Answer:
57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.9, n = 144[/tex]
So
[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{144}} = 0.025[/tex]
What is the probability that the proportion of people who will order coffee with their meal is within 2% of the population mean?
This is the pvalue of Z when X = 0.9 + 0.02 = 0.92 subtracted by the pvalue of Z when X = 0.9 - 0.02 = 0.88. So
X = 0.92
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.92 - 0.9}{0.025}[/tex]
[tex]Z = 0.8[/tex]
[tex]Z = 0.8[/tex] has a pvalue of 0.7881
X = 0.88
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.88 - 0.9}{0.025}[/tex]
[tex]Z = -0.8[/tex]
[tex]Z = -0.8[/tex] has a pvalue of 0.2119
0.7881 - 0.2119 = 0.5762
57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.
basic trigonometry question, picture attached please help
A standard deck of playing cards has 13 cards in each of four suits: hearts, clubs, diamonds, and spades. Two cards are chosen from the deck at random. What is the probability of choosing one club and one spade, without replacement?
A. 25/102
B.13/102
C.13/204
D.1/2
There are 52 cards in the deck.
Picking a spade would be 13/52 which reduces to 1/4
After the first card is picked there are 51 cards left, picking a club would be 13/51
Picking both would be 1/4 x 13/51 = 13/204
The answer is C.
can someone please help me i don’t get this at all!?
pls help me i am confused on what to do
Answer:
x=20
Step-by-step explanation:
you cross multiply then divide. so multiply 8 and 30. you get 240. then you multiply 12 and x. you get 12x. so your new equation is 240=12x so then u divide 240 by 12 and you get 20=z
Answer:
X=20
Step-by-step explanation:
You solve by cross multiplying.
Students voted on a school trip. 56 voted for the museum, 86 for the nature center, 172 for the state capital, and 116 for other venues.
A circle graph titled School trip location. 40 percent is a, 20 percent is b, 13 percent is c, 27 percent is d.
The circle graph shows the data from the table, but the labels are missing.
Choose the correct labels.
a =
b =
c =
d =
Answer:
a = state capital
b = nature center
c = museum
d = other
Step-by-step explanation:
Answer:
other person is correct
Step-by-step explanation:
Simplify the slope of AC.
Answer:
1
Step-by-step explanation:
The slope of a line can be found by dividing the rise over the run, or how much the line rises over a certain amount of sideways movement. In this case, the line AC moves from (0,0) to (a,a), meaning that it rises and moves sideways the same amount. Since a/a=1, the slope of this line is 1. Hope this helps!
Answer:
1
Step-by-step explanation:
Point A is (0, 0) and Point C is (a, a).
The "rise" from A to C is a and the "run from A to C" is also 1.
Thus, the slope of line A is m = rise / run = 1 / 1 = 1.
What is 1+1= Lol :) JUST ANSWER PLZZ
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
A diver dives to 50 feet in 10 minutes, stays there for 30 minutes, and then resurfaces in 10 minutes. Click on the graph until the graph that best represents the given statement appears.
Answer:
50x5
Step-by-step explanation:
The question is an illustration of a distance-time graph.
From the question, we have the following highlights
The distance in the first 10 minutes is 50 feet. i.e. (10, 50)He stays at 50 feet for 30 minutes i.e. (40, 50)Then comes out after 10 minutes i.e. (50, 0)The graphs are not given, so I will attach the graph that represents the scenario.
See attachment for the graph that answers the question.
Read more about distance-time graphs at:
https://brainly.com/question/19836052
Joshua just bought a new fish tank. The tank is 14 inches tall and has a radius of 4 inches. How much water can Joshua put in the tank? Use 3.14 for pi. *
A. 703.36 cubic inches
B. 56 cubic inches
C. 224 cubic inches
D. 175.84 cubic inches
Answer:
V = 703.36 in³ (This matches answer option A.)
Step-by-step explanation:
This fish tank has a cylindrical shape. The formula for the volume of a cylinder of radius r and height h is
V = (pi)(r²)(h).
We are told that h = 14 in and r = 4 in. Using 3.14 for pi:
V = (3.14)(4 in)²(14 in) =
V = 703.36 in³ (This matches answer option A.)
graph the circle x^2+y^2+2x+4y-44=0
plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.
