The data points show the amount of money y (in dollars) in an account after a time x (in years).Each figure has the same data points.However, each figure has a different curve fitting the data.The equation for each curve is also shown.Answer the questions that follow.
Answers
SOLUTION
(a) From the slope of the graph, we can see that this is an exponential function
So, the function that best fits the graph is
[tex]y=601(1.05)^x[/tex]Hence the answer to (a) is Figure 1
(b) From the graph of the function we selected, where y represents the amount of money and x the number of years. To get the amount of money, we will substitute x for 18 into the quatiomn, we have
[tex]\begin{gathered} y=601(1.05)^x \\ y=601(1.05)^{18} \\ y=601\times2.406619234 \\ y=1,446.378159448 \end{gathered}[/tex]Hence the answer is $1,446.38
Related Questions
can you please help me with the work sheet and get all the answers and thank you
Answers
ANSWER
[tex](x+2)(x-4)[/tex]EXPLANATION
7) Given;
[tex]f(x)=x^2-2x-8[/tex]Using factors of 2 and -4;
[tex]\begin{gathered} \lparen x^2+2x-4x-8) \\ \left(x^2+2x\right)+\left(-4x-8\right) \\ \end{gathered}[/tex]Factorise;
[tex]\begin{gathered} x\left(x+2\right)-4\left(x+2\right) \\ \end{gathered}[/tex]Factor out the common term;
[tex]\begin{gathered} x(x+2)-4(x+2) \\ (x+2)(x-4) \end{gathered}[/tex]The graphical solution is attached.
4. Write the equation of the line in SLOPE-INTERCEPT FORM that passes through the given points(4,2) and (0,6)
Answers
The slope intercept form equation is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for determining slope is expressed as
slope, m = (y2 - y1)/(x2 - x1)
From the information given,
y2 = 6, y1 = 2
x2 = 0, x1 = 4
Slope, m = (6 - 2)/(0 - 4) = 4/- 4
m = - 1
We would determine the y intercept, c by substituting m = - 1, y = 6 and x = 0 into the slope intercept equation. It becomes
6 = - 1 * 0 + c
6 = c
c = 6
The equation would be
y = - x + 6
Which expression represents the distance between point (0, a) and point (a,0) on a coordinate grid?
2a
Ο Ο Ο Ο
2a
O
Answers
Answer:
Explanation:
To determine the distance between two points on a coordinate grid, use the formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Solve on the interval [0,27): RCŨsx+c05X +1 = ] T O 3 A. X= 27,x = x=57 4. 4 O B. X = 27,X = O c. X= 7T,X = 1 47T 3 T D. X= ET 6 6 NAMAN
Answers
ANSWER:
C.
[tex]x=\pi,x=\frac{2\pi}{3},x=\frac{4\pi}{3}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]2cos^2x+3cosx\: +1\: =\: 0[/tex]Using the substitution method, we can calculate the value of x, like this:
[tex]\begin{gathered} u=\cos x \\ \text{ therefore:} \\ 2u^2+3u+1=0 \\ 3u=2u+u \\ 2u^2+2u+u+1=0 \\ 2u(u+1)+u+1=0 \\ (u+1)(2u+1)=0 \\ u+1=0\rightarrow u=-1 \\ 2u+1=0\rightarrow2u=-1\rightarrow u=-\frac{1}{2} \\ \text{ replacing:} \\ \cos x=-1\rightarrow x=\cos ^{-1}(-1)\rightarrow x=\pi \\ \cos x=-\frac{1}{2}\rightarrow x=\cos ^{-1}(-\frac{1}{2})\rightarrow x=\frac{2\pi}{3},\frac{4\pi}{3} \end{gathered}[/tex]Measure the dimensions of all the walls of the bedroom in your home, in feet. Find the dimensions of any windows or doorways as well.
