Answer:
The margin of error is approximately 0.39.
Step-by-step explanation:
Formular for the margin of error is
Margin of error = z* (sd/√n)
Where z* is 95% confidence level = 1.96, sd is 1.8 and n is 81
Margin of error = 1.96 (1.8/√81)
= 1.96(1.8/9)
= 1.96*0.2
= 0.392
In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly. How much did the population grow between 2009 and 2017?
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.
Answer:
100
Step-by-step explanation:
aaaaa
If a = i - 9k and b = j + k , find ab .
Answer:
solution
given a=1_9k and b=j+k
Now,ab=(1_9k)(j+k)
=1((j+k)-9k(j+k)
=j+k_9jk-9k^2
=k_9k^2+j_9jk
=k((1_9k)+j(1_9k)
=(1_9k)(k+k)
The length of a side of a square is \sqrt(x^(2)-4) If the area of the square is 12, find x. A. 16 B. 4 C. 12 D. \sqrt(148)
Answer:
B. 4
Step-by-step explanation:
Let the side of the square= a
Then the area of the square= a²
Given:
a= √x²-4 and a²=12Then:
a²= (√x²-4 )²= x²-4Considering the value of the area, 12 units
x²-4 =12x²=16x= √16x= ±4x= -4 is not considered as the length can't be negativex= 4 is the answerCorrect choice is B. 4
Determine the value of x and y
Answer:
x = 28, y = 23
Step-by-step explanation:
5y - 4 and 3y are alternate exterior angles and are supplementary, thus
5y - 4 + 3y = 180
8y - 4 = 180 ( add 4 to both sides )
8y = 184 ( divide both sides by 8 )
y = 23
Thus
3y = 3 × 23 = 69
2x + 13 and 3y are corresponding angles and congruent, thus
2x + 13 = 69 ( subtract 13 from both sides )
2x = 56 ( divide both sides by 2 )
x = 28
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If
x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this
situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Mark this and retum
Save and Exit
Nexi
Submit
Answer: B) 10 three-point questions and 14 five-point questions
Step-by-step explanation:
x represents three-point questions
y represents five-point questions
3x + 5y = 100 → 1(3x + 5y = 100) = 3x + 5y = 100
x + y = 24 → -3(x + y = 24) = -3x -3y = -72
2y = 28
y = 14 (five-point questions)
x + y = 24
x + 14 = 24
x = 10 (three-point questions)
Given: FGKL is a trapezoid, m∠F=90°, m∠K=120°, FK=LK=a Find: The length of midsegment.
Answer:
(3/4)a
Step-by-step explanation:
The angle at K is 120°, so the angle at L is its supplement: 60°. That makes triangle FKL an equilateral triangle with a base of FL = a. The vertex at K is centered over the base, so is a/2 from G.
The midsegement length is the average of GK and FL, so is ...
midsegment = (GK +FL)/2 = (a/2 +a)/2
midsegment = (3/4)a
A committee has members. There are members that currently serve as the board's . Each member is equally likely to serve in any of the positions. members are randomly selected and assigned to be the new . What is the probability of randomly selecting the members who currently hold the positions of and reassigning them to their current positions? The probability is nothing.
Complete Question
A committee has six members. There are three members that currently serve as the board's chairman comma vice chairman comma and treasurer . Each member is equally likely to serve in any of the positions. Three members are randomly selected and assigned to be the new chairman comma vice chairman comma and treasurer . What is the probability of randomly selecting the three members who currently hold the positions of chairman comma vice chairman comma and treasurer and reassigning them to their current positions?
The probability is ?
Answer:
The probability is [tex]P(3 ) = \frac{ 1 }{20 }[/tex]
Step-by-step explanation:
From the question we are told that
The total number of members is n = 6
The number of member to be selected is r = 3
Generally the number of ways of selecting 3 members from 6 is mathematically evaluated as
[tex]\left n } \atop {}} \right. C _r = \frac{n! }{(n-r ) ! r !}[/tex]
=> [tex]\left 6 } \atop {}} \right. C _ 3 = \frac{6 ! }{(6-3) ! 3 !}[/tex]
=> [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 * 3! }{3 ! 3*2 * 1}[/tex]
=> [tex]\left n } \atop {}} \right. C _r = \frac{6* 5* 4 }{3 *2 * 1}[/tex]
=> [tex]\left n } \atop {}} \right. C _r =20[/tex]
Now the number of ways of selecting the 3 members who currently hold the position is n = 1
So the probability is mathematically represented as
[tex]p(k ) = \frac{ n }{\left n } \atop {}} \right. C _r }[/tex]
substituting values
[tex]P(3 ) = \frac{ 1 }{20 }[/tex]
Complete the table
Distance(ft)
Height(ft)
Answer:
a = 6, b = 7, c = 8, d = 7 and e = 6
Step-by-step explanation:
Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.
