Find the length of the third side. If necessary, write in simplest radical form.DV895
Answers
In order to solve the missing side for a right triangle, we can use the Pythagorean theorem
[tex]a^2+b^2=c^2[/tex]then, we rewrite the expression for on of the sides different from the hypotenuse
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{c^2-b^2} \end{gathered}[/tex]replace with the values
[tex]\begin{gathered} a=\sqrt[]{(\sqrt[]{89})^2-5^2} \\ a=\sqrt[]{89-25} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}[/tex]Related Questions
A) What does the point (1,8) represent in the context of the situation? B) Is the amount of money proportional to the number of hours worked? C) Write an equation that represents this situation? D) What will be Amber’s Wages after 6 hours worked?
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Answer:
A) Amber's wages for 1 hour is $8.
B) Yes
C) y = 8x
D)
Explanation:
A) Looking at the graph, we can deduce that the point (1, 8) shows how much Amber makes in one hour. So in 1 hour, Amber makes $8.
B)To determine whether the amount of money is proportional to the number of hours worked, we have to look at the graph and see if it starts from the origin (0, 0), if it does then we can conclude that they are proportional.
Since the graph starts from the origin (0, 0), then the amount of money is proportional to the number of hours worked.
C) The slope-intercept equation of a line is given as;
[tex]y=mx+b[/tex]where m = slope of the line
b = y-intercept of the line
So let's go ahead and determine the slope of the line at points (1, 8) and (2, 16) using the below formula;
[tex]m=\frac{y_2-y_1_{}_{}_{}}{x_2-x_1_{}}=\frac{16-8}{2-1}=\frac{8}{1}=8[/tex]Since the line starts from the origin, therefore the y-intercept, b, is zero.
Since m = 8 and b = 0, the equation can then be written as;
[tex]\begin{gathered} y=8x+0 \\ y=8x \end{gathered}[/tex]D
(calc) which graph shows a function and its inverse ?
Answers
Answer: We have to pick a graph that represents a function and its inverse function, or:
[tex]\begin{gathered} f(x)\rightarrow\text{ and }\rightarrow f^{-1}(x) \\ \end{gathered}[/tex]The inverse function switches the x and y variables, therefore the axes with it, the final result is two functions that are symmetrical about y = x line.
Example:
[tex]\begin{gathered} f(x)=\sqrt{x}\rightarrow\text{ Function} \\ \\ f^{-1}(x)=x^2\rightarrow\text{ Inverse Function} \end{gathered}[/tex]Graph:
Therefore the graph out of the options which has these properties is:
[tex]\text{ Graph\lparen C\rparen}[/tex]The answer, therefore, is Graph(C).
Is this correct? If not can you show me how to do it?
Answers
D. The rental cost in dollars, for each paddleboard.
Explanation:
You were in the right track with linking 40 to the paddleboards.
But remember that t represent the total cost and not the total number of paddleboards and kayak, and also since p represent the number of paddleboards (while k represent the number of kayak)
To find t, you need to sum the cost of all the kayaks and the sum of all the paddleboards.
=> t = 25k + 40p
with 25k = total cost of all the kayaks
and
with 40p = total cost of all the paddleboards => in others words the total number of paddleboards (p) * the cost of each paddleboards (40)
Sketch a line of best fit: The graph shows the depth y in centimeters of water filling a bathtub after x minutes. An equation for this line of best fit could be y = 2.4x-3.2. Use the sketch tool to sketch the line of best fit. A) interpolate: Use the given data to determine how much water is in the tub after 7 min. B) Extrapolate: Use the model (your equation) to predict the amount of water in the tub after 30 min. (Extrapolate means you are outside the known data.) I just want to make sure I created the line of best fit and that my answers to each question are correct.
Answers
The given equation of the line that best fits the data is:
[tex]y=\text{2}.4x-3.2[/tex]In order to graph it we can solve the equation for different x-values, and then find the coordinates of the points to draw the line.