Answers
Explanation
we can fill up the dimensions as follow
solve for C -3 (C + 5)- (c-3)=32
Answers
Given the equation:
[tex]-3(c+5)-(c-3)=32[/tex]To find the value of 'c', the first step to do is to get rid of the parenthesis. We can do this using the distributive property on both cases:
[tex]\begin{gathered} -3(c+5)-(c-3)=32 \\ \Rightarrow-3\cdot c+(-3)\cdot5-c-(-3)=32 \\ \Rightarrow-3c-15-c+3=32 \end{gathered}[/tex]Now that we don't have any parenthesis in our equation, we start moving similar terms: we leave on the left the terms with the variable 'c' and we move the rest of the terms to the right side with it's sign changed:
[tex]\begin{gathered} -3c-15-c+3=32 \\ \Rightarrow-3c-c=32+15-3 \end{gathered}[/tex]We can make the operations on each side since now we have the similar terms apart:
[tex]\begin{gathered} -3c-c=32+15-3 \\ \Rightarrow-4c=47-3=44 \\ -4c=44 \end{gathered}[/tex]Finally, we move the -4 that is multiplying the 'c' to the other side doing its opposite operation:
[tex]\begin{gathered} -4c=44 \\ \Rightarrow c=\frac{44}{-4}=-11 \\ c=-11 \end{gathered}[/tex]therefore, c=-11
Evaluate 10y-15 for y=5
Answers
10 y - 15
y = 5
We replace 5 in the expression
10 * 5 - 15 =
50 - 15 = 35
____________________
Answer
35
(linear approximation calc !) The radius of a disc is 24 cm if the radius has a maximum error of 0.2 cm. estimate the relative percentage air in the calculated area the area of a circle = pi r ^2
Answers
Given:
The radius of the circular disk is 24cm.
The radius has a maximum error of 0.2 cm.
To find:
The area
Explanation:
Using the area of the circle,
[tex]A=\pi r^2[/tex]The area of the disk is,
[tex]\begin{gathered} A=\pi\times24^2 \\ =576\pi cm^2 \end{gathered}[/tex]If the radius is increased from 24 by 0.02, then the radius becomes, r = 0.02
The change in the calculated area will be,
[tex]\begin{gathered} \Delta A=Area\text{ of the cirlce with radius of 24.02-Area of the circle with radius of 24} \\ =\pi\times24.02^2-\pi\times24^2 \\ =576.96\pi-576\pi \\ =0.96\pi cm^2 \end{gathered}[/tex]The relative percentage of area is,
[tex]\begin{gathered} \frac{\Delta A}{A}\times100=\frac{0.96\pi}{576\pi}\times100 \\ =0.0017\times100 \\ =0.17\text{ \%} \end{gathered}[/tex]Final answer:
The maximum error in area is,
[tex]0.96\pi cm^2[/tex]The relative percentage error in the area is 0.17%.
Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Answers
Answer: X = -2
Step-by-step explanation:
-6 time x is -6x and -6 times 3 is -18
Now you have -6x + -18 = 30
Add the now add 18 to both the -18 and 30 now your left with -6x = 12
And at last divide both -6 and 12 to -6
And you have X = -2
Answer: -8
Step-by-step explanation:
-6(x + 3) =30
-Distribute -6 and x = -6x
-Distribute -6 and 3 = -18
-6x -18 = 30
+18 +18. Take away 18 on both sides of the equation
_________
-6 / -6x = 48/-6 Divide -6 on both sides to get x by itself
X = -8
Final Answer : -8
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
Answers
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
step 1
Find z score
z=(92-80)/15
z=0.8
step 2
using the z-score table
For z=0.8
P=0.7881
therefore
answer is
P=0.7881I need to know which point is the solution and I need a check for it to make sure it’s correct and the line on the graph
Answers
The system of equations are given as
[tex]\begin{gathered} y-2x=-4 \\ y=-x-1 \end{gathered}[/tex]The graph of the system of equations is
The point which is the solution is
[tex](1,-2)[/tex]Number of Hours13.5Total Cost$2.00$6.50$7.00$9.00$12.507.59Identify the domain and range. Select the two correct answers.АDomain: {1, 2.00}BDomain: (1.3.5, 5, 7.5,9)CDomain: 2. 6.50, 7.9. 12.50)DRange: 19. 12.50)ERange: (1,3,5,5, 7.5.9}F.Range: (2,6 50, 7, 9, 12.50)
Answers
Domain is the set of x values, or the inputs.
