ANSWER :
5.9 years
EXPLANATION :
Exponential function can be expressed as :
[tex]y=A(1\pm r)^t[/tex]where A = initial amount
r = (+) growth or (-) decay rate
t = time
y = amount after t years
From the problem, the initial value of the car is A = $32,500
It depreciates at a rate of 11.1% annually, so r = -11.1% or -0.111
The value of the car will be 50% of its original value, so y = 0.50(32,500) = $16,250
Using the formula above :
[tex]\begin{gathered} 16250=32500(1-0.111)^t \\ \frac{16250}{32500}=(0.889)^t \\ \\ 0.5=(0.889)^t \\ \text{ Take the ln of both sides :} \\ \ln(0.5)=\ln(0.889)^t \\ \ln(0.5)=t\ln(0.889) \\ \\ t=\frac{\ln0.5}{\ln0.889}=5.89\sim5.9yrs \end{gathered}[/tex]The graph of F(x), shown below, has the same shape as the graph of G(x) = x4, but it is shifted to the right 1 unit. What is its equation?
Given:-
The graph of x power 4.
To find the equation when the graph is shifted right 1 unit.
So the equation in vertex form is,
[tex]y=a(x-h)^2+k[/tex]Substituting the values. we get,
[tex]g(x)=1(x-1)^4+0[/tex]Since the graph is shifted right side the value will be in negative. so we get,
[tex]g(x)=(x-1)^4[/tex]Question number 2.7T: (Please help!)
The values of function F(5) is 35 and F(-10) is 4.
For F(5), x≥5
So, the appropriate function will be
[tex]F(x)=6x+5\\\\F(5)=6(5)+5\\\\F(5)=30+5\\\\F(5)=35[/tex]
For f(-10), x≤-8
So, the appropriate function will be
[tex]F(x)=4\\\\F(-10)=4[/tex]
Thus, the values of function F(5) is 35 and F(-10) is 4.
To learn more about value of function refer here
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Isabelle is designing a sandbox for her backyard. the sandbox will be a regular pentagon 3 ft each side. how much wood does she need to enclose the entire sandbox? how many square ft will the sandbox take up?
Area of rectangular Pentagon = 5 * s^2 / (4tan(36°)) =5 × (3)^2 / (4*tan(36) ) = 17.73
the sides of the box are squares. their sides are 3 ft long. So the area of each square is 25 ft^2
Now, there are 5 sides, so if we mutiply 5 * 25 ft^ = 125 ft^2
So the answers are:
She needs 125 ft^2 to enclose the entire sandbox
and it would take up 142.73 ft^2
the volume of a cylinder is 1269 pi cm^3 and its height is 16 cmthe length of the cylinders radius is ___ cm
The volume of cylinder is.
[tex]V=1296\pi[/tex]The height of cylinder is h = 16.
The formula for the volume of the cylinder is,
[tex]V=\pi(r)^2h[/tex]Determine the length of radius of cylinder.
[tex]\begin{gathered} 1296\pi=\pi(r)^216 \\ r^2=\frac{1296\pi}{16\pi} \\ =81 \\ r=\sqrt[]{81} \\ =9 \end{gathered}[/tex]So length of cylinder radius is 9 cm.
how much is 1 + 1 bc i’ve been failing high school
Explanation
to add two natural numbers, just move n units the initial to the rigth in the numeric line, so
fo
Which function's graph is shown below? ད་ལྟ་བ་དང་ o = A. Y = COS X O B. y = -cos x C. y = sin x OD. y = -sin
Given:
Consider the given graph in figure.
To find:
Select the correct option that shows the given function's graph.
Explanation:
Here, graph is in the form of,
[tex]y=acos(bx)[/tex]Where, a is amplitude and the period of a cosine function is the length of the shortest interval on the x axis over which the graph repeats.
[tex]\text{ period =}\frac{2\pi}{|b|}[/tex]Here, at x = 0, the y value is 1. so, the graph starts at (0, 1) which indicates the graph of
[tex]y=cosx[/tex]Consider the below graph:
So, the correct option is (A) y = cosx.
Final answer:
Hence, the required correct option is (A) y = cos
If x = 11 and y=5, what is the value of the following expression?X-9 + 2y
Given:-
[tex]x=11,y=5[/tex]To find the value of x-9+2y.
