Using the z-distribution, the 95% confidence interval for the population proportion is (0.5791, 0.7133).
What is a confidence interval of proportions?
A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters are given as follows:
[tex]n = 195, \overline{p} = \frac{126}{195} = 0.6462[/tex]
Hence the bounds of the interval are:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6462 - 1.96\sqrt{\frac{0.6462(0.3538)}{195}} = 0.5791[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6462 + 1.96\sqrt{\frac{0.6462(0.3538)}{195}} = 0.7133[/tex]
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2. In factored form, a quadratic function can be written as y = (-2-x) (x-8). This parabola goes through the points (-2, 0) and (8, 0). Use your knowledge of the symmetry of the parabola to find the vertex. Show all work. 4 mark
Answer:
(3, 25)
Step-by-step explanation:
The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation: [tex]\frac{-2+8}{2}=\frac{6}{2}=3[/tex]. This means that the axis of symmetry is at: [tex]x=3[/tex], and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x
y = (-2-3)(3-8)
y = (-5)(-5)
y = 25
So this means the vertex is at (3, 25)
Graph the given functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of the functions to obtain ordered pairs. Describe how the graph of g is related to the graph of f
Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.
How the graphs are related?
Here we have:
[tex]f(x) = \sqrt{x}[/tex]
first we want to evaluate it in x = 0, 1, 4, 9.
Doing that we get:
[tex]f(0) = \sqrt{0} = 0\\f(1) = \sqrt{1} = 1\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]
The other function is:
[tex]g(x) = \sqrt{x} -3[/tex]
Evaluating in the same values of x.
[tex]g(0) = \sqrt{0} -3 = -3\\g(1) = \sqrt{1} -3 = -2\\g(4) = \sqrt{4} -3 = -1\\g(9) = \sqrt{9} -3 = 0[/tex]
Then we can see that for all the values of x, g(x) is 3 units less than f(x).
Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.
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Suppose $24,000 is deposited into an account paying 7.25% interest, which is compounded continuously.
How much money will be in the account after ten years if no withdrawals or additional deposits are made?
$49,553.54
$48,326.40
$47,897.10
$46,414.20
Answer:
$49,553.54
Explanation:
[tex]\sf Continuously \ compound \ interest : {A = P e^{rt}[/tex]
[tex][\sf where \ A \ is \ final \ amount, \ P \ is \ principal \ amount, \ r \ is \ interest \ rate, \ n \ is \ years][/tex]
Here given following:
principal amount (P) = $24,000rate of interest (r) = 7.25%years (t) = 10 yearsInserting these values in formula:
[tex]\rightarrow {A = 24000e^{7.25\% (10)}[/tex]
simplify following
[tex]\rightarrow {A = 49553.54[/tex]
2.5 pts Each week 5 new office phones are installed in a major network company. At the beginning of March, 200 phones had already been installed. Write a linear equation to model this situation. Do not use spaces in the equation.
Use your equation if the company wanted to replace all phones in the building (500 total). How many weeks would it take to finish this project?
The linear equation formed is y = 200 +5x and 60 weeks will be required to finish the project.
What is an Equation ?A statement that relates two mathematical expressions by an equal sign is called an Equation.
It is given that
No. of phones Per week installed in the office = 5
Let the no. of phones installed at the present week is given by y
and let x weeks have passed by before that
then the linear equation is formed as
y = 200 +5x
If the company wants to replace all the phones
Total phones = 500
No. of week required = ?
500 = 200+5x
300 = 5x
x = 60
Therefore 60 weeks will be required to finish the project.
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There are ten rappers performing live, the other 14 ill. what is the percentage of the ill rappers, and what would happen if you add 5 rappers to the performance. Does this make it more complicated?
Answer:
14/24 are ill so
58 percent
if you add 5 it does not get more complicated you just add 5 so 14/29
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Calculate the slope of the line between the pairs of points in each of the tables to determine which table represents a linear function.
Answer:
B
Step-by-step explanation:
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you randomly select one card from a 52 card deck find the probability of selecting a ace or a two
Katelyn was asked to solve for the unknown the problem shows that n +6=13 her steps are shown below
The solution of the unknown equation n + 6 = 13 will be n = 7.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
The given equation is
n +6=13
To solve for n
Subtract 6 on both sides;
n +6=13
n = 13- 6
n = 7
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Ramona Oden deposited $6,000 at 5.5% interest compounded daily for 25 days.
Find the a) amount, and b) compound interest
22, 66, 198, ...
Find the 8th term.
Answer:
The 8th term will be 48114.
Step-by-step explanation:
This series is an geometric series.
