Answer:
Total Charge = Initial Charge + Daily Charge x Number of Days
Step-by-step explanation:
Let's assume that x is the number of days that Frank rented the car.
The initial charge for the rental is $40, which is a one-time charge, so it does not depend on the number of days.
The daily charge for x days is $35 per day. Therefore, the total charge for x days can be calculated as:
Total Charge = Initial Charge + Daily Charge x Number of Days
Total Charge = $40 + $35x
We know that Frank was charged $180, so we can set the total charge equal to $180 and solve for x:
$40 + $35x = $180
Subtracting $40 from both sides gives:
$35x = $140
Dividing both sides by $35 gives:
x = 4
Therefore, Frank rented the car for 4 days.
-) A freight train left Berlin and traveled
toward Johannesburg at an average speed
of 45 km/h. Sometime later a passenger
train left traveling in the same direction
but at an average speed of 72 km/h. After
traveling for ten hours the passenger train
caught up with the freight train. Find the
number of hours the freight train traveled
before the passenger train caught up.
4
Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.
let's call the time it took for the passenger train to catch up with the freight train "t" (in hours).
During this time, the freight train traveled at its average speed of 45 km/h for t + 10 hours, while the passenger train traveled at its average speed of 72 km/h for t hours.
We know that the distance both trains traveled is the same, since the passenger train caught up with the freight train. So, we can set up the following equation:
distance traveled by freight train = distance traveled by passenger train
[tex](45 km/h) x (t + 10 h) = (72 km/h) x t[/tex]
Simplifying this equation, we get:
[tex]45t + 450 = 72t[/tex]
[tex]27t = 450[/tex]
t = 16.67 hours
Therefore, the freight train traveled for 16.67 + 10 = 26.67 hours before the passenger train caught up with it.
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A yoghurt brand produces a regular yoghurt
and a low-sugar yoghurt. Adverts for both
yoghurts are shown below.
If the recommended daily allowance of sugar
is 30 g, how much sugar does the low-sugar
yoghurt contain?
Give your answer in grams (g).
Regular yoghurt
Only 7% of your recommended
daily allowance of sugar!
Low-sugar yoghurt
Contains 26% less sugar than
our regular yoghurt!
Reduced
sugar
As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.
what is unitary method ?A proportion is put up using a single unit when using a unitary method. For instance, the price of 1 apple is $2/3 if 3 bananas cost $2. The cost among one unit of something like the quantity "apples" is represented by this value of $2/3. In a similar vein, if a car can drive 300 km on 20 litres of gas, how far can it go on one litre of gas? The answer is 15 km (300/20). Finance, science, and engineering are just a few of the fields where the unitary technique can be applied to solve issues.
given
Regular yoghurt contains: If only 7% of the daily required amount of sugar is present in it:
7% of 30 g = [tex](7/100) * 30 g = 2.1 g[/tex]
This indicates that 2.1 g of sugar are present in ordinary yoghurt.
Hence, if the low-sugar yoghurt has 26% less sugar than the standard yoghurt, it contains:
[tex]1.554 g = 2.1 g - (26/100) x 2.1 g = 2.1 g - 0.546 g[/tex]
As a result, 1.554 g of sugar are included in the low-sugar yoghurt as if the low-sugar yoghurt has 26% less sugar.
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how do i solve this step by step
the probability that the correct combination is written on the paper is 1/1000, or 0.001.
How to solve?
To find the probability that the correct combination is written on the paper, you need to first determine the total number of possible combinations that can be created with the 3 wheels, each numbered from 0 to 9. This can be done using the multiplication principle, which states that if there are m ways to perform one task and n ways to perform another task, then there are m × n ways to perform both tasks.
So, the total number of possible combinations is:
10 × 10 × 10 = 1000
This means that there are 1000 possible combinations for the lock.
Next, you need to determine the number of ways you can choose five different numbers from 0 to 999. This can be done using the combination formula, which is:
nCr = n! / r!(n - r)!
where n is the total number of items to choose from, r is the number of items to choose, and ! represents the factorial function (i.e., the product of all positive integers up to and including that number).
