Answer:
a
[tex]0.716 < p < 0.744[/tex]
b
[tex]0.3498 < p < 0.4089[/tex]
c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1003[/tex]
The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]
The number that complained about loud or distracting diners at other tables is [tex]q = 381[/tex]
Given that the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
The sample proportion is mathematically represented as
[tex]\r p = \frac{e}{n}[/tex]
=> [tex]\r p = \frac{732}{1003}[/tex]
=> [tex]\r p = 0.73[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]
[tex]E = 0.01402[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]
[tex]0.716 < p < 0.744[/tex]
Considering question b
The sample proportion is mathematically represented as
[tex]\r p = \frac{q}{n}[/tex]
=> [tex]\r p = \frac{381}{1003}[/tex]
=> [tex]\r p = 0.3799[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]
[tex]E = 0.0300[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]
[tex]0.3498 < p < 0.4089[/tex]
0 to 100 miles per hour in a mere 0.8 seconds. Calculate its acceleration. Show your work and include units.
Answer:
Answer: so the answer is 80 miles per 0.8 Step-by-step explanation: consistence
What is the degree of
the polynomial below?
I
x2 + 2x - 3x4 +5 + 3x?
The width of a rectangle is 4 inches (in) and the area of the rectangle is 32 in2? Which of the following represents the length of the rectange?
a. 8 in
b. 128 in
c. 28 in
d. 36 in
Answer:
A. 8
Step-by-step explanation:
32 divided by 4 = 8
The answer is a. 8 in.
Since the width of the rectangle is 4 inches (in) and the area of the rectangle is 32 in², we need to find the length of the rectangle.
We know that the area of a rectangle with length, L and width, W is A = LW.
Since we need to find the length of the rectangle, we make the length, L subject of the formula.
Since A = LW,
L = A/W
Given that A = 32 in² and W = 4 in
Substituting the values of the variables into the equation, we have
L = 32 in²/4 in
L = 8 in
So, the length of the rectangle is 8 in
So, the answer is a. 8 in.
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Simplify 55/66 to lowest terms ?
Answer:
5/6
Step-by-step explanation:
To simplify this fraction, we need to find the GCF (greatest common factor) of the numerator and denominator. In this case, the GCF of 55 and 66 is 11. Now, all we have to do is divide both the numerator and denominator by the GCF. The numerator will become 55 / 11 = 5 and the denominator will become 66 / 11 = 6 so the simplified fraction is 5 / 6.
How many ounces of a 30% alcohol solution must be mixed with 18ounces if a 35% alcohol solution to make a 33% alcohol solution
Answer:
12 ounces
Step-by-step explanation:
0.30 x + 0.35 (18) = 0.33 (x + 18)
0.30 x + 6.3 = 0.33 x + 5.94
0.36 = 0.03 x
x = 12
The map shows the route for a race.You are at X, 6000 ft from the first checkpoint C.The second checkpoint D is located at the midpoint between C and the end of the race Y.The total race is 3 miles how far apart are the 2 checkpoints? I know the answer is 4920 but i don’t know how to work it out
Answer:
Distance between the two check point (C and D) is 4920 ft.
Step-by-step explanation:
From the question given above, we obtained the following information:
X is 6000 ft from C (1st check point)
D (2nd check point) is the midpoint point between C and Y ( the end of the race)
Total race = 3 miles
1 mile = 5280 ft
Next, we shall express the total race in feet (ft).
This is illustrated below:
1 mile = 5280 ft
Therefore,
3 miles = 3 × 5280 = 15840 ft
Next, we shall determine the distance between the 1st check point (C) and the end of the race (Y)
This can be obtained as follow:
Total distance = 15840 ft
Distance between X and C = 6000 ft
Distance between C and Y =?
Distance between C and Y = (Total distance) – (Distance between X and C)
Distance between C and Y = 15840 – 6000
Distance between C and Y = 9840 ft
Finally, we shall determine the distance between the two check point (C and D) as follow:
Since D is midpoint between C and Y, therefore, we shall we shall divide the distance between C and Y by 2 in order to obtain the distance between the two check point (C and D).
This is illustrated below:
Distance between C and Y = 9840 ft
Distance between the two check point (C and D) = 9840/2 = 4920 ft
Therefore, the distance between the two check point (C and D) is 4920 ft
Bodie Raptor's Iphone 11 has 4/5 of the battery still remaining. His phone battery drains at a rate of 1/3 every hour. If he uses his phone continuously, how many more hours will his phone last. Please give your answer as a mixed number in simplest form in the form of A . b/c
Answer:
[tex]2\frac{2}{5}[/tex] hours, or 1 hours and 24 minutes
Step-by-step explanation:
4/5 battery remaining
drains at rate of 1/3 per hour
[tex]\frac{1}{3}h=\frac{4}{5}\\\frac{3}{1}(\frac{1}{3}h)=\frac{3}{1}*\frac{4}{5}\\h=\frac{3*4}{1*5}=\frac{12}{5}=2\frac{2}{5}[/tex]
He has 2 2/5 hours or 2 hours and 24 minutes left until his phone dies. (A fifth of an hour is 12 minutes and we have 2/5 to deal with, so 12 times 2 is 24 mins.)
