since birth hakem has had a savings account that started at $3,000 and had been growing at a rate of 13% per year the amount of money in the account can be modeled by the equation y equals P =(1.13)^ Z where why is the value of the count is the number of years and pee was original deposit amount is it possible for hakem account to grow to $31812 11.42 in hakem lifetime?( try to figure out the bounds of the perameter)
Answers
Solution
For this case we have the following formula:
[tex]y=3000(1.13)^x^{}[/tex]And we want to find the value for t in order to have y = 3181211.42 , solving for y we got:
[tex]3181211.42=3000(1.13)^x[/tex]and solving for x we got:
[tex]\ln (\frac{3181211.42}{3000})=x\cdot\ln (1.13)[/tex][tex]x=56.99\approx57[/tex]for this case we need 57 years to reach the amount so then assuming that a person lives about 80 years , then is possible
yes
Related Questions
Select the correct answer.Christi is using a display box shaped like a regular pentagonal prism as a gift box. About how much gift wrap does she need to completely coverthe box?A 800 cm²B. 480 cm2C. 1,020 cm²D. 1,600 cm²
Answers
Given: A regular pentagonal prism with base edge 8cm and height 20 cm .
Find: wrap need to cover the box.
Explanation: for to find the length of wrap we need to find the area of regular pentagonal prism .
[tex]A=5ah+\frac{1}{2}\sqrt{5(5+2\sqrt{5)}}a^2[/tex]
where a=base edge=8cm and h =height=20 cm
[tex]\begin{gathered} A=5\times8\times20+\frac{1}{2}\sqrt{5(5+2\sqrt{5})}\times8^2 \\ =1020.2211\text{ cm}^2 \end{gathered}[/tex]Final answer: the required answer is 1020 square centimeter.
Answer:
C. 1,020 [tex]cm^{2}[/tex]
Hope this helps!
Step-by-step explanation:
The mayor of a town proposes to fence off a triangular area of a building that includes two sides of the building as shown below.Which distance, in feet could be the length of the proposed fence line?100280220130
Answers
Solution
Using triangle inequality
The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.
The fence line is the longest size
100, 130 can't be the answer
[tex]200+70=270[/tex]280 can't be the answer be ause the triangle inequality says it should be less than the sum
[tex]Z<\text{ X +Y}[/tex]Therefore, the correct answer is 220
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. How many bags of sand are needed? Use 3.14 for pi. Round bags up.
I am getting hung up on the last part of doing this problem.
Any help is greatly appreciated.
Answers
Sand will be placed under the base of a circular pool with a diameter of 14 feet. 1 bag of sand covers about 5 square feet. the number of bags of sand required is 30bags.
The area of the pool is
A = πr²
A = 3.14×(7 ft)² = 153.8 ft²
The number of bags of sand required is ...
(153.8 ft²)/(5 ft²/bag) ≈ 30.76bags
bags of sand are needed.
What is diameter?The diameter is defined as twice the length of the radius of the circle. The radius is measured from the centre of the circle to one endpoint on the boundary of the circle, while the diameter is the distance measured from one end of the circle to a point on the other end of the circle that passes through the centre. This is indicated by the letter D. The circumference of a circle has an infinite number of points, which means that the circle has an infinite number of diameters and each diameter of the circle is the same length.
Ø is the symbol used in the design to indicate the diameter. This symbol is often used in technical data and drawings.
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7) A math teacher asked 60 randomly selected 7th graders whether they 10 pointsare left handed or right handed. The table below shows the results of thesurveyLeft or Right-Handed?Hand FrequencyLeftRight4218A school has a total of 280 seventh-grade students. Based on the resultsshown in the table above, how manyof those seventh-grade studentswould you expect to be left-handed?A 60B 72C 84D 120
Answers
Answer:
C. 84
Explanation:
First, we will calculate the percentage of left-handed students in the group of 60 that the teacher asked.
So, the percentage is equal to:
[tex]\frac{18}{60}\times100\text{ \% = 30\%}[/tex]Therefore, 30% of the randomly selected students are left-handed.