So, the number of ways to choose five different numbers from 0 to 999 is:
nCr = 1000! / 5!(1000 - 5)!
nCr = 1000! / 5!995!
nCr = (1000 × 999 × 998 × 997 × 996) / (5 × 4 × 3 × 2 × 1)
nCr = 831,600,000
This means that there are 831,600,000 ways to choose five different numbers from 0 to 999.
Finally, to find the probability that the correct combination is written on the paper, you need to divide the number of ways to choose the correct combination (which is 1) by the total number of possible combinations:
P(correct combination) = 1 / 1000
So, the probability that the correct combination is written on the paper is 1/1000, or 0.001.
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Expand (x-y)3 using Pascal triangle
Answer:
To expand (x-y)³ using Pascal’s triangle, we can write:
1
1 1
1 2 1
1 3 3 1
Each row of the triangle represents the coefficients of the binomial expansion of (a+b)ⁿ, with the top row being n=0.
So for (x-y)³, we take the fourth row of the triangle (starting with n=0), and substitute x and y into the formula, alternating the signs of y:
1x³ + 3x²(-y) + 3x(-y)² + 1(-y)³
= x³ - 3x²y + 3xy² - y³
Thus, (x-y)³ = x³ - 3x²y + 3xy² - y³.
The area of the triangle below is 2/15 square feet. What is the length of the base? Express your answer as a fraction in simplest form.
The base of the triangle is 3/2 feet or 1 1/2 feet
What is area of triangle?Triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
The area of triangle is expressed as ;
A = 1/2 bh
The area of the of the triangle is 2/15 and the height is 2/5.
2/15 = 1/2 b × 2/5
2/15 = 2b/10
20 = 30b
divide both sides by 30
b = 30/20
b = 3/2
there the base of the triangle is 3/2.
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Matthew catches a fish that weighs 7.25 pounds. His dad catches a fish that weighs 1.3 pounds less than Matthew’s fish. 1. Matthew’s sister says, “That means dad’s fish weighs 7.12 pounds.”
According to the calculation below, Matthew's dad's fish would weigh 5.95 pounds, not 7.12 pounds. Therefore, Matthew's sister is incorrect in her statement.
What is pounds?Both the imperial and US customary systems of measurement utilise the unit of measurement known as pounds (lb) to indicate weight or mass.
The US customary system defines a pound as precisely 0.45359237 kilogrammes, but the imperial system defines a pound as 16 ounces.
The weight of goods in daily life, such as groceries or home items, as well as the weight of the human body are frequently expressed in pounds.
The letter "lb" stands for pounds.
To check if Matthew's sister is correct, we can subtract 1.3 pounds from Matthew's fish weight of 7.25 pounds:
7.25 pounds - 1.3 pounds = 5.95 pounds
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For which of the following operations must two rational functions first have a common denominator? Select all that apply.
addition
division
multiplication
subtraction
Answer:
addition and subtraction
Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.
Answer
Select all that apply.
4:1
6:1
19:1
18:1
Answer:
Step-by-step explanation:
4:1 and 6:1
2a^2 - 4b - 4a (b - a) = ?
a=4 b=7
7+ 3(v - 2u)
u+1
=
10
[?
u=2 v=5
Answer:
10/3
Step-by-step explanation:
u = 2
v = 5
7 + 3(v - 2u)
= 7 + 3(5 - 2*2)
= 7 + 3(5 - 4)
= 7 + 3(1)
= 7 + 3
= 10
u + 1
= 2 + 1
= 3
7 + 3(v - 2u)/u + 1
= 10/3
11.find the values of c that satisty the Mean Value Theorem. Show steps
Note that the value of C that satisfies the mean value theorem is -11/6
What is the mean value theorem?
The mean value theorem in mathematics says that for each given planar arc between two end points, there exists at least 1 point where the tangent to the arc is parallel to the secant between its ends. It is one of the most significant findings in real - world analysis.
To apply the mean value theorem, we need to check 2 conditions
f(x) is continuous on [-3, -1]
f(x) is differentiable on (-3, -1)
f(x) = (x^2-1/3x) satisfies both conditions.
