tex]b. Express the mass of 21,000 molecules of oxygen in scientific notation.
grams
(Type your answer using the appropriate number of significant digits. Type you
The mass of 21,000 molecules of oxygen in scientific notation is expressed as 1.1151 x [tex]10^{-28}[/tex] grams in the proper significant digits.
What are Significant Digits?The number that is provided as digits is tried and established using significant figures. A meaningful representation of numbers is carried by these digits.
The crucial or important digits that can accurately represent the exact meaning of a certain number are known as the significant figures of that number.
Frequently, significant digits are employed in place of figures. By counting out each of the values beginning with the first non-zero digit on the left, we can use it to determine the number of significant digits.
The molecular mass of Oxygen is seen as 32 grams.
So, 6.023 x [tex]10^{23}[/tex] molecules of oxygen have mass as 32 grams
So, one molecule of oxygen has mass = [tex]\frac{32}{6.023 * 10^{23}}[/tex] grams
= 5.31 x [tex]10^{-23}\\[/tex] grams
So, 21,000 molecules will have mass = 21,000 x 5.31 x [tex]10^{-23}\\[/tex] grams
= 111510 x [tex]10^{-23}\\[/tex] grams
= 1.1151 x [tex]10^{-28}[/tex] grams
Thus 21000 molecules of oxygen have a mass of 1.1151 x [tex]10^{-28}[/tex] grams.
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If you save $750 monthly for the next 30 years, how much would your retirement fund be worth, assuming that you can earn 3%, compounded monthly?
The amount compounded monthly is 1092.63.
The expression for calculating the amount compounded monthly is given by the formula
CI = P[tex](1 + (\frac{r}{12} ) )^{12t}[/tex] - P
where P is the principal amount, r is the interest rate in decimal form, and t is the time.
The Data and information which are provided in the question are,
The principle amount, P = 750
The rate of interest, R = 3%, so 3÷100 = 0.03
The period, t = 30.
By substituting the data in the equation, the equation becomes
CI = 750×[tex](\frac{1+0.03}{12}) ^{360}[/tex] - 750.
By solving the above equation, the result is obtained as CI = 1092.63
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Please help. Need help bad don’t know what to do
The combination that gives the most profit exists 12nVIP rings and 12 SST rings (900 day).
What is meant by linear programming?When a linear function is exposed to various constraints, it is maximized or reduced using the mathematical modeling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
R = 40 V + 35 S
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
Amount of rings (less or equal than 24 a day):
V + S ≤ 24
Amount of man-hours (up to 60 man-hours per day):
3 V + 2 S ≤ 60
The number of rings of each type is a positive integer:
V, S ≥ 0
This restrictions can be graphed and then limit the feasible region. The graph is attached.
In which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V = 0 and S = 24
R = 40 V + 35 S = 40 × 0+35 × 24 = 0 + 840
R = 840
Point 2: V = 12 and S = 12
R = 40 V + 35 S = 40 × 12 + 35 × 12 = 480 + 420
R = 900
Point 3: V = 20 and S = 0
R = 40 V + 35 S = 40 × 20+35 × 0 = 800 + 0
R = 800
The combination that gives the most profit is 12nVIP rings and 12 SST rings (900 day).
The complete question is:
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
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(10) Use the following freauency bar graph to answer the following questions.Chart of MTH 150 GradescountGradesa) How many students received a C for the course?b) How many students passed the course (with a C or higher)?c) How many students received no credit for the course (i.e. got an F)?d) How many total students took the course?e) Which letter grade represents the mode?
From the frequency bar graph, we can read the following information.
15 students got an A
6 students got a B
5 students got a C
10 students got a D
14 students got an F
a) As described above, 5 students got a C
b) Adding up the frequencies of the students who got C or higher:
5 + 6 + 15 = 26
26 students passed the course
c) Assuming the students who did not pass got any credits, then we add up the students with D and F: 10 + 14 = 24
24 students received no credit for the course
d) Total students in the course: 15 + 6 + 5 + 10 + 14 = 50
e) The mode is the letter grade that got the highest frequency:
Mode = A
A got 15
Aidan buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.
What is the probability that Aidan reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Write your answer as a percent. Round to the nearest tenth of a percent.