For x=2, the y-value is:
[tex]\begin{gathered} y=2.4\cdot2-3.2 \\ y=4.8-3.2 \\ y=1.6 \end{gathered}[/tex]For x=7, the y-value is:
[tex]\begin{gathered} y=2.4\cdot7-3.2 \\ y=16.8-3.2 \\ y=13.6 \end{gathered}[/tex]And for x=12, the y-value is:
[tex]\begin{gathered} y=2.4\cdot12-3.2 \\ y=28.8-3.2 \\ y=25.6 \end{gathered}[/tex]Then, by placing these 3 points in the coordinate plane, we can draw the line, as follows:
The graph with the given points is:
b. Interpolate: the water is in the tube after 7 minutes 13.6 centimeters. We have already made the calculation in part a. When x=7, then y=13.6
c. Extrapolate: the amount of water after 30 minutes will be:
[tex]\begin{gathered} y=2.4\cdot30-3.2 \\ y=68.8 \end{gathered}[/tex]The predicted amount of water after 30 minutes will be 68.8 centimeters.
RATIOS, PROPORTIONS, AND PERCENTSFinding the principal, rate, or time for a simple interest loan...Ann took out a loan for $17,000 and was charged simple interest at an annual rate of 6.8%.The total interest she paid on the loan was $867.How long was the loan for, in months?Do not round any intermediate computations. If necessary, refer to the list of financial formulas.monthsI need help with this mathProblem
Answers
The time formula for simple interest is:
[tex]t=\frac{I}{Ci}[/tex]Where I is the interest, C is the capital and i is the rate
In this case, we have:
I= 867
i=6.8%
C=17000
Replace and solve:
[tex]t=\frac{867}{17000*0.068}[/tex][tex]t=0.75\text{ years}[/tex]The time is 0.75 years because the rate is in years.
Convert years to months:
[tex]0.75years*\frac{12months}{1years}=9\text{ months}[/tex]1. Graph each of the following equations below using a tale of values or by another method. Fill in theInformation for each graph.X-intercept:a) y = x2 + 4x - 5y-intercept:хуVertex:Max/MinAxis of SymmetryDomain:Range:
Answers
The equation is
[tex]y=x^2+4x-5[/tex]We can already find the vertex using the vertex formulas
[tex]\begin{gathered} x_V=-\frac{b}{2a}=\frac{-4}{2}=-2 \\ \\ \\ y_V=-\frac{\Delta}{4a}=-\frac{b^2-4ac}{4a}=-\frac{16+20}{4}=-\frac{36}{4}=-9 \end{gathered}[/tex]Therefore the vertex is
[tex](x_V,y_V)=(-2,-9)[/tex]Now we have the vertex we also have the axis of symmetry and the max/min of the function, in that case, it's a minimum because a > 0. Therefore
[tex]\begin{gathered} \text{ axis of symmetry = }x_V=-2 \\ \\ \min\lbrace y\rbrace=y_V=-9 \end{gathered}[/tex]We can find the x-intercept easily
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-4\pm\sqrt{4^2+4\cdot5}}{2} \\ \\ x=\frac{-4\pm\sqrt{16+20}}{2} \\ \\ x=\frac{-4\pm\sqrt{36}}{2} \\ \\ x=\frac{-4\pm6}{2} \\ \\ \end{gathered}[/tex]Hence
[tex]\begin{gathered} x=\frac{-4\pm6}{2}=-2\pm3 \\ \\ x_1=-1 \\ x_2=-5 \end{gathered}[/tex]The y-intercept is just the c value, then it's -5.
Now we can do the domain, there's no restriction for parabolas in the domain, then
[tex]\text{ domain = }\mathbb{R}[/tex]And the range is
[tex]\text{ range = \lbrack}y_V,+\infty)=[-9,+\infty)[/tex]Question 8 of 10The table below shows the number of e-mails received each day by acompany employee for two separate weeks. If the data were represented witha comparative dot plot, which day would have more dots for week 2 than forweek 1?Week 1 Week 2Monday74.Tuesday83Wednesday52Thursday97Friday69
Answers
Solution
It's Friday
Because, the number of dots for week 2 is 9, while the number of dots for week 1 is 6.
