The 85% confidence interval for the mean time at lunch is (25.01, 31.79) minutes.
In a random sample of eighteen people, the mean time at lunch was 28.4 minutes.
Standard deviation of 8.2 minutes.
A common method to calculate the confidence interval for the mean of a normal distribution is to use the Z-score. For a 85% confidence interval, the Z-score is 1.44. Therefore, the confidence interval can be calculated as:
The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.
If [tex]$$n \geq 30$ & Confidence Interval $=\bar{x} \pm z_{\alpha / 2}(\sigma / \sqrt{ n})$ \\[/tex][tex]$$n\le 30$ & Confidence Interval $=\bar{x} \pm z_{\alpha / 2}(\sigma / \sqrt{ n})$ \\[/tex]Where,
n= Number of terms
[tex]$\overline{\mathrm{x}}[/tex]= Sample Mean
[tex]$\sigma[/tex]=Standard Deviation
[tex]$z_{\alpha / 2}[/tex]= Value corresponding to a2 in z table
[tex]$t_{\alpha / 2}[/tex]= Value corresponding to a2 in t table
[tex]$\alpha[/tex]=(1 - Confidence Level /100)
So for the given data, the confidence interval would be:
=28.4 ± 1.44 * 8.2 / √18
=28.4 ± 1.44 * 8.2 / 4.24
=28.4 ± 3.39
=(25.01, 31.79)
Therefore, the 85% confidence interval for the mean time at lunch is (25.01, 31.79) minutes.
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Please help with this, im so confused
The required equivalent expression to the given expression is Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
An expression is given in the question that is,
[tex]Z(t) = 4000(12^{2t +2})[/tex]
We have to form a problem that represents the format of a function same as shown above.
Expression and problem is given as, Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.
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If investments double every 9 years and you
start with a $600 investment, how much
money would you have after 27 years?
First, complete the equation:
Future Amount = [?](1+
↑
initial amount
growth rate
Xtime
periods
After 27 years, you would have $4800 in the account.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
Investment double every 9 years,
and you start with $600 investment.
So, by the exponential growth function,
y = 600(1+r)ˣ,
To find the growth rate:
1200 = 600(1 + r)⁹
r = 1.08006
So, the equation is,
y = 600(1+0.8006)ˣ
After 27 years,
y = 600 x 8
y = $4800
Therefore, $4800 is the required amount.
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for many medical tests, it is standard procedure to repeat the test when a positive signal is given. if repeated tests are independent, what is the probability that a man will test positive on two successive tests if he has the disease?
The probability that a man will test positive on two successive tests if he has the disease 81%.
In mathematical terms, probability can be represented as the ratio of the number of favorable outcomes to the number of possible outcomes. The formula for probability is as follows:
P(E) = n(E) / n(S)
Where:
P(E) is the probability of event E occurring
n(E) is the number of favorable outcomes for event E
n(S) is the number of possible outcomes in the sample space S
Let's assume the probability of a man testing positive for a disease if he has it is represented by the symbol "P".
If the tests are independent, meaning that the outcome of one test does not affect the outcome of the other, then the probability of a man testing positive on two successive tests can be calculated as the product of the probabilities of each individual test.
Therefore, the probability of a man testing positive on two successive tests if he has the disease is P * P, or P².
If the probability of a man testing positive for a disease if he has it is 90%, represented by P = 0.9, then the probability of him testing positive on two successive tests is 0.9 * 0.9 = 0.81, or 81%.
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PLS HELP MEEEEEEEE PLS
The complex number z = 4√3 - i 4 has a norm 8 and a direction 330°. Its representation is in the image shown below.
How to graph a complex number and identify its norm and direction
In this question we find the definition of complex number in rectangular form, whose definition is shown below:
z = a + i b, where a, b are real numbers.
Where:
a - Real componentb - Imaginary componentGraphically speaking, the real component is associated to the horizontal axis of Cartesian plane and the imaginary component is associated to the vertical axis of that plane. The norm (r) and direction (θ) of the complex number are, respectively:
Norm
r = √(a² + b²)
Direction
θ = tan⁻¹ (b / a)
The norm and the direction of the complex number are, respectively:
r = √[(4√3)² + (- 4)²]
r = 8
θ = tan⁻¹ [(- 4) / (4√3)]
θ ≈ 330°
Lastly, we represent the complex number with the help of a graphing tool.
