Answer:
the number of students that enrolled after 15 year is 317
Step-by-step explanation:
The computation of the number of students that enrolled after 15 year is shown below;
We know that
Future value = Present value × (1 +rate of interest)^number of years
= 100 × (1+8%)^15
= 100 × 1.08^15
= 317
Hence, the number of students that enrolled after 15 year is 317
The same should be considered and relevant
Find the volume and surface area of the rectangular solid. The length is 4 meters, the width is 6 meters, and the height is 3 meters.
Answer:
Volume = h * w * l (height, width, length)
Volume = 4* 6 * 3
Volume = 72 cube meters
Surface area is finding the are of every 2D plane on the solid.
2(w * h) + 2(l*h) + 2(w * l)
Surface are = 108 square meters
Use an appropriate series in (2) in Section 6.1 to find the Maclaurin series of the given function. Write your answer in summation notation. 1 5 x
Answer:
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
Step-by-step explanation:
Poorly formatted question.
The given parameters can be summarized as:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex] ----- the series
Required
Determine [tex]e^\frac{1}{5}^x[/tex]
We have:
[tex]e^x = \sum\limits^{\infty}_{k=0} \frac{x^k}{k!}[/tex]
Substitute [tex]\frac{1}{5}x[/tex] for x
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{(\frac{1}{5}x)^k}{k!}[/tex]
Split
[tex]e^{\frac{1}{5}x} = \sum\limits^{\infty}_{k=0} \frac{1}{5}^k \cdot \frac{x^k}{k!}[/tex]
the size of an interior angle of a regular polygon is 3x. It's exterior is (x- 20)°. Find number if the sides of the polygon.
Answer: 12
Step-by-step explanation: Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.
Answer:
Step-by-step explanation:
Since the angles are supplements, 3x + x - 20 = 180. Solving this, we find that x = 50, and 3x = 150. Since dodecagons have interior angles of 150 degrees, the answer is 12 sides.
At 3:15 p.m., Sten began packing snacks to take to the park.
He spent 20 minutes packing snacks for his friends.
He spent 5 minutes loading the snacks into his backpack.
Using the number line, how many minutes does he now have until he leaves for the park at 4:00 p.m.?
Answer:
20 minutes
Step-by-step explanation:
20 minutes after 3:15 is 3:35, then 5 more minutes is 3:40. Therefore Sten has 20 minutes left until 4pm.
Convert 7,34 cm to meters
Answer:
Value of 7.34 centimeter into meter is 0.0734
Step-by-step explanation:
Given value;
7.34 centimeter
Find:
Value of 7.34 centimeter into meter
Computation:
We know that
⇒ 1 centimeter = 0.01 meter
So,
⇒ 7.34 centimeter = 7.34 x 0.01
⇒ 7.34 centimeter = 7.34 x 1/100
⇒ 7.34 centimeter = 7.34 / 100
⇒ 7.34 centimeter = 0.0734 meter
Value of 7.34 centimeter into meter is 0.0734
A triangle has sides measuring 2 inches and 7 inches. If x represents the
length in inches of the third side, which inequality gives the range of possible
values for x?
O A. 5sxs 9
O B. 2 sxs7
O C. 2
OD. 5
Answer is
5 gives the range of possible values for x.
Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants.
Class Frequency
8.26 20
10.01-11.75 38
11.76 36
13.51-15.25 25
15.26-17.00 27
Sample Variance: ___________
Sample Standard Deviation: _________
Answer:
(a) The sample variance is 16.51
(a) The sample standard deviation is 4.06
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}[/tex]
Solving (a); The sample variance.
First, calculate the class midpoints.
This is the mean of the intervals.
i.e.
[tex]x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13[/tex]
[tex]x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88[/tex]
[tex]x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63[/tex]
[tex]x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38[/tex]
[tex]x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13[/tex]
So, the table becomes:
[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}[/tex]
Next, calculate the mean
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}[/tex]
[tex]\bar x = \frac{1845.73}{146}[/tex]
[tex]\bar x = 12.64[/tex]
Next, the sample variance is:
[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]
So, we have:
[tex]\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}[/tex]
[tex]\sigma^2 = \frac{2393.6875}{145}[/tex]
[tex]\sigma^2 = 16.51[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{16.51}[/tex]
[tex]\sigma = 4.06[/tex]
Brooke decided to ride her bike from her home to visit her friend Adam. Two miles away from home, her bike got a flat tire and she had to walk the remaining four miles to Adam's home. She could repair the tire and had to walk all the way back home. How many more miles did Brooke walk than she rode.
Answer:
8 miles
Step-by-step explanation:
I'm going to assume the question said that she "couldn't" repair the tire and was forced to walk back home, that makes more sense.