Now, we can use this percentage to estimate the number of left-handed students in the group of 280.
Then, 30% of 280 is equal to:
[tex]30\text{ \% }\times280=\frac{30}{100}\times280=84[/tex]So, the answer is C. 84.
PLEASE I NEED THIS ANSWER ASAP!!!!!!
46% of employees judge their peers by the cleanliness of their workspaces. You randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces. The random variable represents the number of employees who judge their peers by the cleanliness of their workspaces. Complete parts (a) through (c) below.
Answers
Using the binomial distribution, the probabilities are given by the image at the end of the answer.
Binomial distributionThe probability mass function is given as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the function are described as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.x is the number of successes that we want to find the probability of.In the context of this problem, the values of these parameters are given as follows:
p = 0.46, as 46% of employees judge their peers by the cleanliness of their workspaces.n = 8, as you randomly select 8 employees and ask them whether they judge their peers by the cleanliness of their workspaces.To complete the table, we find each probability, as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.46)^{0}.(0.54)^{8} = 0.0072[/tex]
[tex]P(X = 1) = C_{8,1}.(0.46)^{1}.(0.54)^{7} = 0.0493[/tex]
[tex]P(X = 2) = C_{8,2}.(0.46)^{2}.(0.54)^{6} = 0.1469[/tex]
[tex]P(X = 3) = C_{8,3}.(0.46)^{3}.(0.54)^{5} = 0.2503[/tex]
[tex]P(X = 4) = C_{8,4}.(0.46)^{4}.(0.54)^{4} = 0.2665[/tex]
[tex]P(X = 5) = C_{8,5}.(0.46)^{5}.(0.54)^{3} = 0.1816[/tex]
[tex]P(X = 6) = C_{8,6}.(0.46)^{6}.(0.54)^{2} = 0.0774[/tex]
[tex]P(X = 7) = C_{8,7}.(0.46)^{7}.(0.54)^{1} = 0.0188[/tex]
[tex]P(X = 8) = C_{8,8}.(0.46)^{8}.(0.54)^{0} = 0.0020[/tex]
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What is the center of the circle simplify any fractions
Answers
Answer:
[tex](x,y)\rightarrow(0,4)[/tex]Explanation: We have to find the center of the circle, the equation of the circle is as follows:
[tex]x^2+y^2-8y-48=0\rightarrow(0)[/tex]Ploting the equation (0) gives the following result:
Therefore the center of the circle has the coordinates (0,4).
Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^2 is shifted up 1 unit and to the left 2 units.The new equations f(x)=Answer
Answers
Given the function f(x) defined as:
[tex]f(x)=x^2[/tex]We need to obtain the graph after performing two shifts: 1 unit up and 2 units left. For the first shift, we do the transformation:
[tex]f(x)\rightarrow f(x)+1[/tex]Now, for the second shift:
[tex]f(x)\rightarrow f(x+2)[/tex]Combining these transformations:
[tex]\begin{gathered} f(x)\rightarrow f(x+2)+1 \\ \therefore f(x)=(x+2)^2+1 \end{gathered}[/tex] Write the equation of a line that passes through the point (-2,-12) is parallel to the equation y= 2x +3
Answers
The most appropriate choice for equation of line in slope intercept form will be given by-
y = 2x - 8 is the required equation of line
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
Here,
The given equation of line is y= 2x +3
Slope of this line = 2
Slope of the line parallel to this line = 2
The line passes through (-2, -12)
Equation of the required line = y - (-12) = 2(x - (-2))
= y + 12 = 2x + 4
= y = 2x + 4 - 12
= y = 2x - 8
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Greg's youth group is collecting blankets to take to the animal shelter. There are 38 people in the group, and they each gave 2 blankets. They got an additional 29 by asking door-to-door. They set up boxes at schools and got another 52. Greg works out that they have collected a total of 121 blankets. Does that sound about right?
Answers
We want to know the total of blankets that Greg's collected.
As there are 38 people in the group, and they each gave 2 blankets, they brough a total of 79 blankets.