Hence, the correct option is A.
If Karen has 6 cups of oatmeal and she divides it into 1/3 cup servings, how many servings of oatmeal will she have?
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Problem
If Karen has 6 cups of oatmeal and she divides it into 3/4 cup servings, how many servings of oatmeal will she have?
Solution
For this case the operation that we need to do is:
[tex]\frac{6\text{cups}}{\frac{3}{4}\frac{\text{cups}}{\text{serving}}}=\frac{6\cdot4}{3}==\frac{24}{3}=8\text{servings}[/tex]And for this case the final answer would be 8 servings
I need help with this. I want to understand 7a first
Answers
Answer:
The exact length of segment XY is √4765 and the approximate length is 69.029
Explanation:
The length of a segment that goes from (x1, y1) to (x2, y2) can be calculated as
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]So, replacing (x1, y1) by X(-32, 88) and (x2, y2) by Y(11, 34), we get:
[tex]\begin{gathered} \sqrt{(11-(-32))^2+(34-88)^2} \\ \sqrt{(11+32)^2+(-54)^2} \\ \sqrt{43^2+(-54)^2} \\ \sqrt{1849+2916} \\ \sqrt{4765} \\ 69.029 \end{gathered}[/tex]Therefore, the exact length of segment XY is √4765 and the approximate length is 69.029
Suppose that y varies directly as the square root of x, and that y = 25 when x = 289. What is y when x= 134? Round your answer to two decimal places if necessary.
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Answer
When x = 134, y = 17.02
Explanation
We are told that y varies directly as the square root of x.
y ∝ √x
Introducing the constant of proportionality, k
y = k√x
We are then told that
when y = 25, x = 289, with this, we can solve for k
y = k√x
25 = k × √289
25 = k × 17
25 = 17k
17k = 25
Divide both sides by 17
(17k/17) = (25/17)
k = (25/17)
We are then to solve for y when x = 134
y = k√x
y = (25/17) × √134
y = (25/17) × 11.58
y = 17.02
Hope this Helps!!!
I don't understand how to do either elimination or substituion.
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We will solve by elimination as follows:
-3x - 8y = 20 [We multiply one of the equations by a number so we obtain an equal value in one of them]
8(-5x + y = 19)
-----------------------
-3x - 8y = 20
-40x + 8y = 152
------------------------- [We now add both expressions and solve for the resulting equation]
-43x = 172 => x = -4
Now that we know the value of one of the variables we replace this in one of the first equations:
=> -3(-4) - 8y = 20 => 12 -8y = 20=>-8y = 8 => y = -1
So, from this, we have that the solution for the system is (-4, -1)
simple interest interest: $50principal:$350rate: 6.5time:x
Answers
Given:
Interest (SI) = 50
Principal (P) = 350
rate (R) = 6.5. (Here, rate is 6.5 %)
To find time,
[tex]\begin{gathered} S\mathrm{}I\mathrm{}=P\times R\times T \\ 50=350\times\frac{6.5}{100}\times x \\ x=\frac{50}{22.75} \\ x=2.197 \\ x\approx2\text{ years ( approximated) } \end{gathered}[/tex]Answer: x = 2 years.
FEΗIdentify the similar triangles.ΔH FEΝΔΔΗFE Δ
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According to the given figure, the common parts between triangles are angle G, side GH and angles H and E being equal to 90°.
So, the similar triangles are FHG and HEG because that's the position where the corresponding equivalent parts match.
Additionally, triangle HFE would be similar to triangles FGH and HGE.The constant of variation for a function is 2. Which of the following graphs best represents this situation
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The required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
Given that,
To determine the graphs which show the constant of variation for a function is 2.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
in the graphs only graph, A and B show the given condition of the constant of variation for a function is 2. Because in both graphs shows that y = 2x and 2y = x.