To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, we can follow these steps:
1. Complete the square for the x-terms:
Rearrange the equation to group the x-terms together:
x^2 + 2x + y^2 + 4y = 44
To complete the square for the x-terms, add (2/2)^2 = 1 to both sides of the equation:
x^2 + 2x + 1 + y^2 + 4y = 44 + 1
Simplify:
(x + 1)^2 + y^2 + 4y = 45
2. Complete the square for the y-terms:
To complete the square for the y-terms, add (4/2)^2 = 4 to both sides of the equation:
(x + 1)^2 + y^2 + 4y + 4 = 45 + 4
Simplify:
(x + 1)^2 + (y + 2)^2 = 49
3. Identify the center and radius:
The equation is now in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2
Comparing this with our equation, we can see that the center of the circle is (-1, -2) and the radius is √49 = 7.
4. Plot the graph:
The center of the circle is (-1, -2), which represents the point where the circle is centered. From this point, we can draw a circle with a radius of 7 units in all directions.
By following these steps, we can plot the circle on a coordinate plane, with the center at (-1, -2) and a radius of 7 units.
For more questions on circle .
https://brainly.com/question/28162977
#SPJ8
Note the full question may be:
To graph the equation of the circle x^2 + y^2 + 2x + 4y - 44 = 0, first rewrite it in standard form by completing the square for both x and y terms. Then identify the center and radius of the circle and plot the corresponding points to draw the graph.
Sid starts with savings of £13
Tim starts with no savings
Each week from now,
- Sid will save £3.50 and Tim will save £3
In how many weeks will Sid and Tim have savings in the ratio 17 : 9
Your final line must say, 17 : 9 in weeks
Answer:
after 6 weeks
Step-by-step explanation:
Sid and Tim starts saving each week.
Sid starts his savings with initial amount of £13.00
Tim starts his saving with initial amount of £00.00
Each week from now Sid will save = £3.50
Tim will save each week = £3.00
Let's assume after 'x' weeks the amount of Sid would be = £ (13 + 3.50x)
and the amount of Tim's saving after x weeks = £ (3x)
The ratio of their savings in x weeks would be = 17 : 9
Now the expression we get,
(13 + 3.50x) : (3x) = 17 : 9
[tex]\frac{13+3.50x}{3x}=\frac{17}{9}[/tex]
9(13 + 3.50x) = 17(3x)
117 + 31.5x = 51x
117 = 51x - 31.5x
117 = 19.5x
[tex]x=\frac{117}{19.5}[/tex]
x = 6
After 6 weeks the savings of Tim and Sid would be in the ratio of 17 : 9.
A box of chocolates contains five milk chocolates and six dark chocolates. Mike randomly picks a chocolate and eat it. Then Mike randomly picks another chocolate and eats it. Determine the probability Mike eats two milk chocolates. Round to the hundredths place.
Answer: 0.182
Step-by-step explanation:
For the first selection, the probability of picking a milk chocolate bar is equal to the number of milk chocolate bars divided the total number of bars, this is:
p1 = 5/(6 + 5) = 5/11
In the second selection we have the same equation, but now we have 4 milk chocolate bars (because one is alredy taken)
p2 = 4/(4 + 6) = 4/10
the joint probability is:
P = p1*p2 = (5/11)*(4/10) = 0.182
Factor the following equation:
x^2 -x-90
Answer:
(x - 10)(x + 9)
Step-by-step explanation:
[tex] {x}^{2} - x - 90 \\ = {x}^{2} - 10x + 9x - 90 \\ = x(x - 10) + 9(x - 10) \\ = \red{ \boxed{ \bold{ (x - 10)(x + 9) }}}\\ [/tex]
Simplify the expression:
6V + 10 - V
Answer:
5V + 10
Step-by-step explanation:
Add the like terms.
-5v - 4
If you add the like terms this is what you get
J/-2 + 7 = -12 Please help guys!
Answer:
J=17
Step-by-step explanation:
J/-2 + 7 = -12
multiply both sides by -2 to cancel out the J/-2 and turn it into J + 7 = 24
transfer the 7 to the other side to get J = 24 - 7
J = 17
hopefully this helps.
Can someone help me on this
Answer:
1. C) quadratic
2. b) exponential
Step-by-step explanation:
xion orders 5 loves of bread from the website bakery the total shipping weight is 9 pounds as model of the bread what is in pounds each of the lovaes
The local theater sold 260 tickets to their most recent performance. Admission was $9 for adults and $5 for children. If they made $2,140, how many adult tickets did they sell?