The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.
When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.
So the height will be a = 6 + 0 = 6 ft
When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.
So the height will be b = 6 + 1 = 7 ft
When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.
So the height will be c = 6 + 2= 8 ft
When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.
So the height will be d = 6 + 1 = 7 ft
When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.
So the height will be e = 6 + 0 = 6 ft
So the answers are:
a = 6, b = 7, c = 8, d = 7 and e = 6
Answer:
6, 7, 8, 7, 6
Step-by-step explanation:
Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.
Kesha has a total of 100 coins, all of which are either dimes or quarters. The total value of the coins is $14.50. Find the number of each type of coin.
Which choice satisfies the given conditions?
O A. 70 dimes, 30 quarters
B. 20 dimes, 80 quarters
C. 40 dimes, 42 quarters
Answer:
A. 70 dimes, 30 quarters
Step-by-step explanation:
Only options A and B create a total of 100 coins. It cannot be option B because 80 quarters by itself, is already over $14.50.
what is the standard form for these 2 quadratic equations ASAPP!!!!
Problem 3
Answer: y = x^2 - 7x + 10----------
Work Shown:
Use either the FOIL method, distributive property, or the box method to get the following
(x-2)*(x-5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10
==========================================
Problem 4
Answer: y = x^2 - x - 6----------
Work Shown:
Same idea as problem 3 above
(x-3)(x+2) = x^2+2x-3x-6 = x^2 - x - 6
Answer:
3. y = x² - 7x + 10
4. y = x² - x - 6
Step-by-step explanation:
Point Q'Q ′ Q, prime is the image of Q(-7,-6)Q(−7,−6)Q, left parenthesis, minus, 7, comma, minus, 6, right parenthesis under the translation (x,y)\to(x+12,y+8)(x,y)→(x+12,y+8)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 12, comma, y, plus, 8, right parenthesis. What are the coordinates of Q'Q ′ Q, prime?
Answer:
5,2
Step-by-step explanation: (-7+12=5,-6=8=2) And I Got It Correct On Khan Academy :)
Hope this helps you!!
The coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)
Translation of image is a mathematical term used to move an object through a distance.
Given the coordinate point Q(-7, 6), if this coordinate is under the translation (x,y)→(x+12,y+8), this means we are to shift the x coordinate of Q to the right by 12units and the y-coordinates of Q up by 8 units to get the new location at Q'. Hence:
Q' = (-7 + 12, -6 + 8)
Q' = (5, 2)
This shows that the coordinate of Q under the translation (x,y)→(x+12,y+8) will be located at Q'(5, 2)
Learn more about translation here: https://brainly.com/question/10704056
PLEASE HELP I WILL GIVE BRAINLIEST TO CORRECT ANSWER
A greengrocer has 38 lb of carrots when he opens on Monday morning. During the day
he gets a delivery of 60lb of carrots and sells 29 lb of the carrots. How many pounds of
carrots are left when he closes on Monday evening?
Answer:
9 is the answer
Step-by-step explanation:
got a delivery of 60ib...but dont have enough .thats why he or she sells 29..totally he or she have 38ib of carrots ...so when we subtract 38_29
its =9
In an ANOVA the F-calculated for the treatment 4.76 with 3 degrees of freedom in the numerator and 6 degrees of freedom in the error term. What is the approximate p-value
Answer:
0.0499
Step-by-step explanation:
The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.
The p-value shows that the for 5% level of significance the null hypothesis can be rejected.
The mid term exam had a normal distribution with mean 70 and standard deviation 10. To get a C you have to be in the middle 40% of the class. Which two grades will define the middle 40%.
Answer:
64.8 and 75.2
Step-by-step explanation:
A suitable probability calculator can show you the middle 40% is between about 64.8 and 75.2.
Evaluate 2x^+2x+8 when x=4
Please help. I’ll mark you as brainliest if correct!