Thus, the required graph shows the constant of variation for a function is 2 is A and B. Option A and B is correct.
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3. Marisol made 12 cups of party mix. She gave 3 cups to her mother and 3 cups to her grandmother. How much party mix did Marisol have left for herself? 3 cups ( 6 7 cups 4 cups 6 cups
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We will have the following:
[tex]12-2(3\frac{3}{4})=12-2(\frac{12}{4}+\frac{3}{4})[/tex][tex]=12-2(\frac{15}{4})=\frac{9}{2}[/tex][tex]=4\frac{1}{2}[/tex]So, she will have 4 & 1/2 cups.
Michael and Karim are eating buffalo wings at a constant rate. Michael can eat 5.5 wings per minute. Karim's eating information is shown in the table below. Time (minutes) Wings eaten 1 6 2 12 18 3if they both ate 6 min how many wings would each person eat
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a) Karim eats faster
b) Number of wings Micheal will eat = 33 wings
Number of wings Karim will eat = 36 wings
Explanation:a) Michael eat 5.5 wings per minute
we need to find the constant rate Karim eats from the table
The constant rate = change in wings eaten/ change in time
The constant rate = (12 - 6)/(2-1) = (18-12)/(3-2)
= 6/1 = 6/1
The constant rate Karim eats = 6 wings per minute
Rate of Mcheal eating = 5.5
Rate of Karim eating = 6
Karim eats faster
Reason: Because Karim consumes more wings than Micheal when they are given same time, he will eat faster.
6 > 5.5
b) If they both ate 6 min:
Number of wings = rate × time
Number of wings Micheal will eat = 5.5 × 6 = 33 wings
Number of wings Karim will eat = 6 × 6 = 36 wings
A map is created on a coordinate plane . Typ's house is located at (7,8) and the library is located at (7,-6) Each unit on the coordinate plane represents 1 block. How many blocks is it from Ty's house to the library? explain
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We will have to calculate the distance between the two points ( that is between Ty's house to library
[tex]\text{distance betw}en\text{ two points = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex](x_1,y_1)=(7,8)and(x_2,y_2)=(7,-6)_{}[/tex][tex]\begin{gathered} d=\text{ }\sqrt[]{(7-7)^2+(-6-8)^2}\text{ =}\sqrt{\text{ }0^2+(-14)^2}\text{ =}\sqrt[]{14^2\text{ }} \\ d=\text{ 14} \end{gathered}[/tex]There are 14 blocks between Ty's house to the library
(x + y)² – 3zz when X = -2, y = -4, and z = 5.
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-39
Explanation
[tex]\begin{gathered} \mleft(x+y\mright)^2-3zz \\ \end{gathered}[/tex]Step 1
let
x=-2
y=-4
z=5
Step 2
Now, replace those values in the expression
[tex]\begin{gathered} (x+y)^2-3zz \\ (-2+(-4))^2-3\cdot5\cdot5 \\ (-2-4)^2-75 \\ (-6)^2-75 \\ 36-75 \\ -39 \end{gathered}[/tex]I hope this helps you
PLS HELP FAST I WILL GIVE 25 POINTS simplify 10^6/10^-3. answers:A. 1/10^3. B. 1/10^18. C. 10^3. D. 10^9
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D
Let's simplify that expression
1) Remember of the Exponents Rule, we have to subtract them
2) Note that for the exponents 6 -(-3) = 6+3 = 9 So it's D
(08.01 MC)Find the height of a square pyramid that has a volume of 12 cubic feetand a base length of 3 feet. (1 point)
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Recall that we can do the following picture
We want to find the height of this pyramid and are told the volume of the pyramid. Recall that the volume of a square pyramid of height h and base length b is given by the formula
[tex]V=\frac{1}{3}b^2\cdot h[/tex]In our case, we have V=12, and b=3. So we have the following equation
[tex]12=\frac{1}{3}\cdot3^2\cdot h=3\cdot h[/tex]So, we should find the value of h from this equation. To do, we simply divide both sides by 3, so we get
[tex]h=\frac{12}{3}=4[/tex]so the height of the pyramid is 4 feet.