Answer:
210 adult tickets were sold
Step-by-step explanation:
let x be the number of adult tickets sold
let y be the number of children tickets sold
x+y=260 equation 1
9x+5y=2140 equation 2
multiply equation 1 by 5
multiply equation 2 by 1
5x+5y=1300
9x+5y=2140
subtract equation 1 from 2
4x=840
x=840/4 =210 tickets
substitute for x in equation 1
210+y=260
y=260-210=50
Miguelito vende camisas de vestir . En el local le cobran $150 de alquiler; comprq cada camisa en $3.00 y la vende en $5.00. Cuanto es el numero minimo de camisas que debe vender para tener ganancias.
Answer:
[tex]x_{min} = 75\,camisas[/tex]
Step-by-step explanation:
El número mínimo de camisas a vender es igual al costo de alquiler del local dividido por la diferencia entre los valores de venta y compra de cada camisa. (The minimum amount of shirts to be sold is equal to the rental cost of the retail space divided by the difference between sell and purchase cost per shirt):
[tex]x_{min} = \frac{\$ 150}{\$ 5 - \$ 3}[/tex]
[tex]x_{min} = 75\,camisas[/tex]
Miguelito debe vender un mínimo de 75 camisas para obtener ganacias. (Miguelito must sell a minimum of 75 shirts to make a profit.)
please help quickly !
Answer:2490-2312=w; w=178 so 178 pounds
Step-by-step explanation:
Answer:
hey!
Your answer is 178 pounds!!
Step-by-step explanation:
by doing 2490lb-2312lb gives us the value of w
soo w=178 pounds!!
HOPE THIS HELPS!!
hey can anyone help me in dis!!!!!!!!
Answer:
the red is longer
Step-by-step explanation:
A football team tries to move the ball forward as many yards as possible on each play, but sometimes they end up behind where they started. The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25. A positive number indicates moving the ball forward, and a negative number indicates moving the ball backward. 1). Which number in the list is the greatest? 2). What is a better question to ask to find out which play went the farthest from where the team started? 3). The coach considers any play that moves the team more than 4 yards from where they started a "big play." Which play(s) are big plays?
Answer:
Given:
The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25.
Solved:
1. The greatest number is 25
2. If the moved distances are square, which one is largest?
3. The move which is greater than 4 is considered "big play"
=> 21 and 25 are big play (21 > 4, 25 > 4)
Hope this helps!
:)
Please Help! ASAP! WIll give Brainliest
Figure A is a scale image of Figure B.
What is the value of x?
Answer:
x/2 = 12.5/5
5 · x = 12.5 · 2
5x = 25
5x / 5 = 25 / 5
x = 5
Step-by-step explanation:
Pound: 1/2 __ 5 Ounces: __ 32 __
Answer:
pounds - ½, 2, 5
ounces - 8, 32, 80
Step-by-step explanation:
Translate the difference of a number and 7 is -8 into an equation.
Answer:
-1
Step-by-step explanation:
7 - 8 = -1
hope its helpful
Answer:
n - 7 = -8
Step-by-step explanation:
Find the area of the triangle below.
Be sure to include the correct unit in your answer.
Answer:
A =70 ft^2
Step-by-step explanation:
The area of the triangle is equal to
A = 1/2 bh where b is the base and h is the height
A = 1/2 (20) *7
A =70 ft^2
Unit 5. 9) Please help. A soda can holds approximately 25.5 cubic inches of soda and is 4.8 inches tall. What is the approximate area of its base?
Answer:
5.3125 in^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = Bh
Where B is the area of the base
25.5 = 4.8 B
Divide each side by 4.8
25.5/4.8 = B
5.3125 = B
what does this expression represent five times the quotient of some number and ten
Answer:
5(n/10)
Step-by-step explanation:
quotient of some number and ten=n/10
five time=*5
put it togther=5(n/10)
Which solution set is graphed on the number line?
Answer:
An inequality, such as x>2 can be graphed on the number line.
Step-by-step explanation:
An inequality, such as x>2 can be graphed on the number line. An open circle as a stating point, indicates the number is NOT included in the solution. Where as a closed circle or "dot" indicates the number IS included in the solution.
Answer:
An inequality, such as x>2 can be graphed on the number line.
Step-by-step explanation:
(x-3)(x+5) the product
Answer:
x^2 +2x -15
Step-by-step explanation:
FOIL
(x-3)(x+5)
first x*x = x^2
outer 5x
inner -3x
last -3*5 = -15
Add them together
x^2 +5x-3x-15
Combine like terms
x^2 +2x -15