The formula for the nth term in an geometric series is [tex]ar^{n-1}[/tex], where a is the first term, r is the ratio (how much each term is multiplied by and n is the term you want to find.
In this question, the 8th term will be [tex]22\times3^7[/tex] = 48114
In 2000, the total population of the U.S. was 281.4 million people. In 2010, it was 308.7 million people. What is the average rate of change in the total population over this time period?
2.73 million people per year
27.3 million people per year
13.6 million people per year
1.36 million people per year
Answer:
2.73 million people per year
Step-by-step explanation:
Turn sentences into coordinates/points:
In 2000, 281.4 million people
(x₁, y₁) = (2000, 281.4)In 2010, 308.7 million people
(x₂, y₂) = (2010, 308.7)Rate of population per year:
[tex]\sf \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf \dfrac{308.7-281.4}{2010-2000}[/tex]
[tex]\rightarrow \sf 2.73 \ million \ people[/tex]
The volume of a cube is 27 cubic in. Which expression represents s, the lenght of a side of the cube
Answer:
Hello i am here to give the answer of the above question................................................................................................................................
Solution:Here
Given,
Volume of a cube is 27 so.
Length of a side of the cube =?
So I think the correct answer of this question is 3
Thank you......... ..................
Look at angle UVY and angle YVW in the image below. Which of the following is the best description for this pair of angles?
Daphne and Josephine earn commission on the sales they each make. Daphne earned $80 in commission on a sale of $1,600 . Josephine earn: twice the commission percentage as Daphne. If the commission Josephine earns is $150 , how much were her sales, in dollars?
Josephine's sales in dollar is $1500.
What is Josephine's sales in dollars?The first step is to determine the percentage commission earned by Daphne.
Percentage commission : ($80 / $1600) x 100 = 5%
Percentage commission of Josephine: 5% x 2 = 10%
Josephine's sales = dollar commission / percentage commission
$150 / 0.1 = $1500
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The equation of a line is y equals 4 over 3 x minus 5 over 3.
What would be the slope of a line perpendicular to this line?
A. -3/4
B. 5/3
C. -4/3
D. 3/5
Answer:
-3/4
Step-by-step explanation:
So you have the equation: [tex]y=\frac{4}{3}x-\frac{5}{3}[/tex]. For a perpendicular line, the only thing that matters is the slope. The slope of the perpendicular line can be defined as: [tex]\frac{a}{b} = > -\frac{b}{a}[/tex]. It's the reciprocal with the sign being the opposite. So if the sign of the original line was negative it's now positive, and if it's positive, it's not negative. The fraction is also flipped, even if it's an integer, it can be defined as a fraction e.g ([tex]6 = > -\frac{1}{6}[/tex] (sign also changed too))
So in this case the slope is 4/3x, since it's given in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept. So we flip it to get 3/4 and change the sign to negative to get -3/4
Dollar General sold garden hoses at a reduced price of $7.64 and took an end of the season markdown of $12.35. What was the original selling price of each hose? Use formula M=S-N = selling price-reduced price
The original selling price of the garden hoses is $19.99
How to find the original selling price?Using the given formula,
M = S - N
where
M = markdownS = original selling price,N = reduced priceHence,
M = $12.35.
N = $7.64
Therefore,
S = M + N
S = 12.35 + 7.64
S = $19.99
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Solve for x in the diagram below.
Answer:
X = 15
Step-by-step explanation:
We can tell that the two sides that show the degrees are equal because of the arc. We can set up a simple equation:
x + 45 = 60
x = 15
Answer:
x = 15°
Explanation:
The two marked angles are equal as they are vertically opposite angles.
∴ x + 45° = 60°
⇒ x = 60° - 45°
⇒ x = 15°
Susan begins counting backward from 1298 by 4's, saying one number every 5 seconds. At the same time, Jim begins counting forward from 171 by 3's, saying one number every 5
seconds. What number will they both say at the same time? (By the way I'm only in 6th grade so please explain well :)
Answer:
Step-by-step explanation:
Let z = equals 38 (cosine (startfraction pi over 8 endfraction) i sine (startfraction pi over 8 endfraction) ) and w = 2 (cosine (startfraction pi over 16 endfraction) i sine (startfraction pi over 16 endfraction) ) . what is the product of zw?