Range is the set of y values, or the outputs.
They are unique.
Looking at the table,
the number of hours is the input on which we have the cost, the output.
So,
We get domain from number of hours
We get range from total cost
1, 3.5, 5, 7.5, and 9 ---- hours (domain)
B is right.
Now,
Range would be the total costs, which are:
2, 6.5, 7, 9, 12.5
F is right.
Correct answers are B and F
use the functions f (×) and g (×) to complete the comparison statements using <,>,or =.F(x)= -×-5
Answers
First Question:
f(3) = (-3)-5 (Replacing x in the equation)
f(3) = -8 (Operating integers)
From the table we see that g(3) = 8, therefore, f(3)< g(3)
Second Question:
The slope of f is the coefficient of x in the equation, so, the slope of f is -1.
Using the slope formula for g(x) with points (0,2) and (3,8) we find that:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]The slope of g is 2.
Therefore, the slope of f is less (<) than the slope of g
Third Question:
The y-intercept of f is the value next to the term -x, so, it is equal to -5
The y-intercept of g can be found with the point (0,2), when x=0, y is equal to 2, then the y-intercept is 2.
Therefore, the y-intercept of f is less(<) than the y-intercept of g.
Convert 57•F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas.C=5/9 (F-32)F= 9/5 C+32
Answers
ANSWER
[tex]13.9°C[/tex]EXPLANATION
We want to convert 57°F to degrees Celsius.
To do this, apply the formula:
[tex]C=\frac{5}{9}(F-32)[/tex]where F = temperature in Fahrenheit
Therefore, 57°F to degrees Celsius is:
[tex]\begin{gathered} C=\frac{5}{9}(57-32) \\ \\ C=\frac{5}{9}*25 \\ \\ C=13.9°C \end{gathered}[/tex]That is the answer.
Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
Answers
Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]Persuade Mr. Zion whether the numbers 12,16,and 20 make a right triangle or not. Make sure to state reasons for and against your belief
Answers
we can corrobarate this using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where:} \\ c>a,c>b \end{gathered}[/tex]Let:
[tex]\begin{gathered} a=12 \\ b=16 \\ c=20 \\ 20^2=12^2+16^2? \\ 400=144+256 \\ 400=400 \\ \end{gathered}[/tex]since the equality is satisfied, we can conclude that it is possible to make a right triangle using those numbers
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
Answers
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
describe and correct the error solution error a student made when graphing a linear equation y equals -3 / 4 x - 6
Answers
we have two points (0, 6) and (4, 3)
this can be represented as (x, y)
the equation of a straight line is
y = mx + c
slope = m = y2 - y1/ x2 - x1
x1 = 0, y1 = 6, x2 = 4 and y2 = 3
slope = 3 - 6 / 4 - 0
slope = -3/4
slope = -3/4
from the equation of a straight line
(y - y1) = m(x - x1)
y1 = 6 and x1 = 0
y - 6= -3/4(x - 0)
y - 6 = -3/4x + 0
y = -3/4x + 6
the error he made was that he used - 6 instead of +6 in the final answer
I do not understand the problem on how to to write an equation.