If y=-4 when x = 10, find y when x = 2.
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With the help of the cross-multiplication method, we know that the value y is -4/5 when x is 2.
What do we mean by the cross-multiplication method?In mathematics, more specifically in elementary arithmetic and elementary algebra, one could cross-multiply an equation between two fractions or rational expressions to make the equation easier or to determine the value of a variable.
To cross-multiply two fractions, multiply the numerator of the first fraction by the denominator of the second, and the numerator of the second fraction by the denominator of the first.
So, the value of y when x = 2 is:
We know that when y = -4, then x = 10.
Now, calculate y when x = 2.
y/x = y/x
-4/10 = y/2
10y = -8
y = -8/10
y = -4/5
Therefore, with the help of the cross-multiplication method, we know that the value y is -4/5 when x is 2.
Know more about the cross-multiplication method here:
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Choose the correct answer. 1. Shari made a net of a box to find how much wrapping paper she will need to . wrap the box 8 in. 5 in.
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The total area needed to be covered is 158 square inch.
It is calculated by adding all the area
[tex]2\ast(8\ast5)+\text{ 2}\ast(5\ast3)+2\ast(8\ast3)=158in^2\text{ }[/tex]4^2 * 4^3 simplified
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]4^2\ast4^3[/tex]STEP 2: Simplify the expression using the law of indices
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c} \\ 4^2\cdot \:4^3=4^{2+3} \\ =4^{\left\{2+3\right\}} \\ =4^5=1024 \end{gathered}[/tex]Hence, the evaluation gives:
[tex]1024[/tex]Need help finding the x-intercepts for equation in picture. I can see them on the graph but I need to work it out by solving.
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Answer:
The x-intercepts of the function are;
[tex]\begin{gathered} x=-2 \\ \text{and} \\ x=-4 \end{gathered}[/tex]Explanation:
Given the function;
[tex]f(x)=-2(x+3)^2+2[/tex]We want to derive the x-intercepts of the function.
The x-intercept is at f(x)=0;
[tex]\begin{gathered} f(x)=-2(x+3)^2+2=0 \\ -2(x+3)^2+2=0 \\ -2(x^2+6x+9)^{}+2=0 \\ -2x^2-12x-18^{}+2=0 \\ -2x^2-12x-16=0 \\ -x^2-6x-8=0 \\ x^2+6x+8=0 \end{gathered}[/tex]solving for x;
[tex]\begin{gathered} x^2+6x+8=0 \\ x^2+2x+4x+8=0 \\ (x+2)(x+4)=0 \\ x+2=0 \\ x=-2 \\ \text{and} \\ x+4=0 \\ x=-4 \end{gathered}[/tex]Therefore, the x-intercepts of the function are;
[tex]\begin{gathered} x=-2 \\ \text{and} \\ x=-4 \end{gathered}[/tex]Method 2: quadratic root property;
[tex]\begin{gathered} f(x)=-2(x+3)^2+2=0 \\ -2(x+3)^2+2=0 \\ -2(x+3)^2=-2 \\ \text{divide both sides by -2;} \\ (x+3)^2=1 \\ \text{square root both sides;} \\ \sqrt{(x+3)^2}=\sqrt{1} \\ x+3=\pm1 \\ x=-3\pm1 \\ so\text{ the values of x are;} \\ x=-3+1=-2 \\ \text{and} \\ x=-3-1=-4 \end{gathered}[/tex]Therefore, the x-intercepts are;
[tex]\begin{gathered} x=-2 \\ \text{and } \\ x=-4 \end{gathered}[/tex]List the sides of FGH in order from least to greatest if m
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We have a triangle FGH
The three angles of the triangle FGH are given as
[tex]\begin{gathered} m\angle F=4x+7 \\ m\angle G=5x-31 \\ m\angle H=7x-52 \end{gathered}[/tex]Recall that the sum of all three angles of a triangle must be equal to 180°
[tex]\begin{gathered} m\angle F+m\angle G+m\angle H=180\degree \\ 4x+7+5x-31+7x-52=180 \\ 16x-76=180 \\ 16x=180+76 \\ 16x=256 \\ x=\frac{256}{16} \\ x=16 \end{gathered}[/tex]Now, we can calculate the exact measure of the angles
[tex]\begin{gathered} m\angle F=4x+7=4(16)+7=64+7=71\degree \\ m\angle G=5x-31=5(16)-31=80-31=49\degree \\ m\angle H=7x-52=7(16)-52=112-52=60\degree \end{gathered}[/tex]Let us draw the triangle FGH
Recall that the side opposite the least angle is the least side and vice versa.