It sounds like you're saying
[tex]z = \dfrac38 \left(\cos\left(\dfrac\pi8\right) + i \sin\left(\dfrac\pi8\right)\right)[/tex]
[tex]w = 2 \left(\cos\left(\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi{16}\right)\right)[/tex]
The product [tex]zw[/tex] is obtained by multiplying the moduli and adding the arguments. In other words
[tex]z = |z| e^{i\arg(z)} \text{ and } w = |w| e^{i\arg(w)} \implies zw = |z||w| e^{i(\arg(z)+\arg(w))}[/tex]
where [tex]e^{it}=\cos(t)+i\sin(t)[/tex], so that
[tex]zw = \dfrac38\times2 \left(\cos\left(\dfrac\pi8+\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi8 + \dfrac\pi{16}\right)\right) = \boxed{\dfrac34 \left(\cos\left(\dfrac{3\pi}{16}\right) + i \sin\left(\dfrac{3\pi}{16}\right)\right)}[/tex]
identify the asymptotes and state the end behavior of the function f(x)=5x/x-25
Using it's concepts, it is found that for the function [tex]f(x) = \frac{5x}{x - 25}[/tex]:
The vertical asymptote of the function is x = 25.The horizontal asymptote is y = 5. Hence the end behavior is that [tex]y \rightarrow 5[/tex] when [tex]x \rightarrow \infty[/tex].What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity. They also give the end behavior of a function.In this problem, the function is:
[tex]f(x) = \frac{5x}{x - 25}[/tex]
For the vertical asymptote, it is given by:
x - 25 = 0 -> x = 25.
The horizontal asymptote is given by:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5[/tex]
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Determine the most precise name for ABCD (parallelogram, rhombus, rectangle, or square). Explain how you determined your answer. You must support your answer using length or slope.
A(3, 5), B(7, 6), C(6, 2), D(2, 1)
======================================================
Reason:
Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\[/tex]
Segment AB is exactly [tex]\sqrt{17}[/tex] units long, which is approximately 4.1231 units.
If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.
-------------------------
Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.
Let's find the slope of AB.
[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\[/tex]
Segment AB has a slope of 1/4.
Do the same for BC
[tex]B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\[/tex]
Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.
We don't have perpendicular lines, so the interior angles are not 90 degrees each.
Therefore, this figure is not a rectangle and by extension it's not a square either.
The best description for this figure is a rhombus.
Answer:
Rhombus
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. That is, they have the same midpoint. If they are the same length, that parallelogram is a rectangle. If they cross at right angles, it is a rhombus. If it is a rectangle and rhombus, then it is a square.
Diagonal midpointsThe midpoints of AC and BD are ...
(A+C)/2 and (B+D)/2
To determine if the midpoints are the same, we can skip the division by 2 and simply look at the sums:
A +C = (3, 5) +(6, 2) = (9, 7)
B +D = (7, 6) +(2, 1) = (9, 7)
The midpoints of the diagonals are the same, so the figure is at least a parallelogram.
Diagonal vectorsThe diagonal vectors will be the same length if the figure is a rectangle. They will be perpendicular if the figure is a rhombus. The vectors are ...
AC = C -A = (6, 2) -(3, 5) = (3, -3)
BD = D -B = (2, 1) -(7, 6) = (-5, -5)
The length of each of these is the root of the sum of squares of its components. These are obviously different lengths (3√2 vs 5√2).
The dot-product of these will be zero if they are perpendicular:
AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0
ConclusionThe diagonals are different length and mutual perpendicular bisectors, so the figure is a rhombus.
__
Additional comment
Looking at the dot-product is a simple way to check that the slopes are opposite reciprocals. The slope of a vector with components (x, y) is m = y/x.
The requirement that slopes be opposite reciprocals means ...
y1/x1 = -1/(y2/x2) . . . . . . . . slope relationship
(y1)(y2)/((x1)(x2)) = -1 . . . . . multiply by y2/x2
y1·y2 = -x1·x2 . . . . . . . . . . multiply by (x1·x2)
x1·x2 +y1·y2 = 0 . . . . . . . . add x1·x2
This shows the vector dot product being zero is equivalent to the slopes being opposite reciprocals. The vectors are perpendicular in this case.
Statistics 4. Hol (a) The average age of 5 students is 9 years. Out of them, the ages of 4 students are 5, 7, 8, and 15 years. What is the age of the remaining student?
Answer:
10 years
Step-by-step explanation:
the average or mean value is the sum of all data points divided by the number of data points.
x = the unknown age of the 5th student.
average = 9 = (5 + 7 + 8 + 15 + x)/5
45 = 5 + 7 + 8 + 15 + x = 35 + x
x = 45 - 35 = 10
the 5th student is 10 years old.
The population of Nowhere, USA was estimated to be 886,000 in 2004, with an expected increase of 4% per year. At the percent of increase given, what was the expected population in 2005? Round your answer to the nearest whole number.