Answer:
[tex]\large \boxed{\sf \ \ x=0, \ \ y=-5 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
We have two equations:
(1) -2x - 4y = 20
(2) -3x + 5y = -25
5*(1)+4*(2) gives
-10x - 20y -12x + 20y = 100 - 100 = 0
-22x = 0
x = 0
I replace in (1)
-4y = 20
y = -20/4 = -5
There is one solution x = 0, y = -5
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
The two equations are
-2x-4y=20
-3x+5y=-25
multiply equation 1 by 5 and equation 2 by 4
-10x-20y=100
-12x+20y=-100
-22x=0
x=0
Substitute value in either equation
y=-5
So,option 1 is correct only one solution
plzzz help 6≥ -6(a+2)
Answer:
a[tex]\geq[/tex]-3
Step-by-step explanation:
Answer:
-3 ≤ a
Step-by-step explanation:
6≥ -6(a+2)
Divide each side by -6, remembering to flip the inequality
6/-6 ≤ -6/-6(a+2)
-1 ≤ (a+2)
Subtract 2 from each side
-1 -2 ≤ a+2-2
-3 ≤ a
Which set of three numbers can be used to make a right triangle? select Yes or no
Answer:
answer is
B) 36,72,80
Step-by-step explanation:
because is the right angle it is exactly 90°
matthew grew 2.7 inches last year and 4.4 inches this year. How many inches has Matthew grown over the last two years combined
Answer:
7.1 inchesStep-by-step explanation:
Total inches grown last year by matthew = 2.7inches
Total inches grown this year by Matthew = 4.4 inches
Total inches grown by Matthew over the last two years combined will be the sum of heights of matthew for both the previous year and the current year.
Total inches grown = 2.7 inches + 4.4 inches
Total inches grown over the last two years = 7.1 inches
A random sample of 64 observations produced a mean value of 86 and standard deviation of 4.5. The 95% confidence interval for the population mean μ is between:_________.
Answer: (84.876, 87.124)
Step-by-step explanation:
Confidence interval for population mean if population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}(\dfrac{s}{\sqrt{n}})[/tex]
, where n= sample size
s= sample standard deviation
[tex]\overline{x}[/tex] = sample mean
[tex]\alpha=[/tex] significance level
[tex]t_{\alpha/2}[/tex] = critical-t value
Given: n= 64
Degree of freedom = n-1 = 63
s= 4.5
[tex]\overline{x}[/tex] = 86
[tex]\alpha=[/tex] 0.05
[tex]t_{\alpha/2}[/tex] = 1.9983
Now, the required 95% confidence interval would be:
[tex]86\pm (1.9983)(\dfrac{4.5}{\sqrt{64}})\\\\=86\pm (1.9983)(\dfrac{4.5}{8})\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)[/tex]
The 95% confidence interval for the population mean μ is between: (84.876, 87.124)
Solve the following rational equation for x.
1/4x-3/4=7/x
Answer:
x1= -4, x2 = 7
Step-by-step explanation:
Move expression to the left-hand side:
1/4x-3/4-7/x=0
Write all the numerators above a common denominator:
x^2 - 3x - 28 /4x =0
When the quotient of expressions equal 0, the numerator has to be 0
x^2 + 4x - 7x - 28 = 0
x(x+4) - 7(x+4) =0
(x+4) × (x-7) =0
Separate into possible cases:
x+4=0
x-7=0
Answer: -9
Step-by-step explanation:
A company finds that if they price their product at $ 35, they can sell 225 items of it. For every dollar increase in the price, the number of items sold will decrease by 5.
What is the maximum revenue possible in this situation? (Do not use commas when entering the answer) $
What price will guarantee the maximum revenue? $
The price that guarantees the maximum revenue is $40.
The maximum revenue possible in this situation is $8000.
Given that the company can sell 225 items at a price of $35, and for every dollar increase in price, the number of items sold decreases by 5, we can set up a relationship between price and quantity sold.
Let's denote the price as "P" and the quantity sold as "Q". We can express this relationship as follows:
Q = 225 - 5(P - 35)
This equation represents the decrease in quantity sold as the price increases.
To find the price that guarantees the maximum revenue, we need to find the price at which the quantity sold multiplied by the price is maximized. This is equivalent to finding the maximum value of the revenue function.
Revenue (R) is calculated as:
R = P × Q
To find the price that guarantees the maximum revenue, we need to maximize the revenue function R(P).