So now we substitute the known values. we get,
[tex]x-9+2y=11-9+2(5)=11-9+10=12[/tex]So the required solution is 12.
h(x) = x² – 5 – x; Find h(8)
hello
to solve this question, we simply need to substitute 8 as the value of x in the expression
[tex]\begin{gathered} h(x)=x^2-5-x \\ h(8)=8^2-5-8 \\ h(8)=64-5-8 \\ h(8)=51 \end{gathered}[/tex]from the calculation above, the value of h(8) is equal to 51
Mr Tcha's recipe for fruit protein shake states that 2/3 of the total amount of ingredients should be fruit. The amount of yogurt in the recipe should be 1/4 of the amount of the fruit. If Mr. Tcha has 24 grams of fruits left over, how many grams of fruits and grams of yogurt did he use? What fraction of the total amount of ingredients is neither fruit nor yogurt?
A1Okay, here we have this:
Considering the provided information, we are going to calculate the requested questions, so we obtain the following:
To know how many grams of fruit and yogurt I use then let's consider that I use 2/3 of the total fruit,
Task:Dilate the extra gum package by a scale factor of 8.Will the small pack of gum cover the whole billboard given thedimensions? Explain your answer in complete sentences.
No, because the length of the billboard is larger than the dilated gum cover length.
If we dilate the gum package by a scale factor of 8:
Original = 3 x 2.5 in
3 x8 = 24 (length)
2.5x8 = 20 (width)
New measures: 24 x 20 ( Lenght by width)
Since the billboard is 48x14, the small pack of gum can't cover the billboard.
24<48
The length of the gum cover can't cover the length of the billboard.
List all the possible rational roots, then find all the roots of the function
Take into account that for a polynomial function, the possible roots are given by the following quotient:
roots = p/q
where p is the constant of the function (and its factors) and q is the coefficient of the term with the greates degree (variable with greatest exponent) or its factors.
Then, based on the previous explanation, you have:
p = -9
q = 5
factors -9: -1, 1, -3, 3, -9, 9
factors 5: -1, 1, -5, 5
Hence, the possible factors are:
±1, ±3, ±9, ±1/5, ±3/5, ±9/5
and the roots:
roots = {i(√15)/5 , -i(√15)/5, √3, -√3}
The roots can be also obtained by using quadratic formula for x^2, and then, by applying square root to the result to obtain x.
Solve by graphing. If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initally. When will the amount left be 2 grams? Round to the nearest tenth of a day. Be sure to label your answer.
The exercise describes an exponential decay, you can express this using the general form:
[tex]y=ab^x[/tex]Where
a is the initial amount
b is the decay factor
x is the time intervals
y is the amount after x time intervals
The half-life of a substance indicates the time it takes for the amount to decrease by half.
If the initial amount is a=5 grams, the half-life indicates that after x=20 days, the amount will be
y= 5/2 = 2.5 grams.
You can replace these values on the formula above to obtain an expression where the decay factor will be the only unknown:
[tex]\begin{gathered} y=ab^x \\ 2.5=5b^{20} \end{gathered}[/tex]To solve for b, first, divide both sides of the equation by 5:
[tex]\begin{gathered} \frac{2.5}{5}=\frac{5b^{20}}{5} \\ 0.5=b^{20} \end{gathered}[/tex]Then apply the square root with index 20 to both sides of the equal sign no reach the value of b:
[tex]\begin{gathered} \sqrt[20]{0.5}=\sqrt[20]{b^{20}} \\ b=0.97 \end{gathered}[/tex]Now that you know the value of the decay factor, you can determine how much time it will take for the substance to decrease to 2grams.
The expression for the exponential decay in this case is:
[tex]y=5\cdot0.97^x[/tex]For y=2grams:
[tex]2=5\cdot0.97^x[/tex]Now, you have to solve the expression for x:
-Divide both sides by 5:
[tex]\begin{gathered} \frac{2}{5}=\frac{5\cdot0.97^x}{5} \\ 0.4=0.97^x \end{gathered}[/tex]-Apply the logarithm to both sides of the equal sign:
[tex]\begin{gathered} \log (0.4)=\log (0.97^x) \\ \log (0.4)=x\log (0.97) \end{gathered}[/tex]-Divide both sides by the logarithm of 0.97 to determine the value of x:
[tex]\begin{gathered} \frac{\log(0.4)}{\log(0.97)}=\frac{x\log (0.97)}{\log (0.97)} \\ x=30.08\approx30.1 \end{gathered}[/tex]It will take approximately 30.10 days to have 2 grams of substance left.