Answer- 62%
Step-by-step explanation
5+5+8+8= 26 There are 8 peanut butter cookies,so 8/26 is the chance we will get a peanut butter cookie. In percentage form that is 0.307692308 or 30% chance that a peanut butter cookie will be selected. This also means that since there are 8 oatmeal there is a 30% percent chance for those as well.5/26 is 0.192307692, which is almost 20 percent. 30 +30 +20+20 is 100 percent. Now that we know there is a 30 percent for both peanut butter and oatmeal, we would have to have the percent of 8+8/26. 16/26 is 0.615384615. This means that the chance of picking a peanut butter then oatmeal cookie, back-to-back would be around 62%
Hope this helps good luck.
at a shoe store shoes are one third of their original price the sale price of a pair of gym shoes is $ 15.50 write and solve an equation that could be used to find the original cost of the shoes
We will write an equation to find the original cost as follows:
[tex]15.50=\frac{x}{3}[/tex]And the general equation will be:
[tex]y=\frac{x}{3}[/tex]Here y is the price after discount and x the price without discount.
****
Since we have that the price is a third of the original, then the discounted price is found by multiplying the original value of the shoe times 1/3. After this operation takes place, the value we will obtain is the discounted prices [1/3 their original value].
Question 5
Use technology to find the line of best fit for the following data.
(1,4), (2, 3), (3,5), (4,4), (5,5)
When the equation of the line is in the form y=mx+b, what is the value of **m**?
Enter your answer as a decimal rounded to the nearest tenths place, like this: 42.5
Click on the following link to use the GeoGebra graphing calculator .
The value of b is equal to 0 in slope-intercept form equation .
What is slope-intercept form?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is frequently known as the y = mx + b form.The data points are:
(1,4), (2, 3), (3,5), (4,4), (5,5)
The equation of best fit line in the form of and then find the value of b.
The general form of best fit line is
y = mx + c ...(i)
Where, m is the slope of best fit line and b is the y-intercept of the line.
Using the graphing calculator, we get the equation for the best fit line and the equation is
y = x ...(ii)
On comparing (i) and (ii), we get
c = 0
Therefore, the value of m is equal to 0
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How many gallons of water does the full tank hold?
Given:
a.) After 2 minutes, the tank contains 400 gallons.
b.) After 5 minutes, the tank is full.
For us to be able to determine how many gallons of water does the full tank hold, let's first determine the discharge rate of the water filling in the tank.
We get,
[tex]\text{ Rate of discharge = }\frac{\text{ Volume}}{\text{ Time}}\text{ = }\frac{400\text{ Gallons}}{2\text{ Minutes}}[/tex][tex]\text{ Rate of discharge = 200 Gallons/Minute}[/tex]Since the tank is after 5 minutes of pumping water at a constant rate, we will just multiply the rate of discharge by the time it took for the tank to be full.
We get,
[tex]\text{Volume of the Tank = Time x Rate of Discharge = 5 (Minutes) x 200 Gallons/(Minute)}[/tex][tex]\text{ Volume of the Tank = 1000 Gallons}[/tex]Therefore the volume of the tank is 1000 Gallons
Please help!! Will give brainliest
f(x)=3/[tex]4\sqrt{x}[/tex] evaluate function f ' (3) = [tex]-1/4.3 root 1/4[/tex]
f(x)=3/[tex]4\sqrt{x}[/tex] evaluate function f ' (7)= [tex]-3/4.7root5/4[/tex]
How is a function evaluated?
Finding the value of f(x) =... or y =... that corresponds to a certain value of x is what it means to evaluate a function. Simply swap out all instances of x with the value of x to do this. For instance, x has been given the value 4 if we are asked to evaluate f(4).
root function illustration
F(x)=x f (x) = x is the square root function. The formula for the cube root is f(x)=3xf(x)=x3. A function that is defined by a radical expression is known as a radical function.
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For the following function, determine whether the function is one-to-one.{(4,9), (3,6), ( - 8,11), (1, -17)}Is the function a one-to-oneYES OR NO
Answer
The function is one-to-one.
Check Explanation.
Explanation
Like the name suggests, one-to-one functions have each input variable having exactly one unique output. That is, multiple inputs never give the same output.