Let's substitute the expression for Q into the revenue function:
R(P) = P × (225 - 5(P - 35))
Now, simplify and expand the equation:
R(P) = P × (225 - 5P + 175)
= P × (400 - 5P)
To find the maximum revenue, we need to find the value of P that maximizes R(P). This can be done by finding the critical points of the function, which are the values of P where the derivative of R(P) equals zero.
Let's take the derivative of R(P) with respect to P:
dR(P)/dP = 400 - 10P
Setting the derivative equal to zero and solving for P:
400 - 10P = 0
10P = 400
P = 40
Therefore, the price that guarantees the maximum revenue is $40.
To find the maximum revenue, substitute P = 40 into the revenue function:
R(40) = 40 × (225 - 5(40 - 35))
= 40 × (225 - 5(5))
= 40 × (225 - 25)
= 40 × 200
= 8000
Hence, the maximum revenue possible in this situation is $8000.
To learn more about the derivative;
https://brainly.com/question/24898810
#SPJ12
Consider the function f(x) = 2 ^x.and the function g(x).
g(x) = f(x + 4)
= 2^(x+4)
How will the graph of g(x) differ from the graph of f(x)?
A.
The graph of g(x) is the graph of f(x) shifted 4 units to the left.
B.
The graph of g(x) is the graph of Ax) shifted 4 units upward.
C.
The graph of g(x) is the graph of Ax) shifted 4 units to the right.
D.
The graph of g(x) is the graph of f(x) shifted 4 units downward.
Answer:
A.
Step-by-step explanation:
Hello,
g(x-4)=f(x) so the graph of g is the graph of f shifted 4 units to the left.
For any x, the point (x-4, g(x-4)) is 4 units to the left of the point (x,f(x)).
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
:) i just took the test and it was right
Apply the distributive property to factor out the greatest common factor. 56+32=56+32=56, plus, 32, equals
Answer:
8(7 + 4) = 88
Step-by-step explanation:
56:
1 x 56
2 x 28
4 x 14
7 x 8
32:
1 x 32
2 x 16
4 x 8
Answer:
8(7+4)
Step-by-step explanation:
Draw a pie chart for the percent of the money spent on various types of books by a library in a year.
Answer:
The pie chart representing for this question is presented in the attached image to this solution.
Step-by-step explanation:
Complete Question
Draw a pie chart for the percent of the money spent on various types of books by a library in a year.
Type of book | %
Fiction | 20%
Classics | 15%
Sports | 10%
Biography | 12.5%
Magazines | 22.5%
Others | 20%
Solution
A pie chart is a graphical representation of a set of numerical data which comes in a circular shape divided into slices, with the size of each slice corresponding to the proportion of the numerical data it represents.
Because it is a circle, the total angles in a pie chart is 360°.
The angles are divided into slices with the size of each slice corresponding to how large the data it represents is.
So, we first convert the data given into degrees.
Since the data is given in percentage, for each of the groups, the conversion from percentage will be
Angle = (Proportion) × 360°
Type of book | % | Angle
Fiction | 20% | 72°
Classics | 15% | 54°
Sports | 10% | 36°
Biography | 12.5% | 45°
Magazines | 22.5% | 81°
Others | 20% | 72°
The pie chart representing this data is presented in the attached image to this solution.
Hope this Helps!!!
A type of golf ball is tested by dropping it onto a hard surface from a height of 1 meter. The height it bounces is known to be normally distributed. A sample of 25 balls is tested and the bounce heights are given below. Use Excel to find a 95% confidence interval for the mean bounce height of the golf ball. Round your answers to two decimal places and use increasing order.
Height
81.4
80.8
84.4
85.6
82.9
76.0
80.0
83.2
80.8
79.6
82.9
83.4
82.2
86.0
76.2
84.8
82.0
76.3
77.0
75.4
82.0
79.8
80.4
86.9
82.1
Answer:
79.95, 82.62
Step-by-step explanation:
using excel to find a 95% confidence interval for the mean bounce height of the golf ball
Heights given are :
81.4
80.8
84.4
85.6
82.9
76.0
80.0
83.2
80.8
79.6
82.9
83.4
82.2
86.0
76.2
84.8
82.0
76.3
77.0
75.4
82.0
79.8
80.4
86.9
82.1
The statistical out put of the problem after solving with excel is attached below
therefore the 95% confidence interval from the attached solution will be ( 79.95, 82.62 )
Answer: (79.95, 82.61)
Step-by-step explanation:
Use Excel to calculate the 95% confidence interval, where α=0.05 and n=25.