At a local bakery, at a local bakery Ariel Bots for oatmeal cookies four $1.20 Mia bought 9 mil cookies for $2.70 Becky bought 12 oatmeal cookies for $3.60 Larry purchased 15 oatmeal cookies $4.5. Graph the data on the graph
EXPLANATION
Drawing given set data ni a graph, will give us:
As we can see in graph, this is a proportional relationship given by a straight line.
Simplify the expression⅜b - ¾b
-3b / 8
Explanations:The given expression is:
[tex]\frac{3}{8}b\text{ - }\frac{3}{4}b[/tex]Which can be re-written as:
[tex]\frac{3b}{8}-\frac{3b}{4}[/tex]Note that the LCM of 8 and 4 is 8
Therefore, the expression can be simplified as:
[tex]\begin{gathered} \frac{3b-2(3b)}{8} \\ \frac{3b-6b}{8} \\ \frac{-3b}{8} \end{gathered}[/tex]The simplified expression is -3b/8
Claudia dumped her 200-penny coin collection on the floor and counted the number of pennies that landed heads up. Claudia repeated this process 5 times and had an average of 84 pennies landing heads up on each try. Which of the following statements is true?A. Each penny has a greater probability of landing heads up than tails up.B. If Claudia had repeated this process more times, the average number of pennies landing heads up would be closer to 100.C. The theoretical probability of a penny landing heads up is 21/50.D. If Claudia had repeated this process fewer times, the average number of pennies landing heads up would be closer to 100.
Given:
Claudia dumped her 200-penny coin.
Claudia repeated this process 5 times and had an average of 84 pennies landing heads up.
The theoretical probability of a penny landing heads up is 21/50.
Option C is the final answer.
Would you be able to assist me in answering these questions ?
A direct variation is a relationship between 2 variables in which the changes are proportionate. The variables are related by a constant. This is also called a slope. Thus, the graph would always be a straight line. Therefore,
c) Direct variation models are always a type of linear models
a) The straight line always pass through the origin(0, 0)
b) A polynomial is an expression containing variables and coefficients. The variable can be in the form x^n where n can be any positive integer. This means that n can be 1,2,3,4.....If n is 1, the polynomial expression is linear. Thus, it can be a direct variation model. Therefore,
Direct variation models are sometimes a type of polynomial models
d) An exponential model is not linear. The form of a linear model is
y = ax
where a is the constant of pro
An exponential model is y = ab^x
The models are not the same. Thus,
Direct variation models are never a type of exponential model
Solve for a.69a = = √ [?]Pythagorean Theorem: a2 + b² = c²a
1) In this problem, we need to find the leg "a". Note that in the Pythagorean Theorem the hypotenuse, the largest leg is opposed to the right angle.
2) So, we can write out the following:
[tex]\begin{gathered} 9^2=6^2+a^2 \\ 81=36+a^2 \\ 81-36=a^2 \\ a^2=45 \\ a=\sqrt{45} \end{gathered}[/tex]Note that we could simplify that, but since the question wants it all under the radical.
For the data shown, answer the questions. Round to 2 decimal places. 5.2 18.8 5.7 5 14.9 4.4 Find the mean : Find the median : Find the standard deviation :
Median:
1. Order the data from less to greater:
4.4
5
5.2
5.7
14.9
18.8
2. As it is a even number of data you take the average of the two data in the middle to find the median:
[tex]\frac{5.2+5.7}{2}=5.45[/tex]The median is 5.45Standard deviation formula (for a sample):
[tex]s=\sqrt{\frac{\Sigma(x_i-\bar{x})\placeholder{⬚}^2}{n-1}}[/tex]To find the standard deviation of the given data:
1. Find the difference between each data and the mean:
[tex]\begin{gathered} (x_i-\bar{x}) \\ \\ 5.2-9=-3.8 \\ 18.8-9=9.8 \\ 5.7-9=-3.3 \\ 5-9=-4 \\ 14.9-9=5.9 \\ 4.4-9=-4.6 \end{gathered}[/tex]2. Find the square of each difference:
[tex]\begin{gathered} (x_i-\bar{x})\placeholder{⬚}^2 \\ \\ (-3.8)\placeholder{⬚}^2=14.44 \\ (9.8)\placeholder{⬚}^2=96.04 \\ (-3.3)\placeholder{⬚}^2=10.89 \\ (-4)\placeholder{⬚}^2=16 \\ (5.9)\placeholder{⬚}^2=34.81 \\ (-4.6)\placeholder{⬚}^2=21.16 \end{gathered}[/tex]3. Find the sum of the squares:
[tex]\begin{gathered} \Sigma(x_i-\bar{x})\placeholder{⬚}^2 \\ \\ 14.44+96.04+10.89+16+34.81+21.16=193.34 \end{gathered}[/tex]4. Use the formula of the standard deviation for n=6:
[tex]s=\sqrt{\frac{193.34}{6-1}}=\sqrt{\frac{193.34}{5}}=\sqrt{38.668}\approx6.22[/tex]Then, the standard deviation is 6.22Write the coordinates of the vertices after a rotation of 90 degrees counter clock wise around the origin. Give me the coordinates and that’s it no explanation
Which of the following is correct based on this picture? A. sinY=38/63B. none of these are correctC. tanY=38/63D. cosY=38/63
Answer
A. sin Y = 38/63
Explanation
Given:
What to find:
To find the correct trigonometric function of the given diagram.