As they got 29 asking door-to-door, and got another 52, we will sum the values, as shown:
[tex]79+29+52=160[/tex]This means that the Greg group collected a total of 160 blankets, instead of 121, and the Greg statement is false.
A paving company has 24 employees, 15 with gross earnings of $365 per week and 9 with gross earnings of $385 per week. What is the total social security and medicade for the first quarter of the year
Answers
The total social security and medicade for the first quarter of the year is $17,781.66.
How to calculate the tax?The computation will be:
Gross earning per week = 15 * 365 + 9 * 385
= $8,940 per week
Here, the number of weeks is 13 in each quarter:
Gross earning =$8,940 * 13
= $116,220
Social security tax = $116,220 * 6.2%
= $7,205.64
Medicare tax = $116,220 * 1.45%
= $1,685.19
Total = $7,205.64 + $1,685.19
= $8,890.83
Now, to involve the employer's share it is required to multiply the total tax by 2
Therefore,
Total tax remitted to IRS = $8,890.83 * 2
= $17,781.66
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Finding the mode and range of a data set Each day, Kaitlin records the number of news articles she reads. Here are her results for the last eight days. 7, 3, 8, 5, 7,7,7,8 Find the mode and the range for the data. Mode: Range: X 5 ?
Answers
Explanation:
The set of values are given below as
[tex]7,3,8,5,7,7,7,8[/tex]Mode:
This the data that occurs highest or the dat that has the highest frequency
Range:
The is the difference between the lowest val and the highest value
[tex]Range=highest-lowest[/tex]Hence,
The final answers are
[tex]\begin{gathered} mode=7(it\text{ occurs 4 times\rparen} \\ range=8-3=5 \end{gathered}[/tex]Hence,
The final answer is
[tex]\begin{gathered} mode=7 \\ Range=5 \end{gathered}[/tex]hello i am haveing some trouble with ineqalles and can you help with this create a word problem that leads to an inequality by filling in the blanks with your corresponding answer.Twenty subtracted from the product of seven and a number exceeds one hundred.
Answers
Step 1
To change word problem to an inequality, you must take the word problem step by step and translate it into an inequality.
Step 2
Take the word problem step by step
[tex]\begin{gathered} \text{Twenty refers to the number }^{\prime}20^{\prime} \\ \text{Twenty subtracted from means 20 was removed from something.} \\ i.e\text{ say x-20} \end{gathered}[/tex][tex]\begin{gathered} \text{Twenty subtract}ed\text{ from the product of seven and a number } \\ \text{Product of seven and a number first} \\ Let\text{ the number be x} \\ so\text{ it now} \\ \text{Product of seven and x=7x } \end{gathered}[/tex][tex]\text{Twenty subtract}ed\text{ from the product of seven and a number}=7x-20[/tex]3. Define and find the value of the central angle theinscribed angle, and the arc associated with both.Central angle:namemeasureInscribed angle:namedoYmeasureArc:namemeasure
Answers
Given
Answer
Central angle
Name XOY
Measure 90
Inscribed angle
name XZY
Measure 45
Arc
name XY
Measure = circumference of circle/4
The following hyperbola has a horizontal transverse axis: (x + 2) (w+7)=11617
Answers
for the given hyperbola
[tex]\frac{(x+2)^2}{16}-\frac{(y+7)^2}{17}=1[/tex]We have the following graph. Visually we can see that this hyperbola does have a transverse axis, however you can do all the calculations to check it
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ h=-2 \\ k=-7 \\ a^2=16 \\ b^2=17 \\ c^2=16+17 \\ c=\sqrt[]{33}=5.7 \\ f_1=(h-c,k) \\ f_1=(-2-5.7,-7) \\ f_2=(-7.7,-7) \\ f_2=(3.7,-7) \\ y=-7\to\text{ is the ecuation of the transversal axis} \end{gathered}[/tex]As we can see y = -7 is a line parallel to the x axis, turning the transversal axis horizontal.
That is, this hyperbola does have a horizontal transverse axis and the answer is TRUE
picture is down below, i have to take another picture of C & D
Answers
Answer
f(x)
domain: all real numbers, range: all real numbers
f⁻¹(x)
domain: all real numbers, range: all real numbers
Step-by-step explanation
Given the function:
[tex]f(x)=-x+5[/tex]This is the equation of a line.