Now, let's find the value of c that satisfies the mean value theorem:
f(-1) - f(-3) = f'(c)(-1 - (-3))
(2/3) - (-26/3) = f'(c)(2)
f'(c) = -4
To find the value of c, we need to solve for c in f'(c) = -4 ...
f '(x) = d/d x(x² -1/3x)
= 2x - 1/3
2c - 1/3 = -4
2c = -4 + 1/3
c = -11/6
So we can state that the value of c that satisfies the mean value theorem is -11/6
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What is the measure of t? *
So
10
to
25°
The calculated measure of t from the given equation is 15 degrees
Calculating the measure of t?From the question, we have the following parameters that can be used in our computation:
10
to
25°
When expressed properly, we have
10° + t° = 25°
Evaluate the like terms
So, we have
t° = 15°
Hence, the value of t° is 25°
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Polygon ABCD with vertices at A(-4,6), B(-2,2), C(4,-2) and D (4,4) is dilated using a scale factor of 3/5 to create polygon A’B’C’D’. Determine the vertices of A’B’C’D’
.
A’(-12,18), B’(-6,6), C’(12,-6), D’(12,12)
Michael has a jar containing 15 dimes and 20 quarters. He randomly draws 3 coins from the jar one after the other without replacement. What is the probability that the second coin he draws is different from the first and third coins? Express your answer as a fraction reduced to lowest terms.
Let X be a random variable with the following probability distribution:
Find the standard deviation.
The standard deviation of the random variable X is 2.73861279.
What is standard deviations?Standard deviations is a measure of the spread of a data set around the mean. It is calculated by taking the square root of the variance of the data set and is used to measure the variability of a data set from the mean. Standard deviations are used to measure the probability of a certain outcome occurring and can be used to compare different data sets to see how much variability there is in the data.
Standard deviation is a measure of dispersion of data points around the mean of the data set. It is a measure of the variability of the data set. It is calculated by taking the square root of the variance of the data set.
Variance is the average of the squared differences of each data point from the mean. It is calculated by taking the sum of the squares of the differences of each data point from the mean and dividing by the number of data points minus one.
In this case, the mean of the data set is 3, because the probabilities of -2 and 5 are equal.
The variance of the data set is calculated as follows:
Variance = (0.3*(3-(-2))2 + 0.2*(3-3)2 + 0.5*(3-5)2) / (3-1)
Variance = (0.3*25 + 0 + 0.5*4) / 2
Variance = 7.5
The standard deviation of the data set is calculated by taking the square root of the variance, which is equal to 2.73861279.
Therefore, the standard deviation of the random variable X is 2.73861279.
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17.Point X is shown on the number
Which number sentence best describes the value represented by point X?
A X 0.36
B X < 0.37nds
C X= 0.36
D X = 0.37
Answer:
Without a visual or additional information, it is difficult to determine the exact value represented by point X. However, we can make some observations based on the answer choices:
A. X < 0.36 would indicate that point X is to the left of 0.36 on the number line, which is not consistent with the position of X in the diagram.
B. X < 0.37 would indicate that point X is to the left of 0.37 on the number line, which is not consistent with the position of X in the diagram.
C. X = 0.36 would indicate that point X is exactly at 0.36 on the number line, which is a possibility based on the diagram.
D. X = 0.37 would indicate that point X is exactly at 0.37 on the number line, which is not consistent with the position of X in the diagram.
Therefore, the best answer choice that describes the value represented by point X is C) X = 0.36.
Theodore and Sarah have a small business selling custom-made T-shirts. They currently sell 175 shirts per month and charge $15 per T-shirt. Sarah thinks they can
increase their revenue by increasing their selling price, but Theodore knows from experience that each $1 increase in price will decrease the number of T-shirts they sell
by 8 shirts per month. Find an expression for the total monthly revenue Theodore and Sarah's business can generate if they change the selling price of their T-shirts. Let
x represent the number of $1 increases in the price of the T-shirts.
Answer
R(x) =
Keypad
Keyboard Shortcut
K
Look at the parallelogram below.
Work out the size of angle KGH.
Give your answer in degrees (º).
48°
G
H
Not drawn accurately
Answer:
The measure of angle KGH is 180° - 48°, or 132°.
Therefore, the size of angle KGH is 48º.
What degree of an angle is it?
An angle is a portion of a circle, where a circle has 360° in total. A right angle is a quarter of a circle and is 90°, but a straight angle is equal to the circumference of the circle and is 180°. Using a protractor, you can gauge the size of an angle.