With that in mind:
She rode her bike 2 miles.
She walked 4 miles on the way there, and 6 miles on the way back.
You can deduce that it was a 6 mile walk back because of the 2 mile bike ride, then the 4 mile walk that it took to get there.
All in all that rounds out to 10 mile walking, and 2 mile biking. That is 8 miles more walking than biking.
What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?
Two-elevenths
Three-elevenths
Five-elevenths
Six-elevenths
The probability that a marble chosen at random is shaded or is labeled with a multiple of 3 is 6/11.
We have given that options
Two-elevenths
Three-elevenths
Five-elevenths
Six-elevenths
We have to determine the probability that a marble chosen at random is shaded or is labeled with a multiple of 3.
What is the probability?Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Therefore the probability that a marble chosen at random is shaded or is labeled with a multiple of 3 is 6/11.
To learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ2
6/11
Step-by-step explanation:
Can someone please help me?
Answer:
use the Desmos graphing calculator. Type the first one in. Then type your answer choices in. See which lines are the same.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Just simplify
Equilateral triangle L N M is shown.
The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?
5 StartRoot 2 EndRoot units
4 StartRoot 3 EndRoot units
10 StartRoot 2 EndRoot units
16 StartRoot 5 EndRoot units
Answer:
4 StartRoot 3 EndRoot units
Hope this answer is right!!
Step-by-step explanation:
Since AD is perpendicular to BC, so ΔABD will be aright-angled triangle. Thus, the length of the altitude is 4√3 units.
The length of the altitude of the equilateral triangle is 4√3 units.
The given parameters;
Length of a side of the equilateral triangle, L = 8 unitsThe half length of the base of the triangle is calculated as follow;
[tex]x = \frac{8 \ units}{2} \\\\x = 4 \ units[/tex]
The height of the triangle is calculated by applying Pythagoras theorem as follows;
[tex]h^2 = L^2 - x^2\\\\h = \sqrt{(8^2) - (4^2)} \\\\h = \sqrt{48} \\\\h = \sqrt{16 \times 3} \\\\h = 4\sqrt{3} \ \ units[/tex]
Thus, the length of the altitude of the equilateral triangle is 4√3 units.
Learn more about equilateral triangle here: https://brainly.com/question/15294703
If the sum of the interior angle of a polygon is 2700 how many sides does the polygon have??
=================================================
Work Shown:
S = sum of all interior angles of a polygon
S = 180(n-2)
2700 = 180(n-2)
180(n-2) = 2700
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
There are 17 sides to this polygon.
-------------------------
Extra info (optional section):
We call this a 17-gon. Simply start with "n-gon" and replace n with 17.
You could also call it a heptadecagon
hepta = 7
deca = 10
so heptadeca means 17. Personally, I prefer 17-gon as the better name since it's easier to remember.
Suppose the true proportion of voters in the county who support a restaurant tax is 0.54. Consider the sampling distribution for the proportion of supporters with sample size n = 168.
What is the mean of this distribution?
What is the standard error of this distribution?
Answer:
The correct answer is:
(a) 0.54
(b) 0.0385
Step-by-step explanation:
Given:
Restaurant tax,
p = 0.54
Sample size,
n = 168
Now,
(a)
The mean will be:
⇒ μ [tex]\hat{p}= p[/tex]
[tex]=0.54[/tex]
(b)
The standard error will be:
[tex]\sigma \hat{p}[/tex] = [tex]\sqrt{[\frac{p(1-p)}{n} ]}[/tex]
= [tex]\sqrt{[\frac{(0.54\times 0.46)}{168} ]}[/tex]
= [tex]\sqrt{[\frac{(0.2484)}{168} ]}[/tex]
= [tex]0.0385[/tex]
Admission prices for a concert are $19 for adults and $11 for students. The concert will not be booked unless total ticket sales are at least $4500. Write the inequality that
expresses this information. (Let the x refer to the number of adult tickets and the y refer to the number of student tickets.)
Answer: [tex]19x+11y \ge 4500[/tex]
=============================================
Explanation:
x = number of adults
y = number of students
The expression 19x represents the money from all the adults while 11y represents the money from all the students (since we get $19 per adult and $11 per student).
In total, the money collected is 19x+11y dollars.
We want this total to be $4500 or larger.
So that's how we get the final answer of [tex]19x+11y \ge 4500[/tex]
The value of the expression
2x²
+ x(100 - 15x) when x = 5 is
Х
0 119.
0 129.
135.
0 145.
Answer:
f(5) = 75
Step-by-step explanation:
The function is f(x) = 2x^2 + x(100 - 15x).