1. Open Excel and enter the given data in column A. Find the sample mean, x¯, using the AVERAGE function and the sample standard deviation, s, using the STDEV.S function. Thus, the sample mean, rounded to two decimal places, is 81.28 and the sample standard deviation, rounded to two decimal places, is 3.23.
2. Click on any empty cell, enter =CONFIDENCE.T(0.05,3.23,25), and press ENTER.
3. The margin of error, rounded to two decimal places, is 1.33. The confidence interval for the population mean has a lower limit of 81.28−1.33=79.95 and an upper limit of 81.28+1.33=82.61.
Thus, the 95% confidence interval for the mean bounce height of the golf balls is (79.95, 82.61).
Complete the following questions on the picture
Answer:
Step-by-step explanation:
Hello!
For this particular organism population the growth rate is so that is doubled every 20 years. Using the starting population of 9 billion individuals by year 2000 you have to calculate the expected population values every 20 years.
All you have to do is multiply the original population by 2 to obtain the next value.
Year 2000:
Population: 9*10⁹ or 9 000 000 000 x 2= 18 000 000 000
To express 18 billion in scientific notation you have to add a "comma" after the first digit and then count the number of digits behind it:
1, 8 000 000 000 there are 10 digits behind the first digit. This notation summarizes the number in base 10 exponents so 18 billion in scientific notation is:
1.8 * ten "exponent the number of digits behind the comma"
1,8*10¹⁰So the population for year 2020 will be 1,8*10¹⁰
Next for year 2040 you have to multiply the population of year 2020 by 2
1,8*10¹⁰ x 2= 3,6*10¹⁰
And so on:
2060: 3,6*10¹⁰ x 2)= 7.2*10¹⁰
2080: 7.2*10¹⁰ x2= 1.44*10¹¹
2100: 1.44*10¹¹ x2= 2.88*10¹¹
2120: 2.88*10¹¹x2= 5.76*10¹¹
2140: 5.76*10¹¹x2= 1.152*10¹²
2160: 1.152*10¹²x2= 2.304*10¹²
2180: 2.304*10¹²x2= 4.608*10¹²
2200: 4.608*10¹² x2= 9.216*10¹²
2220: 9.216*10¹²x2= 1.8432*10¹³
2240: 1.8432*10¹³x2= 3.6864*10¹³
2260: 3.6864*10¹³x2= 7.3728*10¹³
2280: 7.3728*10¹³x2= 1.47456*10¹⁴
2300: 1.47456*10¹⁴x2= 2.94912*10¹⁴
2320: 2.94912*10¹⁴x2= 5.89824*10¹⁴
2340: 5.89824*10¹⁴x2= 1.179648*10¹⁵
2360: 1.179648*10¹⁵x2= 2.359296*10¹⁵
2380: 2.359296*10¹⁵x2= 4.718592*10¹⁵
2400: 4.718592*10¹⁵x2= 9.437184*10¹⁵
So for year 2400 the expected population will be 9.437184*10¹⁵, writen in common notation that is:
9 437 184 000 000 000 individuals
I hope this helps!
please factor!
7x^2+27xy-4y^2
Brainliest for correct awnser! What is the domain of f(x)?
Answer:
[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5
Step-by-step explanation:
If the denominator is equal to 0 then the function would be undefined.
Set the denominator equal to 0.
x² - 7x + 10 = 0
Factor the left side of the equation.
(x - 5)(x - 2) = 0
Set the factors equal to 0.
x - 5 = 0
x = 5
x - 2 = 0
x = 2
The domain is all real numbers except x = 2 and x = 5.
Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit? A: 5n - 300 = 1,500 B: 5n + 300 = 1,500 C: 5n - 200 + 100n = 1,500 D: 5n - 100 - 200n = 1,500
Answer:
The answer should be B: 5n+300=1,500.
Step-by-step explanation:
The number of people to attend is going to vary and 300 is a set variable, so it won't change of be affected. Since the team doesn't know how many people will be able to attend in order to reach their goal, n is going to take the place for the amount of people.
If you were to solve this, the answer would be:
5n+300=1,500
5n=1,500-300
5n=1,200
n=240
So 240 people can attend the dance.
Answer:5n-300=1,500
Step-by-step explanation: