Part A
p = population proportion of inaccurate orders for restaurant A.
There are 240 accurate orders and 73 inaccurate ones.
That gives 240+73 = 313 total orders.
n = 313 = sample size
73/313 = 0.233227 is the approximate sample proportion of inaccurate orders. This is the approximate value of phat. The job of phat is to estimate p.
At 90% confidence, the z critical value is roughly z = 1.645; use a stats table, reference sheet, or calculator to find this value.
Let's calculate the margin of error.
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.645*sqrt(0.233227*(1-0.233227)/313)
E = 0.039320 approximately
Then,
L = lower boundary of confidence interval
L = phat - E
L = 0.233227 - 0.039320
L = 0.193907
L = 0.194
And
U = upper boundary of confidence interval
U = phat + E
U = 0.233227 + 0.039320
U = 0.272547
U = 0.273
The 90% confidence interval for the inaccurate order rate of restaurant A is therefore 0.194 < p < 0.273
We are 90% confident the population proportion p is somewhere between 0.194 and 0.273
=================================================
Part B
The result of part A was 0.194 < p < 0.273
Compare this to 0.211 < p < 0.292 for restaurant B.
Use a number line to see that there is overlap between these intervals. It's possible that both restaurants might have the same inaccurate order rates (or close to the same).
If there wasn't an overlap, then it would be likely the two rates would be different.
Factor 9t–3u.
Write your answer as a product with a whole number greater than 1.
The factor of the expression 9t – 3u will be 3 and 3t – u.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of numbers and symbols and the procedures for using these symbols in formulae.
The expression is given below.
⇒ 9t – 3u
Simplify the expression, then we have
⇒ 3·3t – 3u
⇒ 3(3t – u)
The factor of the expression 9t – 3u will be 3 and 3t – u.
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Jen is making dipping sauce for her book club meeting she uses 3 tablespoons of ketchup for every 1 tbsp of hot sauce how many tablespoons of ketchup and hot sauce does Jen need if she is making a total of 36 tablespoons of dipping sauce
Answer:
9 tablespoons of hot sauce
27 tablespoons of ketchup
Step-by-step explanation:
We know that Jen uses 3x as many tablespoons of ketchup as to hot sauce. We know she is making 36 tablespoons dipping sauce total.
SO, we make the equation x + 3x = 36
we group like terms and have 4x = 36
we need to divide both side by 4 and get 9
this means that we use a total of 9 tablespoons of hot sauce and 27 tablespoons of ketchup.
HELP ASAP!! Find the sum of the series
Answer:
225
Step-by-step explanation:
a1 = 1
a15 = 29
sum = n/2 ( a1 + a15) = (15/2) ( 1 + 29) = 225
A school is arranging a field trip to the zoo. The school spends 778.88 dollars on passes for 28 students and 4 teachers. The school also spends 241.64 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
The total money spent on a pass and lunch for each student is $850.14.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
here,
As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.
Total number of person = 28 + 4
= 32
Cost per pass = 778.88 / 32
= $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14
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I’ve been trying to figure out this question but I am not able to please help
Answer:
its C
Step-by-step explanation:
ik
Answer:
D
Step-by-step explanation:
Since the total degrees of a circle is 360 and half of a circle is 180, 1/4 of a circle is 90 or less, D is the answer :)
Which of the expressions represent the domain -5 ≤ x < 5?
Answer:
It can be written in interval notation as [-5,5)
Find the value of z in parallelogram CDEF
Answer:
z = 13
Step-by-step explanation:
Opposite sides of a parallelogram are equal. Therefore:
3z = z + 26
Subtracf z from each side
3z - z = 26
2z = 26
z = 26/2
z = 13
if you answer your a true king
Answer:
its 29
Step-by-step explanation:
the spinner has three regions 5 0 and 20to play the game you spin one time and then you win the amount in the region that the spinner lands on. what is the expected valuse of the game
Answer:
Step-by-step explanation:
Each region is equally likely.
5 * 1/3 = 5/3 = 1 2/3 = 1.67
0 * 1/3 = 0
20*1/3 = 6 2/3 = 6.67
Total = 8.34
So if this really were a game you should be willing to put up 8.34 to play it.
You can create a simulation. Let the computer play 10000 times (which will take seconds). I'm going to try this for you. and see what happens.
You throw 0 3309 times
You throw 5 3394 times
You throw 20 3290 times
The net result is that you will win 2.71 as you pay, which is what it should be.
Line v passes through points (4, 4) and (9, 8). Line w is parallel to line v. What is the slope of line w?
Answer:
slopeᵥᵥ = 4/5
Step-by-step explanation:
mᵥ = (8-4)/(9-4) = 4/5
I NEED HELP HELP HELP HELP HELP HELPPP ASP
Answer:
it S
Step-by-step explanation:
Every day, Austin packs his favorite sandwich in a plastic sandwich box. Austin's sandwich box is 13 centimeters long and 12 centimeters wide, but only 3 centimeters tall. What is the volume of Austin's sandwich box?
The volume of the rectangular sandwich box of Austin is given by the equation V = 468 cm³
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the volume of the rectangular box be represented as V
Now , the equation will be
The length of the sandwich box = 13 cm
The width of the sandwich box = 12 cm
The height of the sandwich box = 3 cm
And , volume of the rectangular box V = Length x Width x Height
Substituting the values in the equation , we get
Volume of the rectangular box V = 13 x 12 x 3
On simplifying the equation , we get
Volume of the rectangular box V = 468 cm³
Hence , the volume of rectangular box is 468 cm³
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Fatuma invests a total of $26,500 in two accounts paying 10% and 14% annual interest, respectively. How much
was invested in each account if, after one year, the total interest was $3,150.00.
$_____was invested at 10% and
$_____was invested at 14%.
Answer:
$14000 was invested at 10%
$12500 was invested at 14%
Step-by-step explanation:
We'll need a system of equations to find the amounts invested at 10% and at 14%
Let x represent the amount invested at 10% (10% = 0.1 interest rate)Let y represent the amount invested at 14% (14% = 0.14 interest rate)Let 0.1x represent the interest earned at 10%Let 0.14y represent the interest earned at 14%First equation:
amount invested at 10% + amount invested at 14% = total amount invested.
Thus, our first equation is x + y = 26500
Second equation:
interest earned at 10% + interest earned at 14% = total interest earned
Thus, our second equation is 0.1x + 0.14y = 3150
Method to solve: We can solve using substitution by isolating x in the first equation. Then we must substitute the resulting equation for x in the second equation. This will allow us to first solve for y:
Step 1 (Isolating x in first equation):
(x + y = 26500) - y
x = -y + 26500
Step 2 (Plugging in x = -y + 26500 for x in 0.1x + 0.14y = 3150 to solve for y):
0.1(-y + 26500) + 0.14y = 3150
-0.1y + 2650 + 0.14y = 3150
0.04y + 2650 = 3150
0.04y = 500
y = $12500
Step 3: Now we can plug in 12500 for y in the second equation in our system to find x:
x + 12500 = 26500
x = $14000
Thus, the amount invested at 10% is $14000 while the amount invested at 14% is 12500
Optional Step 4: We can check that we've found the correct investment amounts by plugging in 14000 for x and 12500 for y in both equation in our system and checking that we get 26500 and 3150 respectively:
Checking solutions for first equation:
14000 + 12500 = 26500
26500 = 26500
Checking solutions for second equation:
0.1(14000) + 0.14(12500) = 3150
1400 + 1750 = 3150
3150 = 3150
onsider the line =+7x5y−4. Find the equation of the line that is parallel to this line and passes through the point −−4, 5. Find the equation of the line that is perpendicular to this line and passes through the point −−4, 5.
The equation of the line perpendicular to 7x+5y = 4 is y = 5/7(x) -15/7. The equation of the line parallel to 7x+5y = 4 is y = -7/5(x) -53/5
How to find the equation of the lines parallel and perpendicular to 7x+5y = 4?Given that: the line is perpendicular/parallel to the line 7x+5y = 4 and it passes through (−4,-5)
The slope-intercept form of a straight line is:
y = mx + c
where m is the slope and c is the y-intercept
For perpendicular case:
When the two lines are perpendicular, the product of their slope is -1 i.e.
m₁ x m₂ = -1
where m₁ and m₂ represent the slope of the lines
Let the slope of the given line be m₁ and the slope of the unknown line be m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₁ x m₂ = -1
-7/5 x m₂ = -1
m₂= 5/7
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = 5/7 (-4) + c
-5 = -20/7 + c
c = -15/7
Thus, the equation of the line is y = 5/7(x) -15/7
For parallel case:
When the two lines are parallel, they have equal slope i.e. m₁ = m₂
Line1(given):
7x+5y = 4 => y = (-7/5)x + 4/5
Thus, m₁ = -7/5
m₂= -7/5
Line 2(unknown) with the point (−4,-5):
y = mx + c
-5 = -7/5(-4) + c
-5 = 28/5 + c
c = -53/5
Thus, equation of the line is y = -7/5(x) -53/5
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Identfy the equation that translates Y= In(x) five units down.
y= In(x-5)
y= In(x)+5
y= In(x+5)
y= In(x)-5
Please please help me
Answer:
y= In(x)-5
Step-by-step explanation:
Simplify i) ( x-y )( x−y )( x−y )
The simplified expression for ( x - y ) ( x - y ) ( x - y ) is x³ - x²y - xy² + y³.
To simplify ( x - y ) ( x - y ) ( x - y ), we can expand the expression using the distributive property of multiplication. We can also simplify the expression by combining like terms.
In using the distributive property of multiplication, we multiply each term in the first set of parentheses by each term in the second set of parentheses. This gives us:( x - y ) ( x - y ) ( x - y ) = ( x(x - y) - y(x - y) ) ( x - y )= ( x² - xy - xy + y² ) ( x - y )= ( x² - 2xy + y² ) ( x - y )
Now we can further simplify the expression by combining like terms. We can use the difference of squares formula to simplify the second set of parentheses.( x² - 2xy + y² ) ( x - y ) = ( x - y ) ( x - y )²= ( x - y ) ( x² - 2xy + y² )= x³ - x²y - 2xy² + xy² - xy² + y³= x³ - x²y - xy² + y³
Therefore, the simplified expression is x³ - x²y - xy² + y³.
Summary: To simplify ( x - y ) ( x - y ) ( x - y ), we expand the expression using the distributive property of multiplication. We simplify the expression by combining like terms. We use the difference of squares formula to simplify the second set of parentheses. Finally, we simplify the expression further by combining like terms. The simplified expression is x³ - x²y - xy² + y³.
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Find the equation of the line below. No bots!!!
Answer:
y=5x
y2-y1/x2-x1 = 10-5/2-1
Step-by-step explanation:
this questions is reallly complicated can u please solve it
The measure of angle a is determined as 30 degrees.
What is the measure of angle a?The measure of angle a is calculated by applying the following circle theorem as follows;
If line AB is the diameter of the circle, then angle ACB will be equal to 90 degrees.
The value of a is calculated as;
a + 2a = 90 (complementary angles sum up to 90 degrees since angle ACB is equal to 90 degrees)
3a = 90
divide both sides by 3;
3a/3 = 90 / 3
a = 30
Thus, the measure of angle a is calculated by applying the following circle theorem for complementary angles.
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(PLEASE HELP, 100 POINTS!) A young boy has a penny, a nickel, a dime, a quarter, and a half-dollar coin. He puts all the coins in his hand and tells his friend that he can randomly choose two of the coins without looking. What is the probability that the boy’s friend will choose the quarter as one of the two coins? Show your answer in fraction and percent, round to the nearest whole percent.
\(\\ \rm\longmapsto P(Quarter)\)
\(\\ \rm\longmapsto \dfrac{1}{5}\)
\(\\ \rm\longmapsto 20\%\)
Answer:
No of objects=5
\(\begin{gathered}\\ \sf {P(Quarter)}\end{gathered}\)
\(\begin{gathered}\\ \sf \dfrac{1}{5}\end{gathered}\)
\(\begin{gathered}\\ \sf 20\%\end{gathered}\)
_____consists of activities that are
not required as part of one's formal
role in the organization
Select one:
a. None of the above
b. Lobbying
c. Influence
d. Political behaviour
= Political behaviour
Step-by-step explanation:
political behaviour consists of activities that are
not required as part of one's formal
role in the organization
Write down the augmented matrix corresponding to the system of equations shown below.
Note: Write an equation in each answer field and do not solve the system.
The augmented matrix corresponding to the system of equations in this problem is given as follows:
[-6 -5 -4 7].
[7 -9 -1 -7].
[-9 -3 -6 7].
How to construct the augmented matrix?The first row is constructed according to the coefficients of the first equation, hence it is given as follows:
[-6 -5 -4 7].
The second row is constructed according to the coefficients of the second equation, hence it is given as follows:
[7 -9 -1 -7].
The third row is constructed according to the coefficients of the third equation, hence it is given as follows:
[-9 -3 -6 7].
Hence the matrix is given as follows:
[-6 -5 -4 7].
[7 -9 -1 -7].
[-9 -3 -6 7].
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A(4,3) B(1/2, 1/5) C( 3/4, 7/4). Which point lies on the circumstance of the unit circle?
None of the three points (A, B, C) lies on the circumference of the unit circle.
What point is in the circumference of an unit circle?
Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:
Point A
\(d = \sqrt{4^{2}+3^{2}}\)
d = 5
Point B
\(d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }\)
d = √29 /10
d ≈ 0.539
Point C
\(d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}\)
d = √58 /4
d ≈ 1.904
None of the three points (A, B, C) lies on the circumference of the unit circle.
RemarkThe statement presents a typing mistake, correct form is shown below:
A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?
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(6.2 x 10²) x (3.5 x 10³)
Answer:
\(21.7 x 10^5\)
Step-by-step explanation:
(6.2 x 10²) x (3.5 x 10³)
First, multiply the coefficients: 6.2 x 3.5 = 21.7.
Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.
Therefore, the result is 21.7 x 10^5.
Answer:
3286000
Step-by-step explanation:
Find the slope of the treadmill.
Help me out please please
Answer:
490000
Step-by-step explanation:
Substituting \(x=40\),
\(I=-425(40)^2 + 45500(40) - 650000=490000\)
Juan has $120 in his checking account. He buys 4 equally priced shirts and pays with a check. If Juan now has -$60 in his account, how much was each shirt ?
Answer:
45
Step-by-step explanation:
Step 1. 120+60=180
Step 2. 120-180=-60
Step 3. 180 divded by 4
Janet ran 4 miles in 30 minutes yesterday. She ran 45 minutes at the same rate today. How far did Janet run today?
No matter which direction an object is going in, speed is a scalar variable that quantifies how swiftly it is moving. The rate at which an object changes its position in a particular direction is measured by a vector quantity called velocity.
Speed: The amount of time it takes to cover a certain distance is stated in units like meters per second (m/s) or miles per hour (mph). For instance, a car's speed is 60 mph if it covers 60 miles in an hour.
Both the speed and direction of motion are included in the displacement per unit of time, which is stated in terms like meters per second (m/s) or miles per hour (mph). For instance, a car's velocity is 60 mph due north if it drives 60 miles in an hour in that direction.
In other words, velocity informs us on the direction and speed of an object's motion in addition to its speed.
Janet completed a 4 mile run yesterday in 30 minutes. We can calculate her running speed using the following data:
rate = distance/time = 4 miles/30 minutes = 0.1333 miles/minute
Today Janet ran for 45 minutes at the same pace. We can calculate how far she ran today using her rate:
Rate = Distance 45 minutes at a speed of 0.1333 miles per minute equals 6 miles.
Janet completed 6 kilometers of running today.
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Question 2
5 pts
You deposit $5000 in an account earning 7% interest compounded
monthly. How much will you have in the account in 10 years?
5 nts
\(s = 5000(1.07) {}^{t} \)
\(s = 5000(1.07) {}^{10} \)
\(s = 5000(1.96715)\)
\(s = 9835.756 \: dollars\)
To win at Lotto in a certain state, one must correctly select 6 numbers from a Corbin of 52 numbers (one through 52). The order in which the selecting is made does not matter. How many different selections are possible?
Answer:
the answer is ... look down below
Step-by-step explanation:
52 divided by 6 equals 8.66
Solve 2^x-2=8^4 but not solving for x
Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.
To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.
First, let's simplify the equation:
2^x - 2 = 8^4
We know that 8 can be expressed as 2^3, so we can rewrite the equation as:
2^x - 2 = (2^3)^4
Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:
2^x - 2 = 2^(34)
Simplifying the right side of the equation:
2^x - 2 = 2^12
Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:
x = 12
Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.
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