Answers
Given a line passes through the point (-4,6) and has a slope of 3
We will write the equation of the line in point-slope from
The formula of the point-slope form will be as follows:
[tex]y-k=m(x-h)[/tex]Where (h, k) is the point that lies on the line and (m) is the slope
From the given:
m = 3
h = -4
k = 6
Substitute into the formula
so, the answer will be:
[tex]y-6=3(x+4)[/tex]A support cable runs from the top of a telephone pole to a point on the ground 42.7 feet from its base. Suppose the cable makes an angle of 29.6 with the ground (as shown in the following figure).(a) Find the height of the pole. (Round the answer to the nearest tenth.) feet (b) Find the length of the cable. (Round the answer to the nearest tenth.) feet
Answers
We will draw a sketch to see the position of the cable
From the figure, we can use the tangent ratio to find the height
[tex]\frac{h}{42.7}=tan(29.6)[/tex]By using the cross-multiplication
[tex]\begin{gathered} h=42.7tan(29.6) \\ \\ h=24.3\text{ feet} \end{gathered}[/tex]a) The height of the pole is 24.3 feet to the nearest tenth
To find the length of the cable we will use the cosine ratio
[tex]cos(29.6)=\frac{42.7}{L}[/tex]Switch L and cos(29.6)
[tex]\begin{gathered} L=\frac{42.7}{cos(29.6)} \\ \\ L=49.1\text{ feet} \end{gathered}[/tex]b) The length of the cable is 49.1 feet to the nearest tenth
I need help just a understanding. And show how to get the answer.
Answers
An angle is formed when two lines meet. The angle is named with the lines that forms it. Looking at the diagram, the angle 2 is formed at B by lines CB and DB. The correct name for angle 2 is angle CBD
The last option is correct
what expression is equivalent to 2y+7
Answers
The expression which is equivalent to the given expression (3y - 4) (2y + 7) + 11y - 9 is 6 y²+ 24y- 37
Define an expression.A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
Presented expression = (3y - 4) (2y + 7) + 11y - 9
Solving the expression we get= 6y²+21y-8y-28+11y-9
= 6y²+24y-37
There for the correct response is that the given expression is equivalent to = 6y²+24y-37
To know more about expressions, visit:
https://brainly.com/question/14083225
#SPJ1
The edge of a cube measures 11 m. Find the surface area.
Answers
In order to determine the surface area of the cube, use the following formula:
[tex]S=6a^2[/tex]where a is the length of the side of a cube a = 11 m.
Replace the value of a into the formula for S:
[tex]S=6(11m)^2=726m^2[/tex]Hence, the surface area of the given cube is 726m^2
Question 5 of 15, Step 1 of 14/15CorrectIfy is inversely proportional to x and y = -71 when x = 16, find yifx = 7. (Round off your answer to the nearest hundredth.)
Answers
Answer:
[tex]y=-31.06[/tex]Step-by-step explanation:
Since y and x are inversely proportional, we'll have that:
[tex]y=\beta x[/tex]For a given betha value. Since we have a pair of x and y values, we can plug them in the formula and find our particular value of betha, as following:
[tex]\begin{gathered} y=\beta x\rightarrow-71=\beta\times16\rightarrow\beta=-\frac{71}{16} \\ \end{gathered}[/tex]This way, our formula would be:
[tex]y=-\frac{71}{16}x[/tex]Plugging in x = 7,
[tex]\begin{gathered} y=-\frac{71}{16}x\rightarrow y=-\frac{71}{16}(7)\rightarrow y=-\frac{497}{16} \\ \\ \Rightarrow y=-31.06 \end{gathered}[/tex]Factor 64x3 + 27.(4x – 3)(16x2 – 12x + 9)(4x + 3)(16x2 - 12x + 9)(4x + 3)(16x2 + 12x + 9)(4x - 3)(16x2 + 12x + 9)
Answers
Answer
Option B is correct.