Brand on has 25 buttons.Mason has 6 times as many buttons.How many buttons does Mason have?
Answer: Mason has 150 buttons.
Step-by-step explanation: Brandon has 25 buttons. If Mason has 6 times as many, all you have to do is multiply 25 times 6. You end up with 150 buttons.
9. An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
An air conditioning system can circulate 350 cubic feet of air
per minute. How many cubic yards of air can it circulate per
minute?
About 13.0 cubic yards
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
What is conversion?Conversion means to convert the same thing into different units.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
An air conditioning system can circulate 350 cubic feet of air per minute.
We know that 1 foot = (1/3) yards, then the 1 cubic foot = (1/27) cubic yards.
350 cubic feet / minute = (1/27) x 350 cubic yards / minute
350 cubic feet / minute = 12.96 cubic yards / minute
The amount of air in cubic yards per minute will be 12.96 cubic yards per minute.
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Solve the given initial-value problem by finding, as an appropriate integrating factor.
(x2 + y2 − 3) dx = (y + xy) dy, y(0) = 1
Answer:
hello attached below is the detailed solution
answer : In |x+1| + [2/(x+1)] + [1/(1+x)^2] - [y^2/2(1+x)^2] = 5/2
Step-by-step explanation:
Given
(x^2 + y^2 - 3) dx = ( y + xy ) dy, y(0) = 1
solving the given initial-value problem
What is the value of the underline digit?
14.097
Answer:14.097
Step-by-step explanation:
Determine algebraically whether f(x)=3x-2 and g(x)=(x+2)/3 are inverse functions. Show all work.
Answer:
Yes
Step-by-step explanation:
f(x)=3 x-2
y= 3 x-2
x= 3y - 2
3 y -2 = x
3 y -2 + 2 = x + 2
3 y = x + 2
3 3 3
3 y = x + 2
3 3 3
y = x + 2 replace y with f ^ -1(x)
3 3
f ^-1 (x) = x + 2
3 3
Fifty part-time students were asked how many courses they were taking this term. The incomplete) results are shown below.
Part (b)
What percent of students take exactly two courses?
Part (c)
What percent of students take one or two courses?
%
Answer:
There are 50 part-time students:
15 of them, take only one course.
10 of them, take only two courses.
then the rest, this is:
50 - 10 - 15 = 25
25 students take 3 courses.
b) What percent of students take exactly two courses?
15 out of 50 take exactly two courses, the percentage is:
p = (10/50)*100% = 20%.
c) What percent of students take one or two courses?
This will be the percentage of students that take only one course plus the percentage of students that take two courses:
The percentage of students that take two courses is already known: 20%.
Now, for 1 course we have 15 students out of 50, the percentage is:
p = (15/50)*100% = 30%.
Then the percentage that take 1 or 2 courses is:
P = 30% + 20% = 50%
20% of students take exactly two courses, and 50% of students take one or two courses.
Given that fifty part-time students were asked how many courses they were taking this term, of which 15 take only 1 course, while 10 take 2 courses, to determine what percent of students take exactly two courses, and what percent of students take one or two courses, the following calculation must be performed:
(10/50) x 100 = X 0.2 x 100 = X 20 = X
(25/50) x 100 = X 0.5 x 100 = X 50 =X
Therefore, 20% of students take exactly two courses, and 50% of students take one or two courses.
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Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and the sum is a minimum.
Answer:
Step-by-step explanation:
Given 3 positive integers x, y and z, if their product is 125, then;
xyz = 125 .......... 1
Sum of the integers S(x, y, z) = x+y+z ........... 2
From equation 1; x = 125/yz ........3
Substitute equation 3 into 2
S(x, y, z) = 125/yz+y+z
Sy = -125/y²z + 1
Sz = -125/z²y + 1
For the sum to be minimum, Sy = Sz = 0
-125/y²z + 1 = 0
-125/y²z = -1
-125 = -y²z
125 = y²z
Also; is Sz = 0
-125/z²y + 1 = 0
-125/z²y = -1
-125 = -z²y
125 = z²y
Hence y²z = z²y = 125
From y²z = 125, z = 125/y²
Substitute z = 125/y² into the equation 125 = z²y
125 = (125/y²)²× y
125 = 125²/y⁴ × y
125 = 125²/y³
1 = 125/y³
y³ = 125.