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Find the area of the given rhombus if AC = 2 m, DB = 9 m.
Que pongo?rápido porfiii
Answer:
4xy + 2xy - 3xy +5xz - yz
4xy - 3xy + 2xy + 5xz - yz
1xy+2xy + 5xz - yz
3xy + 5 xz - yz
soooo umm I don't know?
Answer: The last option would be correct p= 75 + 5a. The reason being the last option is the right one is because the expression represents the additional points plus her original 75 she had on her homework assignments.
Find the equation of the line parallel to 8x+5y=1 passing through the point (1,−3)
The equation of the line parallel to 8x+5y=1 passing through the point (1,−3)
is y = (-8/5)x - (7/5).
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is y = m(1)x + c
Now,
The equation of the line parallel to 8x+5y=1 passes through the point (1, -3).
This means,
8x + 5y = 1
5y = - 8x + 1
y = (-8/5)x + 1/5
This is in the form of y = m(2)x + c
m(2) = (-8/5)
Now,
Since the line is parallel.
m(1) = m(2) = (-8/5)
So,
y = (-8/5)x + c
Now,
(1, -3) = (x, y)
-3 = (-8/5) x 1 + c
c = -3 + 8/5
c = (-15 + 8) / 5
c = -7/5
So,
y = (-8/5)x - (7/5)
Thus,
The equation of the line is y = (-8/5)x - (7/5).
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There were 72 runners to start a race. In the first half of the race,1/
4
of them dropped out. In the second half of the race,2/3 of the remaining runners dropped out How many runners finished the race?
Step-by-step explanation:
First find 1/4 of 72 runners. To do this divide by 4.
So
72/4=18
Now take 72 and subtract 18 to get 54
Next find 1/3 of 54 runners
54/3=18
Because it is 2/3 you need to multiply 18 by 2
So
18 x 2 = 36
So
54-36=18 runners that finished the race
If needed in fraction form
18/72
Now simplify
9/16 of the runners finished
how long would it take johnny to watch and finish a show with 61 episodes, if each episode is 23 minutes long?
Answer: 1,403
Step-by-step explanation: None
Answer:
1403
Step-by-step explanation:
First you find out how many minutes is each episodes at that is 23
Then you multiple 23 by 61 and you get 1403
Patch traveled from his office to the seashore at a speed of 62 mph. He traveled the same route on his way back to the office, but on the return trip his speed was 66 mph. If, altogether, Patch spent a total of 4 hours on the road, how many hours did the trip to the seashore take? Round your answer to the nearest hundredth (two decimal places)
Answer:
1.03 hours
Step-by-step explanation:
Let x be the time taken to travel from office to seashore at 62mph
Distance traveled = speed x time = 62x miles
Since both trips together took 2 hours, the time taken for the same distance from seashore to office = 2 - x hours
At a speed of 66 mph, the distance traveled = 66(2-x) = 132 - 66x
Since the distances on each trip are equal:
62x = 132 - 66x
Add 66x to both sides => 62x + 66x = 132 =-66x + 66x
128x = 132
x = 132/128 = 1.03125 hours = 1.03 hours rounded to 2 decimal places
WILL MARK BRAINLIST PLS HELP
Solve for x on the diagram below
Answer:
x = 56
Step-by-step explanation:
64 + x + 60 = 180
124 + x = 180
x = 56
The missing angle x of the diagram is; x = 56°
How to find the sum of angles on a straight line?In geometry, we know that the sum of angles on a straight line sums up to 180 degrees.
Now, in the given image we see that the three angles we are concerned with all form a straight line and as such they will all add up to 180 degrees. Thus;
64 + x + 60 = 180
124 + x = 180
x = 180 - 124
x = 56°
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When air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches, what is the pressure, in pounds, when the volume is 140 cubic inches?
The pressure in the tyre when the volume is 140 cubic inches will be 30 pounds.
What is Boyle's law?Boyle's law states that at a constant temperature, the pressure is inversely proportional to the volume. It means that the product of the pressure and the volume will remain constant for the given system.
Given that when air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches.
The pressure will be calculated as:-
P₁V₁ = P₂V₂
( 35 x 120 ) = 140 x P₂
P₂ = ( 35 x 120 ) / 140
P₂ = 30 pounds
Therefore, when the volume is 140 cubic inches, the tire's pressure will be 30 pounds.