64x³ + 27 = (4x + 3) (16x² - 12x + 9)
Explanation
We are told to factorize
64x³ + 27
To do this, we use the factorization of (x³ + y³) as a guide. First of,
(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)
(x + y)³ = x³ + y³ + 3x²y + 3xy²
So, we can write
x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)
= (x + y) [(x + y)² - 3xy]
= (x + y) (x² + y² + 2xy - 3xy)
= (x + y) (x² - xy + y²)
So, comparing (64x³ + 27) with (x³ + y³), we can see that
64x³ = (4x)³
27 = (3)³
(64x³ + 27) = (4x)³ + 3³
x³ + y³ = (x + y) (x² - xy + y²)
(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]
= (4x + 3) (16x² - 12x + 9)
Hope this Helps!!!
An open box is made from a 30cm by 40cm piece of tin by cutting
Answers
s represents the square
[tex]\begin{gathered} s_{1,\: 2}=\frac{-\left(-35\right)\pm\sqrt{\left(-35\right)^2-4\cdot\:1\cdot\:34}}{2\cdot\:1} \\ s_{1,\: 2}=\frac{-\left(-35\right)\pm\:33}{2\cdot\:1} \\ s_1=\frac{-\left(-35\right)+33}{2\cdot\:1}=\frac{35+33}{2}=\frac{68}{2}=34 \\ s_2=\frac{-\left(-35\right)-33}{2\cdot\:1}=\frac{35-33}{2}=\frac{2}{2}=1 \end{gathered}[/tex]The length of the sides of the square is 1 cm
How much interest is earned on an initial investment of $700 with a 5% annual rate for 2 years? A $700B $350C $70D $35
Answers
Let's calculate the 5% of $700 using a rule of three:
This way,
[tex]\begin{gathered} x=\frac{700\cdot5}{100} \\ \Rightarrow x=35 \end{gathered}[/tex]$35 is earned each year, For two years, the earnings would be $70
Answer: C. $70
Simplify: 7a + 2a - a + 6b - 5b
Answers
We must simplify the following expression:
[tex]7a+2a-a+6b-5b[/tex]From the expression, we see that we have terms with variable a and terms with variable b. In order to simplify the expression, we add the terms with a together (which sums up 8a), and we do the same for the terms with b (which sums up 1b):
[tex]\begin{gathered} 7a+2a-a+6b-5b \\ =(7a+2a-a)+(6b-5b) \\ =8a+b \end{gathered}[/tex]The solution is: 8a+b
This is non graded algebra 1 I need help on question 10
Answers
An exponential decay function can be generically written as:
[tex]y=a\cdot b^x[/tex]The conditions for this function are:
1) The y-intercept is 4.
2) The values of y decrease by a factor of one half as x increases by 1.
The y-intercept corresponds to the value of y when x = 0, so we can express it as:
[tex]\begin{gathered} y=a\cdot b^x \\ 4=a\cdot b^0 \\ 4=a\cdot1 \\ a=4 \end{gathered}[/tex]This condition let us find the value of a.
The next condition will be used to find the value of b.
As x increases by 1, y decreases by one half.
We can write this as a quotient between consecutive values of y:
[tex]\begin{gathered} \frac{y(x+1)}{y(x)}=\frac{1}{2} \\ \frac{4\cdot b^{x+1}}{4\cdot b^x}=\frac{1}{2} \\ b^{x+1-x}=\frac{1}{2} \\ b^1=\frac{1}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Then, we can write the function as:
[tex]y=4\cdot(\frac{1}{2})^x[/tex]Answer: y = 4*(1/2)^x
Find the probability of the event.If a single die is tossed once, find the probability of the following event. Rollinga 3 or a 5
Answers
ANSWER
1/3
EXPLANATION
If we have a fair die, the probability of rolling any of the numbers is the same. In this case, we want to know the probability of rolling a 3 or a 5, which is the sum of the probabilities of rolling each of these values,
[tex]P(3)=P(5)=\frac{1}{6}[/tex]So,
[tex]P(3or5)=P(3)+P(5)=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}[/tex]Hence, the probability of rolling a 3 or a 5 is 1/3