Step-by-step solution:
Using the trigonometric function: SOH CAH TOA
[tex]\begin{gathered} SOH\text{ }is\text{ }sin\text{ }\theta=\frac{Opposite}{Hypotenuse} \\ \\ CAH\text{ }is\text{ }cos\text{ }\theta=\frac{Adjacent}{Hypotenuse} \\ \\ TOA\text{ }is\text{ }tan\text{ }\theta=\frac{Oppos\imaginaryI te}{Adjacent} \end{gathered}[/tex]From the diagram, θ = Y, Opposite = 38, Hypotenuse = 63
So the correct trigonometric function based on the given picture will be:
[tex]sin\text{ }Y=\frac{38}{63}[/tex]Thus, the correct answer is option A. sin Y = 38/63
Construct an isosceles right triangle.
Take into account that an isosceles triangle has two sides with equal lengthd and two internal angles with the same measure.
Then, for instance, you have the following triangle:
As you can notice, you have two angles with the same measure and two sides with the same lengths.
QUESTIONS 13,14 I NEED HELP dont understand ssorry for the caps didnt mean to
Answer
• 13. vertical angles.
,• 14. corresponding angles
Explanation
Assuming r and s are parallel lines, and that the line u (marked with stars) is a transversal cutting r and s, then the angles formed (a, b, and c) acquire some special properties.
• 13
Regarding ∠a and ∠b are vertical angles, which means they have the same measure.
• 14
Regarding ∠a and ∠c they are corresponding angles, which means they have the same measure.
Use associative property of addition to rewrite the following statement -1+(2.8+(-2))
Step 1
Write the additive property of addition.
[tex](a+b)+c=\text{ a+(b+c)}[/tex]Where
[tex]\begin{gathered} a=\text{ -1} \\ b=2.8 \\ c=-2 \end{gathered}[/tex]Step 2
Find the simplified form of the problem using the property in step 1
[tex](-1+2.8)+(-2)=-1+(2.8+(-2))[/tex][tex]\begin{gathered} 1.8-2=-1+0.8 \\ -0.2=-0.2 \end{gathered}[/tex]Hence the rewritten form of the problem using the additive property is
(-1+2.8)+(-2) and the simplified form of the problem = -0.2
Claire wants to determine how her math score, 690, on a standardized college entrance exam compares to her mother's score, 680, when she took the exam 20 years earlier. The year Claire took the exam, the mean math score was 510 with a standard deviation of 110 points. When Claire's mother took the exam, the mean math score was 490 with a standard deviation of 100 points. Who had the better relative performance? Claire did better because her Z-score is greater than her mother's. Claire's mother did better because her z-score is greater than Claire's. Claire did better because her z-score is closer to the mean than her mother's. Claire's mother did better because her z-score is closer to the mean than Claire's.
The z score tells us the number of standard deviations that a given value is from the mean. Recall, standard deviation tells us the spread of the values from the mean
For Claire, the mean score was 510 but she scored 690 which was higher than the mean score
The z score would be
(690 - 510)/110 = 1.63
For Claire's mother, the mean score was 490 but she scored 680 which was higher than the mean score
The z score would be
(680 - 490)/100 = 1.9
We can see that her mother had a higher z score. Compared to the average score, she had a better performance. Therefore, the correct option is
Claire's mother did better because her z-score is greater than Claire's.