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Estimate √487 plsssssss
Answer:
Step-by-step explanation:
=22.068
Answer:
5
Step-by-step explanation:
actual answer 4.69766713281
What’s two fifteen divided by nine
Answer:
23.8888888889 that's the answer
Answer:
215/9=23.8888888889
Step-by-step explanation:
a) Write down the next two numbers in the following sequent
33
22
45
12
10
HELP pls will mark you the brainliest
We can acquire a number of kites of 6 kites for a total price of $ 30 in both stores (Kites-R-Fun, Windy Kites).
What is the solution to a system of linear equations formed by two lines
In this problem we find the case of two lines being represented on Cartesian plane, both have a point of intersection that represents the solution to the system. Each line represents a price function for a kite model sold in a store, where the horizontal axis represents the number of kites and the vertical axis represents the total cost.
According to the given figures, we can acquired a number of kites of 6 kites at a total price of $ 30 in both stores.
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Please help I have a learning disailty and this is due today.PLEASE PLEASE I DONT KNOW THE ANSWER AND SOOOOOOOOOOOO NEED THIS I WILL DO ANYTHING YOU WANT MARK YOU ASK A QUESTION SO YOU GET THE POINTS PLEASE I JUST REALLY NEED HELP.
Start at hexagon A. After you solve the expression find the answer in blue on the edge on the hexagon. The answer will lead you to your next hexagon.
Continue along the maze path until you reach the hexagon with an S in the flower. This is where you will finish.
To answer the questions below, type the letter in each hexagon that you solved along the maze in the order they were answered.
You do not need to include the starting hexagon (of A) or the end hexagon (of S). These are already written in the order below.
Use only capital letters when typing in the hexagon letter
Starting hexagon A
Second hexagon solved ______________________
Third hexagon solved____________________________
Fourth hexagon solved________________________________
A mathematical description of hexagon is given above.
What is a polygon?In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
The segments of a polygonal circuit are called its edges or sides.
Given is hexagon.
In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).
Therefore, a mathematical description of hexagon is given above.
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Martin is walking from Antrim to Randalstown. Randalstown 13 miles Toome 94 miles Antrim 3½ miles (a) Work out the distance from Antrim to Randalstown.
The distance from Antrim to Randalstown is 6 5/6 miles.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Martin is walking from Antrim to Randalstown.
Randalstown 3 1/3 miles, Toome is 9 1/4 miles Antrim 3 1/2 miles.
Therefore, the distance from Antrim to Randalstown is the sum of their distances which is,
= 3 1/3 + 3 1/2 miles.
= 10/3 + 7/2 miles.
= (20 + 21)/6 miles.
= 41/6 miles.
= 6 5/6 miles.
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A playstation 5 sells for $500. today only, it is on sale for 30% off. what is the sale price of the ps5?
The original price of the PlayStation 5 is $500 and there is a 30% discount, calculated as $500 x 30/100 = $150. The sale price is $500 - $150 = $350.
The calculation of the sale price of the PlayStation 5 involves finding the amount of the discount first. The original price of the PlayStation 5 is $500. The discount is 30%, which means that 30% of the original price will be taken off. To find the amount of the discount, we multiply the original price by the discount rate (30% or 0.30).
$500 x 0.30 = $150
Next, we subtract the discount from the original price to get the sale price:
$500 - $150 = $350
So, the sale price of the PlayStation 5 is $350.
The sale price of the PlayStation 5 is an important aspect for customers who are looking for a good deal. By knowing the original price and the discount, one can easily find the sale price. This type of calculation is common in retail and commerce, and is used to determine the savings that a customer can make on a particular item during a sale. Understanding these concepts is crucial for consumers to make informed decisions about their purchases, and for businesses to effectively promote their products and attract customers.
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please help: solve for x
What number is equivalent to
7 x 1,000,000,000 + 5 x 1,000,000 + 9 x
10,000+ 9 x 100 + 7 x 1?
A. 75,997
B. 759,971
C. 7,509,907
D. 7,005,090,907
Answer:
D
Step-by-step explanation:
7 x 1,000,000,000 + 5 x 1,000,000 + 9 x 10,000+ 9 x 100 + 7 x 1
=7,000,000,000
+ 5,000,000
+ 90,000
+ 900
+ 7
answer is D
Question 3(Multiple Choice Worth 5 points)
(Systems of Linear Equations MC)
Which point is a solution to the system of linear equations?
y = -x + 4
x - 3y = 12?