Also noting that the data in the function are written as
(x, y) OR (Input, Output)
For this question, we see that all of the input variables are different and all have unique output variables.
Hence, this function is a one-to-one function.
Hope this Helps!!!
What is the length of a rectangle with width 10 in. and area 97 in.²?
Answer:
9.7
Step-by-step explanation:
97/10= 9.7
formula for rectangle= length x width
area divided by width= 97/10
97/10=9.7
length=9.7
9.7x10=97
Which is the area of the figure, in square units
The area of the given figure ABCDEFG is 28 units².
What do we mean by area?The area is the total amount of space occupied by a flat (2-D) surface or an object's shape. On a piece of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.So, the area of the given figure:
First, let's mark all the points and name the figure ABCDEFG.We can clearly see that side CE = CB = BD = EC = 4 units making ECBD a square.And, rest 3 triangles are divided from the figure of different dimensions.Now, calculate areas separately and as as follows:
Area of square ECBD:
a²4²16The area of square ECBD is 16 units².
Area of triangle ACB:
1/2 × b × h1/2 × 4 × 31/2 × 126The area of triangle ACB is 6 units².
Area of triangle CEG:
1/2 × b × h1/2 × 2 × 41/2 × 84The area of triangle CEG is 4 units².
Area of triangle BDF:
1/2 × b × h1/2 × 1 × 41/2 × 42The area of triangle BDF is 2 units².
Area of the given figure: 16 + 6 + 4 + 2 = 28 units²
Therefore, the area of the given figure ABCDEFG is 28 units².
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graph the line with the slope -3/2 and y intercept -1
Answer: y = -3/2x - 1
Step-by-step explanation:
y = mx + b
1. m is the slope so substitute -3/2 for m. ( y = -3/2x + b)
2. b is the y intercept so substitute -1 in for b. ( y = -3/2x - 1)
which best describes your ability determine best method for solving a system of linear equations
The best method for solving a system of linear equations is the substitution method.
What is a system of equations?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
We have been given the system of the equations as;
y = -2x + 2
y = 4x + -4
Thus, y = -2 x + 2 ........ equation number 1
y = 4 x - 4.............. equation number 2
Then substitute equation number 2 in equation number 1
4 x - 4 = -2 x + 2
4 x + 2 x = 2 +4
6 x = 6
so, x = 1
Now substitute x= 1 in equation number 2;
Therefore y =( 4 × 1) - 4
y = 4 - 4 = 0
For x = 1 and y = 0
Hence, the best method for solving a system of linear equations is the substitution method.
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The complete question is;
which best describes your ability to determine the best method for solving a system of linear equations. Then solve the system.
y = -2x + 2
y = 4x + -4
Mina got a story book of 56 pages from her school library for 7 days. She did not want to complete the book immediately.. She planned to read the book in such a way that all her other activities were not disturbed and wanted to spend equal amount of time in reading. She did it successfully and returned the book on the specific day. How she must have planned her reading?
Please with explanation...
Mina must have planned to read 8 pages everyday.
To accomodate reading in her everyday life, without spending extra time and not disturbing other activities, Mina should read particular number of pages everyday. These pages should be enough to be completed in 7 days.
So, relating the number of pages and days -
Number of pages to be read each day = total number of pages ÷ number of days
Keep the values in relation -
Number of pages to be read each day = 56 ÷ 7
Performing division
Number of pages to be read each day = 8
Thus, to return the book on time Mina should have planned to read 8 pages everyday.
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What is the degree of the power function represented in the table f(x)
-3, -2, -1, 0, 1, 2, 3
The degree of the power function represented in the table f(x) is 2.
How to illustrate the information?In order to find the degree of the power function represented in the given table, you must find the difference of the y-values.
The second difference is illustrated as:
2 - 6 = -4.
-2 - 2 = -4
-6 - (-2) = -4
This illustrates that the second differences are constant.
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What is the degree of the power function represented in the table?
1
2
3
4
x h(x)
−2 −8
−1 −2
0 0
1 −2
2 −8
Evaluate the expression3y if x = 4 and y = -2
Answer:
[tex]-6[/tex]
Step-by-step explanation:
[tex]3y=3(-2)=-6[/tex]