The means that the side opposite the angle G is the least side (FH)
Then the side opposite the angle H is the greater side (FG)
Finally, the side opposite the angle F is the greatest side (GH)
Therefore, the sides of the triangle FGH in order from least to greatest is
FH, FG, GH
I need help with number 7 the first question on the top of the page please
Answers
SK= 13x-5
KY= 2x+9
SY=36-x
By looking at the line segment we can state:
SY = SK+KY
Replacing with the values, and solving for x:
36-x=13x-5+2x+9
Sum and subtract alike terms
36+5-9=13x+2x+x
32= 16x
Divide both sides by 16:
32/16=16x/16
2=x
Replace the value of x in each expression:
SK= 13x-5=13(2)-5=26-5=21
KY= 2x+9=2(2)+9=4+9=13
SY=36-x =36-(2)=34
So, the answers are:
x=2
SK=21
KY=13
SY=34
if your able to answer all of them i will be giving you 5 stars
Answers
The function given is:
[tex]f(x)=-16x^2+60x+16[/tex]PART AThe factorization steps are shown below:
[tex]\begin{gathered} f(x)=-16x^2+60x+16 \\ f(x)=4(-4x^2+15x+4) \\ f(x)=4(-4x^2+16x-x+4) \\ f(x)=4(-4x(x-4)-1(x-4)) \\ f(x)=4(-4x-1)(x-4) \end{gathered}[/tex]PART BTo find the x intercepts, we set f(x) equal to 0 and solve for x:
[tex]\begin{gathered} f(x)=4(-4x-1)(x-4) \\ f(x)=0 \\ 4(-4x-1)(x-4)=0 \\ -4x-1=0--------(1) \\ OR \\ x-4=0---------(2) \end{gathered}[/tex]Solving (1), we have:
[tex]\begin{gathered} -4x-1=0 \\ 4x=-1 \\ x=-\frac{1}{4} \\ x=-0.25 \end{gathered}[/tex]and, solving (2), we have:
[tex]\begin{gathered} x-4=0 \\ x=4 \end{gathered}[/tex]The x-intercepts are
[tex]\begin{gathered} x=-0.25 \\ x=4 \end{gathered}[/tex]PART CThe standard equation of a quadratic is
[tex]f(x)=ax^2+bx+c[/tex]The parabola opens upward when a is positive and opens downward when a is negative
1. When parabola opens upward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow\infty \end{gathered}[/tex]2. When parabola opens downward, the end behavior can be described as:
[tex]\begin{gathered} x\rightarrow\infty \\ y\rightarrow-\infty \\ \text{and} \\ x\rightarrow-\infty \\ y\rightarrow-\infty \end{gathered}[/tex]Our equation has an "a" value that is negative! So, the parabola opens downward and the end behvaior can be described as:
As x goes to infinity (gets infinitely large), y goes to negative infinity (gets infinitely small) and as x goes to negative infinity (gets infinitely small), y goes to negative infinity (get infinitely small).