The domain and range of a linear function are all real numbers.
On the other hand, the range of an inverse function is the domain of the original function and the domain of an inverse function is the range of the original function. Then, the domain and range of the inverse of f(x) are all real numbers.
If $19,000.00 is invested in an account for 30 years. Find the value of the investment at the end of 30 years if the interestis:(a) 7% simple interest:(b) 7% compounded monthly:
Answers
Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.
For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).
For compound interest, the balance will be equal to P(1 + r)^t.
So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:
a) 7% simple interest
It means that r = 7% and then we can use the first formula
19000(1 + 0.07*30)
We converted the rate to decimals above
Multiplying the values, we have:
19000(1 + 2.1)
19000*3.1
$58.900
b) 7% compounded monthly
First, we need to convert the time from years to months, multiplying by 12
30*12 = 360 months
Using the second formula, we have:
19000(1 + 0.07)^(360)
Sum the values into parenthesis
19000*1.07^(360)
Solve the problems below as fast as you can because I’m trying to go to sleep but it’s not an assignment or graded or timed please
Answers
Given the inequality:
4m < 24
Let's solve for m.
To solve for m, divide both sides of the inequality by 4:
[tex]\begin{gathered} \frac{4m}{4}<\frac{24}{4} \\ \\ m<6 \end{gathered}[/tex]ANSWER:
m < 6
The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
Answers
The smaller of two similar balloons has a diameter of 10 inches. If it takes 12 (same sized) breaths to blow up the smaller balloon and 40.5 to blow up the larger, what is the diameter of the larger balloon?
we have that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube.
so
Find the scale factor
ratio volumes=40.5/12=3.375
3.375=(scale factor)^3
[tex]\text{scale factor=}\sqrt[3]{3.375}[/tex]scale factor=1.5
To find out the diameter of the larger balloon multiply the scale factor by the diameter of the smaller balloon
so
1.5*(10)=15 inches
the answer is 15 inches17. A moving company charges a flat rate of $85 plus and additional $0.17 per mile driven. How far must the company drive to earn at least $100? Round to thenearest mile.x2 84x2 78x2 80x2 88
Answers
ANSWER
88
EXPLANATION
Let x be the miles driven and y be the earnings of the company when they drive for x miles.
If the company charges $0.17 per mile driven plus a flat rate of $85, then the total cost for moving x miles away is,
[tex]y=85+0.17x[/tex]Now, we have to find for how many miles, x, the company must drive to earn $100 or more,
[tex]85+0.17x\ge100[/tex]Subtract 85 from both sides,
[tex]\begin{gathered} 85-85+0.17x\geq100-85 \\ \\ 0.17x\ge15 \end{gathered}[/tex]And divide both sides by 0.17,
[tex]\begin{gathered} \frac{0.17x}{0.17}\ge\frac{15}{0.17} \\ \\ x\ge88.24 \end{gathered}[/tex]Hence, the company must drive for at least 88 miles to earn at least $100, rounded to the nearest mile.
Solve the following inequality: 6p - 15 < 33
Answers
WE are to solve an inequality, so we proceed to isolate the variable "p" on one side of the inequality symbol:
6 p - 15 < 33
we add 15 to both sides:
6 p < 33 + 15
6 p < 48
now divide both sides by 6 (notice that since 6 is a positive number, the division doesn't change the direction of the inequality)
p < 48/6
p < 8
So we need to highlight on the number line, the line that starts at "8" and goes all the way to the left (to minus infinity), and make sure that at the point "8" you draw an "empty" circle to indicate that the number 8 itself is NOT included in your set of solutions.
For every 4 songs on Mary's playlist, 3 of the songs are longer than 5 minutes.
Complete the table of values to compare the total money spent to tickets purchased.