7.If you raised $15 byday 2 and by day 7 youhad $75. What is therate of change?
We have the following:
the rate of change is equal to a slope, therefore we can calculate it as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{75-15}{7-2}=\frac{60}{5}=12[/tex]The rate of change is $12/day
this is the question
Kelly, this is the solution:
We have the following system of equations:
y = 1/4x + 4
x + y = - 1
___________
Solving it algebraically:
x + (1/4x + 4) = -1
5/4x + 4 = -1
5/4x = -1 - 4
5/4x = -5
x = -4
-4 + y = -1
y = -1 + 4
y = 3
Solving it graphically:
Find the mass of a cylinder with a volume of 157.08 ft^3 and a density of 0.900 g/cm^3. Final answer should be in kilograms (kg).
Okay, here we have this:
Considering the provided information, we are going to calculate the requested mass, so we obtain the following:
Then we will substitute in the following formula:
density=mass/volume
0.9 g/cm^3=mass/157.08 ft^3
mass=0.9 g/cm^3*157.08 ft^3
Then we will convert the volume from cubic feet to cubic centimeters in order to operate:
mass=0.9 g/cm^3*(157.08 ft^3*(28317 cm^3/1 ft^3)
mass=0.9 g/cm^3*4448034.36cm^3
mass=4003230.924 g
Finally let's convert the mass to kilograms:
mass=4003230.924 g*(1kg/1000g)
mass=4003.230924 kg
Finally we obtain that the mass of the cylinder is approximately 4003.230924 kg.
Write the standard form of the equation and the generalform of the equation of the circle with radius r and center(h,k). Then graph the circle.AY6r=2; (h,k) = (0,2)4The standard form of the equation of this circle is2The general form of the equation of this circle is(Simplify your answer.)-4-2Graph the circle.-2Click toenlargegraph4
coordiantes of the circle center = (h, k) = (0, 2)
h = 0, k = 2
r = 2
[tex]\begin{gathered} Standardform\text{ of the equation of circle:} \\ \text{ }(x-h)^2+(y-k)^2=r^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ }(x-0)^2+(y-2)^2=2^2 \\ x^2+(y-2)^2\text{ = 4} \end{gathered}[/tex][tex]\begin{gathered} \text{General form of the equation of circle:} \\ x^2+y^2\text{ }+\text{ 2gx + 2fy + c = 0} \end{gathered}[/tex][tex]\begin{gathered} center\text{ of circle = (-g, -f)} \\ given\text{ }center\text{ of circle = (0, 2)} \\ -g\text{ = 0 } \\ g\text{ = 0} \\ -f\text{ = 2} \\ f\text{ = -2} \end{gathered}[/tex][tex]\begin{gathered} radius\text{ = }\sqrt[]{g^2+f^2-c} \\ 2\text{ = }\sqrt[]{0^2+(-2)^2\text{ + c}} \\ 2\text{ = }\sqrt[]{0+4\text{ + c}} \\ \text{square both sides:} \\ 2^2\text{ = }4\text{ + c} \\ 4\text{ = 4 + c} \\ c\text{ = 4-4 = 0} \end{gathered}[/tex][tex]\begin{gathered} \text{General form of the equation of circle:} \\ x^2+y^2\text{ }+\text{ 2(0)x + 2(-2)y + 0 = 0} \\ x^2+y^2\text{ - 4y = 0} \end{gathered}[/tex]plotting the graph:
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
9
1) In this right triangle we can find the missing leg by using the Pythagorean Theorem.
2)
a² = b² + c² Note that the hypotenuse is unknown so far
a² = 7² + (4√2)²
a² = 49 +(16 x2)
a² = 49 +32
a² =81 Take the square root on both sides
√a² = √81
a = -9, 9 Negative numbers for dimensions are not convenient.
a = 9
3) Hence, the answer is 9
find the slope of the line that passes through (-82, -25) and (-81, 4)
The slope is 29
Explanation:The slope of a line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where -82 and -81 are the coordinates for x, and
-25 and 4 are the coordinates for y.
[tex]\begin{gathered} m=\frac{4-(-25)}{-81-(-82)} \\ \\ =\frac{4+25}{-81+82} \\ \\ =\frac{29}{1}=29 \end{gathered}[/tex]