PART D
In Part B, we found the x-intercepts. Those are the x-axis cutting points. We can draw those first.
Then,
Using the end behavior information that we found in Part C, we can draw the parabola. The rough sketch is shown:
The exact graph is shown below, for reference:
There are 14 girls and 12 boys in a class. What is the ratio of gris to students in simplest form
Answers
Number of girls = 14
Number of boys = 12
Number of students = 14 + 12 =26
Ratio of girls to students = 14/26 = 7 : 13
The scatterplot shows the average number of hours each of 13 people spends at work every week and the average number of hours each of them spends recreational activities every week.Based on the scatterplot,what is the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week?A.33 hB.95 hC.50 hD.65 h
Answers
We want to find the best prediction of the average number of hours a person spends at work every week if that person spends an average of 10 hours on recreational activities every week.
We will construct a line that adapts to the system by simple linear regression, and then we will find the x-value that makes the line take y=10.
First, we have the data:
We remember that in a simple regression model, we want to write an equation of the form:
[tex]y=\hat{\alpha}+\hat{\beta}x[/tex]where:
[tex]\begin{gathered} \hat{\alpha}=\bar{y}-\hat{\beta}\bar{x} \\ \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \end{gathered}[/tex]And the Sx, Sy and Sxx are the sums over all the x-values, the y-values and the multiplication of the x-values and y-values (respectively).
We will find those values:
[tex]\begin{gathered} S_x=\sum ^{13}_{i=1}x_i=370 \\ S_y=\sum ^{13}_{i=1}y_i=336.5 \end{gathered}[/tex]Also, we have:
[tex]\begin{gathered} S_{xx}=\sum ^{13}_{i=1}x^2_i=12600 \\ S_{xy}=\sum ^{13}_{i=1}x_iy_i=8680_{}_{} \end{gathered}[/tex]And applying the formula, having in mind that n=13, we get:
[tex]\begin{gathered} \hat{\beta}=\frac{nS_{xy}-S_xS_y}{nS_{xx}-S^2_x}_{} \\ =\frac{13(8680)-(370)(336.5)}{13(12600)-(370^2)} \\ =\frac{-11665}{26900} \\ \approx-0.4336 \end{gathered}[/tex]And, for alpha:
[tex]\begin{gathered} \hat{\alpha}=\frac{1}{n}S_y-\hat{\beta}\frac{1}{n}S_x \\ =\frac{1}{13}(336.5)-(-0.4336)\frac{1}{13}(370) \\ \approx38.2255 \end{gathered}[/tex]This means that the linear regression equation will be:
[tex]y=38.2255-0.4336x[/tex]For finding the x-value that will have 10 hours of recreational activities, we replace the 10 value on y, and clear out the variable x:
[tex]10=38.2255-0.4336x[/tex]And thus,
[tex]\begin{gathered} 10-38.2255=-0.4336x \\ \frac{-28.2255}{-0.4336}=x \\ 65.09=x \end{gathered}[/tex]This means that when a person works 65 hours approximately, he will have 10 hours of recreational activities every week.
Susan earns 0.5% interest annually in her savings account. she can model her savings account balance after earning interest for a year as fx=x+0.005x or just fx=1.005x where x is the account balance
Answers
The balance of her account after one year, using simple interest, will be of
$30,150.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = A(0)(1 + rt).
In which the parameters of the equation are explained as follows:
A(0) is the value of the initial deposit.r is the interest rate, as a decimal.Considering that she has $30,000 in her account and the interest rate of 0.5%, the values of the parameters are given as follows:
A(0) = 30000, r = 0.005.
Hence the balance after one year will be of:
B(1) = 30000(1 + 0.005) = $30,150.
Missing InformationThe problem asks for the balance after one year, if she started with $30,000 in her account.
More can be learned about simple interest at https://brainly.com/question/25793394
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