Evaluate this function at x = 5: replace each instance of x with 5:
f(5) = 2(5)^2 + 5(100 - 15·5)
Order of operations rules require evaluating the expression enclosed in parentheses first. We get:
f(5) = 2(5)^2 + 5(100 - 15·5)
= 50 + (100 - 75), so that:
f(5) = 50 + 25 = 75
f(5) = 75
Answer:
175?
Step-by-step explanation:
The scatter plot below shows what kind of trend?
A positive trend
B no trend
C random trend
D negative trend
the answer is b no trend
X- 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? O (1, -1),(-1,1),(0'3/2)
Ik desperate please help the question is:
how many times more people will there be in the town after 15 years than after 10 years??? I need help ASAP!??!?!?!?!? 20 points?!?!?!!
pleaseeeee
Answer:
good point I don't know that either
12 Jy
10
Which statement is true regarding the graphed
functions?
g
18
f(
4
Of(0) = 2 and g(-2) = 0
Of(0) = 4 and g(-2) = 4
Of(2)= 0 and g(-2) = 0
Of(-2) = 0 and g(-2) = 0
2
3 4
5 6 x
t6 -5 -3 -2 -12
-4
16
8
10
-121
Mark this and retum
Save and Exit
Next
Submit
Given:
The graphs of the function f(x) and g(x).
To find:
The correct statement for the given graph.
Solution:
From the given graph it is clear that, the function f(x) passes through the points (0,4) and (2,0). So,
[tex]f(0)=4[/tex]
[tex]f(2)=0[/tex]
[tex]f(-2)\neq 0[/tex]
The graph of the function g(x) passes through the point (-2,0). So,
[tex]g(-2)=0[/tex]
Since [tex]f(2)=0[/tex] and [tex]g(-2)=0[/tex], therefore the correct option is C.
The graphs of the given functions, f(x), and g(x), bounces off the x-axis.
Correct response:
The true statement regarding the graphed function is the option;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0 }[/tex]Method used to find the true statementThe properties of the graph of f(x) and g(x) are;
When x = 0, the value of f(x) is; f(0) = 4
Therefore;
f(0) = 4
When x = 2, the value of f(x), which is the point on the graph corresponding to a x-value of 2 is; [tex]\underline{f(2) = 0}[/tex]
When x = 0, g(x) value is g(0) = 4
When x = -2, g(x) is; g(-2) = 0
The correct option is therefore;
[tex]\underline{f(2) = 0 \ and \ g(-2) = 0}[/tex]Learn more about functions here:
https://brainly.com/question/4179708
what is a line passing through the points (1, -1) and (9, 3) in equation form?
Answer:
[tex]x-2y=3[/tex]
Step-by-step explanation:
[tex]We\ are\ given,\\Line\ passes\ through\ the\ points\ (1,-1) and (9,3). Hence,\ this\ means\ that\ the\\ points\ are\ indeed\ solutions\ of\ the\ equation,\ which\ represents\ the\ line.\\Hence,\\We\ know\ that,\\The\ equation\ of\ a\ line\ (Point-Slope)\ is\ given\ by:\\y-y_1=m(x-x_1),\ where\ m\ is\ the\ slope\ of\ the\ graph.[/tex]
[tex]So\ first,\\Lets\ find\ the\ Slope\ of\ the\ Graph.\\Slope(m)=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}\\Hence,\\Here,\\Considering\ (1,-1)\ as\ the\ First\ Point\ and\ (9,3)\ as\ the\ Second\ Point,\ we\ have:x_1=1,x_2=9\ and\ y_1= -1, y_2=3\\Plugging\ the\ values\ in\ the\ Equation\ for\ the\ Slope,\ we\ have:\\[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-1)}{9-1}=\frac{3+1}{9-1}= \frac{4}{8}=\frac{1}{2}\\Hence,\\Coming\ back\ to\ our\ Point-Slope\ Formula\ for\ the\ equation:\\\ We\ already\ have:\\y-y_1=m(x-x_1)\\Substituting\ m=\frac{1}{2} , x_1=1,\ y_1=-1,\ we\ have: \\y+1=\frac{1}{2}(x-1)\\\therefore 2(y+1)=x-1\\\therefore 2y+2=x-1\\\therefore 2y-x=-3\\Multiplying\ with\ (-1)\ on\ both\ sides:\\\therefore x-2y=3\\Hence,\\x-2y=3,\ is\ our\ desired\ equation.[/tex]
Can someone help please
Answer:
2x^2 + 4
Step-by-step explanation:
f(g(x)) just means to first solved g(x) and put the solution into f(x).
Therefore, it becomes f(x)=(10x^2+5)/5 + 3, and you can simplify that into
2x^2 + 4.