Total Number of Songs on Playlist
Number of Songs Longer Than 5 Minutes
8
32
40
136
Answers
we were told that in every 4 songs on the playlist, 3 of the songs are longer than 5
so if in for 4 songs, 3 is longer than 5
for 8 songs,
we divide the the number of songs in the playlist by 4 in other to get the numbers of 4 in it then muliply by the number of songs longer than 5
for 8 songs on the playlist:
= 8/4 X 3
= 2 X 3
= 6
For 32 songs on the playlist
= 32/4 X 3
= 8 X 3
= 24
For 40 songs on the playlist
= 40/4 X 3
= 10 X 3
= 30
For 136 number of songs on the playlist
= 136/4 X 3
= 34 X 3
= 102
so in completing the table:
Total Number of Songs on the Playlis Number of songs longer than 5min.
8 6
32 24
40 30
136 102
Rosa needs to build a wall. She has to start the wall with one postand then every 5.75 feet put another post. The wall will be166.75 feet long. How many posts will she need?
Answers
For every 5.75 feet, here is one post.
Determine the number of posts in a wall of 166.75 feet.
[tex]\begin{gathered} p=\frac{166.75}{5.75} \\ =29 \end{gathered}[/tex]So 29 posts needed for the wall.
Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.
Answers
Given the table that shows the number of movies and the corresponding frequency, you can determine that the total frequency is:
[tex]Total\text{ }Frequency=25[/tex]By definition:
[tex]Relative\text{ }Frequency=\frac{Frequency}{Total\text{ }Frequency}[/tex]By definition, the Cumulative Frequency can be obtained by adding the corresponding frequency with the previous frequencies and dividing the sum by the Total Frequency.
Therefore, you can determine that:
- For:
[tex]Frequency=3[/tex]You know:
[tex]Relative\text{ }Frequency=\frac{3}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3}{25}[/tex]- Given:
[tex]Frequency=8[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{8}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8}{25}=\frac{11}{25}[/tex]- Given:
[tex]Frequency=9[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{9}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9}{25}=\frac{4}{5}[/tex]- Given:
[tex]Frequency=4[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{4}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9+4}{25}=\frac{24}{25}[/tex]- Given:
[tex]Frequency=1[/tex]You get:
[tex]Relative\text{ }Frequency=\frac{1}{25}[/tex]And:
[tex]Cummulative\text{ }Relative\text{ }Frequency=\frac{3+8+9+4+1}{25}=\frac{25}{25}=1[/tex]Hence, the answer is:
10)BONUSKelll walks into science class and they have 6 hershey kisses and 6 reese cups on a scale that reads82.4 ounces. She wants some chocolate so she eats 2 hersey kisses and 1 reese cup and now thescale reads 63.8 ounces.a) Define your variables and set up a system of equations.
Answers
Leah, this is the solution:
Variables:
Let x to represent the weight of one Hershey kiss
Let y to represent the weight of one Reese cup
System of equations:
6x + 6y = 82.4
4x + 5y = 63.8
______________
Let's multiply the second equation by - 3/2, therefore:
6x + 6y = 82.4
-6x - 15y/2 = -95.7
________________
-15/2 + 6 = -3/2
_________________
-3y/2 = -13.3
Dividing by -3/2 at both sides:
-3y/2 / -3/2 = -13.3 / -3/2
y = 8.87
______________
Replacing y in the first equation and solving for x:
6x + 6 * 8.87 = 82.4
6x + 53.22 = 82.4
Subtracting 53.22 at both sides:
6x +53.22 - 53.22= 82.4 - 53.22
6x = 29.18
Dividing by 6 at both sides:
6x/6 = 29.18/6
x = 4.86
_________________
In conclusion, one Hershey kiss weights 4.86 ounces and one Reese cup weights 8.87 ounces.
If the snow is falling at a rate of 1 inches per hour, how many hours will it take to snow 12 inches?
Answers
Imagine the following, we will place a tube under the snow. So we have the following
After one hour, the tube will be filled with 1 inch of snow.
After 2 hours, we will have one inch more
So, one way to calculate the amount of snow after a specific amount of hours, is simply multiplying the hours by the rate at which the height of the snow changes. IN here, the height changes 1 inch per hour. So after x hours the height of the snow would be
[tex]1\cdot\text{ x }[/tex]We want to find x, such that the height of the snow is 12.