y = 5
Since 125 = y²z
5²z = 125
25z = 125
z = 5
From the product xyz = 125
x(5)(5) = 125
25x = 125.
x = 5
Hence x = y = z = 5
Round 72.46387 to the nearest whole number
Answer:
72Step-by-step explanation:
[tex]72.46387 = 72[/tex]
4 is not up to 5
Solve for x in the equation 3x-5=2x²
Answer:
[tex]3x - 5 = 2 {x}^{2} \\ = > 3x = 2 {x}^{2} + 5 \\ = > x = \frac{2 {x}^{2} + 5 }{3} [/tex]
Considere as mesas com 4 cadeiras, com 6 cadeiras e com 8 cadeiras. ©Shutterstock/jenjira Com base nessa sequência de imagens, qual expressão indica a quantidade de cadeiras utilizadas ao colocarmos n mesas lado a lado?
Responder:
C. Tₙ = 2n + 2Explicación paso a paso:
De la pregunta, la secuencia de imágenes, cuya expresión indica es 4 cadeiras, 6 cadeiras, 8 cadeiras ...
Se puede ver la secuencia una progresión aritmética de la forma 4, 6, 8 ... Para obtener la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra, tendremos que encontrar el enésimo término de la secuencia que usa la fórmula para encontrar el enésimo término de una secuencia aritmética.
El enésimo término de un AP se expresa como Tₙ = a + (n-1) d donde;
a es el primer término
n es el número de términos es la diferencia común
De la secuencia generada, a = 4, d = 6-4 = 8-6 = 2
Tₙ = 4+ (n-1) 2
abre el paréntesis
Tₙ = 4 + 2n-2
Tₙ = 2n + 4-2
Tₙ = 2n + 2
Por lo tanto, la expresión que indica la cantidad de cadenas utilizadas o colocaremos n tablas una al lado de la otra es 2n + 2
Find the pattern and use inductive reasoning to predict the next number in the sequence 100,50,80,40,70,35,…
Answer:
65
Step-by-step explanation:
100, 50, 80, 40, 70, 35, 65.
|____|__|___|___|__|__|
÷2. +30. ÷2. +30 ÷2. +30
A pattern is a recurring arrangement of numbers, forms, colors, and so on. The next number in the given pattern will be 65.
What is a pattern?In mathematics, a pattern is a recurring arrangement of numbers, forms, colors, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.
If the given pattern is observed closely then it can be observed that the second number is decreased by half the previous one, while the next number is formed by adding 30, therefore,
The First Number = 100The second number, half of the previous = 50For the third number, add 30 = 80The fourth number, half of the previous = 40For the fifth number, add 30 = 70The sixth number, half of the previous = 35For the seventh number, add 30 = 65Hence, the next number in the given pattern will be 65.
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How many quarts of pure antifreeze must be added to 5 quarts of a 10 % antifreeze solution to obtain a 20 % antifreeze solution?
14. Line AD is parallel to line EG. If
m<3 is 70°, what is m 24?
F 10°
H 110°
G 20°
| 290°
15. Which angle is congruent to Z 3?
H 22
C 26
B 24
D 28
Answer:
14. H. 110°
15. D. <8
Step-by-step explanation:
14. Given that line AD and line EG are parallel as shown above, m<3 and m<4 are linear pairs and are supplementary. That is, m<3 + m<4 = 180°.
If m<3 = 70°, therefore, m<4 = 180° - 70°
m<4 = 110°
15. <3 corresponds with <8. Corresponding angles are congruent. Therefore, <3 = <8.
5(x - 10) = 30 - 15x
Answer:
x = 4
Step-by-step explanation:
We can first expand 5(x-10), getting 5x - 50.
Thus, 5x - 50 = 30 - 15x
We can then isolate x, getting (5+15) x = 30 + 50
20 x = 80
x = 4.
Answer:
5(x - 10) = 30 - 15x
We distribute 5 (x-10)
So 5x-50 = 30 -15x
5x+15x=50+30
(-15x became 15x because we brought it back to the other side and -50 became 50 because we brought it back to the other side to put the x's with the x's and the digits with the digits.)
So 20x=80
x= 50/20
We simplify 80/20
So x=4
In a poll, 22% of 714 surveyed adults said that . What is the actual number of adults who said that
Answer:
157 surveyed adultStep-by-step explanation:
IF 22% of 714 surveyed adult made a statement, the actual number of those that made the statement can be gotten by simply evaluating 22% of 714 as shown below;
= 22% of 714
= 22/100 * 714
= (22*714)/100
= 15708/100
= 157.08
≈ 157 surveyed adult
This means that about 157 surveyed adults made the statement.