Find the volume. Help please it’s due tomorrow
Answer:
2cm
Step-by-step explanation:
vbjufdxcvhjjkknvxzdhjkbcxdf
if you are just given the two points it is the same formula. Find the midpoint between the points (4,−5) and (−4,5).
Answer:
[tex]M = (0,0)[/tex]
Step-by-step explanation:
Given
[tex](4,-5)[/tex] and [tex](-4,5)[/tex]
Required
The midpoint (M)
This is calculated as:
[tex]M = \frac{1}{2}(x_1 + x_2,y_1+y_2)[/tex]
So, we have:
[tex]M = \frac{1}{2}(4-4,-5+5)[/tex]
[tex]M = \frac{1}{2}(0,0)[/tex]
[tex]M = (0,0)[/tex]
Milauskasville Middle School's Crazy Hair Club sold tickets to it's "Hair Today, Gone Tomorrow" talent show. A total of 55 tickets were sold in the amount of $176.50. If adult tickets cost $3.75 and student tickets cost $2.00, how many adult tickets and student tickets were sold?
Answer:
Adult ticket = 38
Student ticket = 17
Step-by-step explanation:
Let :
Adult ticket = x
Student ticket = y
x + y = 55 - - - - (1)
Cost per x = 3.75
Cost per y = 2
3.75x + 2y = 176.50 - - - (2)
From (1):
x = 55 - y
Put in (2)
3.75(55 - y) + 2y = 176.50
206.25 - 3.75y + 2y = 176.50
-1.75y = - 29.75
y = - 29.75 / - 1.75
y = 17
From :
x = 55 - y
x = 55 - 17
x = 38
Arithmetic or geometric 18,13,8
Answer:
That is Arithmetic
Step-by-step explanation:
Arithmetic Sequence is described as a list of numbers, in which each new term differs from a preceding term by a constant quantity. Which is -5 in this case.
Hope this helps
if x represents the number since 1988 what does x=32 represents
Explanation:
x is the number of years since 1988
x = 0 represents the year 1988
x = 1 is the year 1988+1 = 1989
x = 2 is the year 1988+2 = 1990
etc
x = 32 is the year 1988+32 = 2020
One wall inside an art studio is used to display paintings with oval frames and rectangular
frames. There are a total of 68 paintings on this display. There are 3 times as many
rectangular frames as there are oval frames in this display. How many oval frames and
rectangular frames are on the display?
Answer:
Oval frames = 17
Rectangular frames = 51
Step-by-step explanation:
Given that :
Paintings on wall are either oval or rectangular ;
Let :
Oval painting = x
Rectangular painting = y
According to the information given :
x + y = 68 - - (1)
Rectangular frames = 3 times oval frames
y = 3x - - - (2)
Put y = 3x in equation (1)
x + 3x = 68
4x = 68
x = 68/4
x = 17 frames
From :
x + y = 68
17 + y = 68
y = 68 - 17
y = 51
Oval frames = 17
Rectangular frames = 51
if y equal to-1 calculate the value of the expression
Answer:
thiếu giữ liệu không thể trả lời được
Step-by-step explanation:
Choose all measurements that are equivalent to 45 meters.
a. 450 centimeters
b. 4,500 centimeters
c. 0.045 kilometer
d. 0.45 kilometer
e. 4,500 millimeters
Answer:
option : b, c
Step-by-step explanation:
1 meter = 100 centimeters
45 meters = 4500 centimeters
1000 meter = 1 kilometer
[tex]45 \ meters = \ \frac{45}{1000} = 0.045 \ kilometers[/tex]
1 meter = 1000 millimeters
45 meters = 45, 000 millimeters
A surveyor is estimating the distance across a river. The actual distance is . The surveyor's estimate is . Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.
A surveyor is estimating the distance across a river. The actual distance is 284.5 m. The surveyor's estimate is 300 m. Find the absolute error and the percent error of the surveyor's estimate. If necessary, round your answers to the nearest tenth.
Answer:
(i) Absolute error = 15.5m
(ii) Percent error = 5.5%
Step-by-step explanation:Given:
Actual measurement of the distance = 284.5 m
Estimated measurement of the distance by the surveyor = 300 m
(i) The absolute error is the magnitude of the difference between the estimated value measured by the surveyor and the actual value of the distance across the river.
i.e
Absolute error = | estimated value - actual value |
Absolute error = | 300m - 284.5m | = 15.5m
(ii) The percent error (% error) is given by the ratio of the absolute error to the actual value then multiplied by 100%. i.e
% error = [tex]\frac{absoluteError}{actualValue}[/tex] x 100%
% error = [tex]\frac{15.5}{284.5}[/tex] x 100%
% error = 0.05448 x 100%
% error = 5.448%
% error = 5.5% [to the nearest tenth]