Answer:
y=886000(1.04)^t
t=1 year so answer is 886000*1.04 = 921440
A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per pound. But at the end of the month the peanuts had not sold well, so, in order to sell 10 pounds of peanuts, the manager decided to mix the 10 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?
If you bought 20 pounds of cashews, your bottom line would remain the same.
How many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue?Cashew and peanut butter together represent a linear relationship. Twenty pounds of cashews would have no impact on profits.
Cashews are represented here by the letter c and peanuts by the letter p.
U-4.00
Up=1.50
Um=2.00
p-40 pounds of peanuts that have not been sold.
m=40+c -when 40 pounds of peanuts are combined with cashews, the resulting combination
Generally, the equation for c is mathematically given as
Ue x c+Up xp=Um x m
Therefore
4.00 x c+1.50 x 40 2.00 x (40+c)
4c+60-80+2c
2c= 20
c=10
In conclusion, If you bought 20 pounds of cashews, your bottom line would remain the same.
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monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%, compounded monthly. Add the future values of each payment to calculate the total value of the annuity on september 1.
The annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We have:
Monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%.
Value of annuity as of September 1 calculation:
From the table:
For Jan:
Jan 0 $75.00 1.07214 $80.41
For Feb
Feb 1 $75.00 1.06152 $79.61
And on September 1, the value of the annuity will be: =
= $621.43
Thus, the annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%
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Write the ratios for sin M, cos M, and tan M.
Answer:
Sin M= opposite/hypotenuse, cos M= adjacent/Hypotenuse, tan M= opposite/adjacent
Step-by-step explanation:
Answer:
sinM= [tex]\frac{opposite}{hypotenuse}[/tex]
cosM= [tex]\frac{adjacent}{hypotenuse}[/tex]
tanM= [tex]\frac{opposite}{adjacent}[/tex]
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe the above answers are correct. Thank you!
As the sample size n is less than 30 normal distribution is used.
The values of x are converted into z by using the formula z= x-u/ s and then the z values are found out from the table.
The limits are found by using the formula x±σz or x±sz where s= σ
As the sample size is 10 which is less than 30 the normal distribution is used.
The probability of x< 2.59 is 0.3446
The probability 2.60<X <2.63 is 0.9484
So lower and upper limits are 2.607 and 2.612
Part A
As the sample size is 10 which is less than 30 the normal distribution is used.
Part B
For given value of x= 2.59 z is obtained =0.4
x= 2.59
z= x-u/ s
z= 2.59-2.61/0.05
z= -0.02/0.05
z=- 0.4
P (X<2.59) = P(-0.4 <Z<0) = 0.5 -0.1554= 0.3446
The probability of x< 2.59 is 0.3446
Part C
For two given values of x= 2.60 and 2.63 z is obtained as =0.2 and 0.4
x1= 2.60
z1= x-u/ s
z= 2.60-2.61/0.05
z= -0.01/0.05
z=- 0.2
x2= 2.63
z2= x-u/ s
z= 2.63-2.61/0.05
z= 0.02/0.05
z= 0.4
P (2.60<X<2.63) = P(-0.2 <Z<0.4)
= P(-0.2 <Z<0)+ P(0 <Z<0.4)
=0.793 + 0.1554= 0.9484
The probability 2.60<X <2.63 is 0.9484
Part D"
p= 0.57
From the table z= 0.045
z= x-u/ s
zs= x-u
zs+u = x
x1= 0.045*0.05 +2.61= 2.61225
x2= 2.61- 0.00225= 2.60775
So lower and upper limits are 2.607 and 2.612
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does anyone know how to solve this?
Just put -2 in,where X is and get your answer that way
Northlake High School has two lunch periods. Students can eat their lunch in
the cafeteria or on an outside patio. About 35% of students who have first
lunch eat outside. Compare this with the percentage of second-lunch
students who eat outside.
First lunch
Second lunch
Total
Select the true statement.
Eat outside
0.19
0.18
0.41
Eat inside
0.35
0.24
0.59
Total
0.54
0.46
1.0
Based on the given information on the first and second lunch students, the true statement is B. A greater percentage of second-lunch students (39%) eat outside.
which lunch students eat more outside?the percentage of second lunch students who eat their lunch outside is:
= Second lunch students who eat outside / Second lunch students
this gives:
= 0.18 / 0.46 x 100%
= 39%
options for this question include:
A. A smaller percentage of second-lunch students (24%) eat outside.
B. A greater percentage of second-lunch students (39%) eat outside.
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let A and B sets. when do we say set A is equal to set B
Answer:
We say sets A and B are equal, and write A = B if they have exactly the same elements.
Step-by-step explanation:
Answer:
When set A is equal to set B. It is denoted as A = B.
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