O (0, 3)
O (1, 2)
O (6, -2)
O (4,-4)
Answer:
(6, -2)
Step-by-step explanation:
The only option that satisfies both equations is (6, -2).
Janet is making chocolate chip cookies. One batch of chocolate chip cookies needs of a cup of sugar. Janet wants to make three batches of chocolate chip cookies.
Part A
How many total cups of sugar will Janet need to make three batches of chocolate chip cookies? Show your answer in lowest terms.
Part B:
Janet has 4 cups of sugar. How much sugar will she have left over after making three batches of chocolate chip cookies?
PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.
PART B) One cup of sugar will be left over after making three batches of cookies.
What is the unit price?
A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.
Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.
Part A:
Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.
Now,
1 batch/ 1 cup = 3 batch/ x cups
x= 3
Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.
Part B:
Given that Janet has four cups of sugar.
From part A, we found that she only need three cups of sugar.
Available - Needed = Excess
4-3=1
So, one cup of sugar will be left over after making three batches of cookies.
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Which one of the following simplifications is incorrect ?
94 0 16x4 = 12x4
. در 0
3/ 3.
26 = 22
=
0 2 0 42 = 2017
3
O 264 0 481 = 12
Answer: is A
Step-by-step explanation: if you do the problem youd get 2 root 3x^2
show that the volume V in cubic metres of water in a full container is given by the formul V=2x^2
The volume of a cuboid will be, V = 2x² If it has one side of 2 meters and the other two sides are of equal length.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
We know, The volume of a cuboid is (length×width×height).
Assuming the height of the cuboid to be 2 meters and it has a square base of 'x' meters.
Therefore, The volume of the cuboid V = 2×x×x.
V = 2x².
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a. If Mei has earned 30 points, write and solve a multiplication equation to find how many books she needs to read.
If Mei has earned 30 points, the multiplication equation to find how many books she needs to read is 30=5x.
How to find the number of books she needs to read?Let x represent the number of books she needs to read.
So,
The equation to find the number of books she need to read is:
30=5x
Let solve for x
30 =5x
Divide both side by 5x
x = 30/5
x = 6 books
Therefore the number of books is 6 books.
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Adela paid $71.70 for 6 tickets at the skating rink. Calculate the unit rate per ticket.
$8.37
$11.95
$12.12
$65.70
In linear equation, the unit rate of tickets at the skating rink is; 11.95 per ticket.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
We have been given Adela paid $71.70 for 6 tickets at the skating rink.
We need to find the unit rate per ticket.
Total amount = 71.70
Number of tickets = 6
Unit rate = Total amount/ Number of tickets
Unit rate = 70.70/ 6
Unit rate = 11.95/1
Therefore, the unit rate of tickets at the skating rink is; 11.95 per ticket.
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Answer:B
Step-by-step explanation:
got kinda lost.. anyone know how i could solve??
The perimeter of this triangular park is equal to: 3x² 37x - 4 feet.
How to calculate the perimeter of this triangle?Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:
P = a + b + c
Where:
P represents the perimeter of a triangle.
a, b, and c represents the length of sides of a triangle.
Substituting the given parameters into the perimeter of a triangle formula, we have the following;
Perimeter of triangle, P = 12x + (15x + 4) + (10x + 3x² - 8)
Perimeter of triangle, P = 12x + 15x + 4 + 10x + 3x² - 8
Perimeter of triangle, P = 3x² 37x - 4 feet.
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help pls i don’t understand it
The length of the similar polygon is as follows:
GK = 30 units
TU = 24 Units
How to find similar polygon?Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.
Therefore, the corresponding angles of the polygons are congruent and the sides are in ratio of each other.
Hence, let's find the side GK and TU as follows:
QRSTU ~ IJKGH
Therefore,
24 / GK = 16 /20
cross multiply
16GK = 480
GK = 480 / 16
GK = 30 Units
Hence,
TU / 30 = 16 / 20
cross multiply
20 TU = 480
TU = 480 / 20
TU = 24 Units
Therefore,
GK = 30 units
TU = 24 units
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