Which sum or difference identity would you use to verify that cos (180° - q) = -cos q?
a.
sin (a -b) = sin a cos b – cos a sin b
b.
cos (a -b) = cos a cos b – sin a sin b
c.
cos (a -b) = cos a cosb + sin a sin b
d.
sin (a + b) = sin a cos b + cos a sin b
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, we'd have a = 180 and b = q, so,
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
cos(180 - q) = cos(180)cos(q) + sin(180)sin(q)
cos(180 - q) = -1*cos(q) + 0*sin(q)
cos(180 - q) = -cos(q) + 0
cos(180 - q) = -cos(q)
What is the equation of the slant asymptote of the rational function? f(x)=6x3−15x2+x−43x2−1 y=x−5 y=2x−5 y=x−17/3 y=2x−17/3
Answer:
2x − 5
Step-by-step explanation:
To solve, divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.
We can tell the first term of the quotient will be 2x, so the answer will be either 2x − 5 or 2x − 17/3.
The easiest method here is to simply multiply these by denominator.
(3x² − 1) (2x − 5) = 6x³ − 15x² − 2x + 5
(3x² − 1) (2x − 17/3) = 6x³ − 17x² − 2x + 17/3
So the answer must be 2x − 5.
Alternatively, you can use long division.
Answer:
2x-5
Step-by-step explanation:
f(x)=(6x^3−15x^2+x−4 )/(3x^2−1)
To find the slant asymptote,divide the numerator by the denominator
2x +(-15x^2+3x-4)/ (3x^2-1)
-5 + (3x-9)/(3x^2-1)
The divisor is (2x-5) and the remainder is ( 3x-9)
Three-fifths of the students on a school trip are boys. There are 33 boys on the trip. How many students are on the trip?
Answer:
55 students
Step-by-step explanation:
Write an equation.
3/5 = 33
Divide by 3 to get a unit fraction.
3/5 / 3 = 1/5
33 / 3 = 11
1/5 = 11
Multiply by 5
1/5 x 5 = 1
11 x 5 = 55
1 = 55
So, there are 55 students on the school trip.
Which of the following are solutions to the equation below?
Check all that apply.
9x^2- 6x + 1 = 7
The answer is C and D
First we must make one side of the equation zero, so we subtract 7 on both sides of the equation, making the equation 9x^2 - 6x - 6 = 0
Then we will use the quadratic formula to find the answers.
using the Quadratic Formula where:
a = 9, b = -6, and c = -6
and the formula is 6 +- [tex]\sqrt{6^{2} } -4 (9)(6) /2 (9)[/tex]
Question 1 (1 point) How many terms are in the polynomial? 3x3 + 4x2 - 8x - 5 3 4 7
Answer:
4
Step-by-step explanation:
The polynomial 3x^3 +4x^2 -8x -5 has 4 terms. A term is a product or single variable or constant separated from other terms by a plus or minus sign.
The four terms are ...
3x^34x^2-8x-5When you multiply numbers, the answer is the product of those numbers. Name two different pairs of whole numbers whose product is 12.
Answer: 4 x 3 = 12
6 x 2 = 12
Step-by-step explanation:
PLEASE HELP!! ALGEBRA! For a movie theater 4,000 tickets were sold, and the proceeds were $37,000. Tickets for children 16 and younger, were $10, adults were $12, and seniors 60 and older were $8. There were 4 times more seniors than adults at the movie theater. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the movie theater?
Answer: Fourth answer choice
c+a+s = 4000
10c+12a+8s = 37000
4a = s
==========================================
Explanation:
The first equation
c+a+s = 4000
is fairly straightforward. We add the individual counts of children (c), adults (a) and seniors (s) to get the total number of people (4000) who attended
-------------
If 1 child ticket costs $10, then 2 of them cost 20, and so on. If we don't know how many children there are, then we say 10c is the total cost for just the children alone. The c is a placeholder for some number.
Similarly, 12a represents the total cost for just the adults since 1 adult pays $12
8s is the total cost for all the seniors only
10c+12a+8s is the total cost of everyone and this total cost is 37000 dollars
The second equation is therefore
10c+12a+8s = 37000
----------------
We're told that "There were 4 times more seniors than adults at the movie theater" meaning
number of seniors = 4*(number of adults)
s = 4a
which is the same as 4a = s since we can flip both sides. So this is the third equation of our system.
------------------
We found these three equations
c+a+s = 4000
10c+12a+8s = 37000
4a = s
x+z-w/r=1 solve for z
Answer: z=1−x+w/r
Step-by-step explanation:
Subtract x from both sides.
z-w/r=1-x
Add w/r to both sides.
z=1−x+w/r
hope i helped
-lvr