So we have the equation
[tex]1\cdot x\text{ = 12}[/tex]which gives us that in 12 hours we will have 12 inches of snow.
After adding the two equations to eliminate x you are left with 4y=-8
Answers
solve for y
[tex]\begin{gathered} \frac{4y}{4}=-\frac{8}{4} \\ y=-2 \end{gathered}[/tex]then, solve for x
[tex]\begin{gathered} 2x-2=4 \\ 2x-2+2=4+2 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]x = 3
y = -2
which of the following are the coordinates of point B on the directed line segment AC, such that AB is 1/5 of AC?
Answers
Answer:
The coordinates of point B is;
[tex](5,-7)[/tex]Explanation:
Given the attached image;
The coordinate of point A is;
[tex](8,-8)[/tex]The coordinate of point C is;
[tex](-7,-3)[/tex]If AB is 1/5 of AC;
[tex]\Delta x_{AB}=\frac{1}{5}(\Delta x_{AC})_{}_{}_{}_{}_{}_{}[/tex]So; let (x,y) represent the coordinates of B;
[tex]\begin{gathered} (8-x)=\frac{1}{5}(8-(-7)) \\ 8-x=\frac{1}{5}(15) \\ 8-x=3 \\ x=8-3 \\ x=5 \end{gathered}[/tex]The same applies to y coordinate;
[tex]\Delta y_{AB}=\frac{1}{5}(\Delta y_{AC})_{}[/tex]So;
[tex]\begin{gathered} (-8-y)=\frac{1}{5}(-8-(-3)) \\ -8-y=\frac{1}{5}(-8+3) \\ -8-y=\frac{1}{5}(-5) \\ -8-y=-1 \\ y=-8+1 \\ y=-7 \end{gathered}[/tex]Therefore, the coordinates of point B is;
[tex](5,-7)[/tex]Surface area of a cone: S = πr² + πrl;solve for l.
Answers
Answer:
[tex]l=\frac{S-\pi r^{2}}{\pi r}[/tex]Explanation:
The surface area of a cone is calculated using the formula:
[tex]S=πr^2+πrl[/tex]We want to solve for l.
First, subtract πr² from both sides of the equation:
[tex]\begin{gathered} S-\pi r^2=\pi r^2-\pi r^2+\pi rl \\ S-\pi r^2=\pi rl \end{gathered}[/tex]Next, divide both sides by πr:
[tex]\begin{gathered} \frac{S-\pi r^2}{\pi r}=\frac{\pi rl}{\pi r} \\ l=\frac{S-\pi r^{2}}{\pi r} \end{gathered}[/tex]The equation solved for l is:
[tex]l=\frac{S-\pi r^{2}}{\pi r}[/tex]in the graph below line k,y=-x makes a 45 degree angle with the x and y axescomplete the following
Answers
step 1
The equation of line k is y=-x
The rule of the reflection across the line y=-x is equal to
(x,y) -------> (-y,-x)
so
we have the point (2,5)
Apply the rule
(2,5) -----> (-5,-2)
step 2
Reflection across the x axis
The rule of the reflection across the x axis is
(x,y) ------> (x,-y)
so
Apply the rule to the point (-5,-2)
(-5,-2) ------> (-5,2)
therefore
the answer is
(-5,2)Sales representatives of a new line of computers predict that sales can be approximated by the function (0= 1350 + 6101n(31+ e), where is measured in years.What are the predicted sales in 15 years? Round your answer to the nearest whole number
Answers
It is predicted that sales over time can be approximated by the function:
[tex]S(t)=1350+610\ln(3t+e)[/tex]It is required to find the predicted sales in 15 years to the nearest whole number.
To do this, substitute t=15 into the given function:
[tex]S(15)=1350+610\ln(3\cdot15+e)=1350+610\ln(45+e)[/tex]Evaluate and round to the nearest whole number as required:
[tex]S(15)=1350+610\ln(45+e)\approx3708[/tex]The sales in 15 years is about 3708.