Given that GH and EF are parallel, we can infer from the fact that FHE and HFE are at opposing angles that angle HFE must also be 48o.
Since the opposite angles in a parallelogram are equal, we know that angle KGH is also equal to angle HFE, which is 48º.
Therefore, the size of angle KGH is 48º.
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the rabbit population of springfield ohio was 144000 in 2016. It is expected to decrease by about 7.2% per year. Write the exponential decay function of the rabbit population P(t)
Answer:
The exponential decay function of the rabbit population P(t) can be expressed as:
P(t) = 144,000 * e^(-0.072t)
Step-by-step explanation:
Where t is the time in years.
This function represents the expected decrease in the rabbit population of Springfield, Ohio, assuming a constant rate of decline of about 7.2% per year. The initial population of rabbits in 2016 was 144,000, and this number is multiplied by the exponential factor e^(-0.072t), which represents the proportion of rabbits that will remain after t years.
As time passes, the value of P(t) will decrease exponentially, reflecting the declining rabbit population. For example, after one year (t=1), the rabbit population is expected to be:
P(1) = 144,000 * e^(-0.072*1) = 133,632
This means that the rabbit population is expected to decrease by about 10,368 rabbits in the first year.
The exponential decay function is commonly used in many fields to model phenomena that exhibit exponential decay over time, such as radioactive decay, bacterial growth, and population dynamics.
T divided by 15 equals 3
Answer:
T = 45
Step-by-step explanation:
T ÷ 15 = 3
Time 15 on both sides
T = 45
i need some help, any one knows the answer
Answer:
49216144161000I hope it helped you
Please Mark me brainliest
Answer:
see explanation
Step-by-step explanation:
a
7² = 7 × 7 = 49
b
6³ = 6 × 6 × 6 = 36 × 6 = 216
c
12² = 12 × 12 = 144
d
[tex]2^{4}[/tex] = 2 × 2 × 2 × 2 = 4 × 4 = 16
e
10³ = 10 × 10 × 10 = 100 × 10 = 1000
Select the correct answer.
A straight line is divided into four equal parts. The starting point A is shown with values (1, 5). The end point B is represented with a question mark. Point C with values (1.75, 2.5) is represented at first part from A..
What are the coordinates of point B in the diagram?
The answer is: The coordinates of point B are (4.3, 2.5)
Define the scatterplot?A scatterplot is a type of graph that shows how two variables relate to each other. The values of the two variables are each represented by a point in the set of points that make up the graph.
Let's first find the distance between points A (1, 5) and C (1.75, 2.5).
We can use the distance formula:
[tex]d = \sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]
where x₁ = 1, y₁ = 5, x₂ = 1.75, and y₂ = 2.5
[tex]d = \sqrt{ (1.75 - 1)^2 + (2.5 - 5)^2 }[/tex] = [tex]\sqrt{[0.5625 + 6.25]}[/tex] = √6.8125 = 2.61
Now, since the line is divided into four equal parts, the distance between points C and B is also √6.8125.
Let's assume the x-coordinate of point B is "b". The y-coordinate of point B will be the same as the y-coordinate of point C which is 2.5 (since they are on the same horizontal line).
Use the distance formula for the x-coordinate of point B (b, 2.5):
d = √6.8125 = [tex]\sqrt{ [(b - 1.75)^2 + (2.5 - 2.5)^2] }[/tex]
√6.8125 = [tex]\sqrt{ (b - 1.75)^2 }[/tex]
6.8125 = (b - 1.75)²
6.8125 = b² - 3.5b + 3.0625
Simplifying:
b² - 3.5b - 3.75 = 0
Using the quadratic formula:
b = (3.5 ± √(3.5² + 4(3.75)))/2
b = (3.5 ± √(27.25))/2
b = (3.5 ± 5.22)/2
So, b = 4.36 or b = -0.86. Since the line segment goes from left to right, the x-coordinate of point B must be greater than the x-coordinate of point A (which is 1). Therefore, the answer is:
The coordinates of point B are (4.3, 2.5).
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Please solve this for me
Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1. Therefore, the displacement of P from the origin when t = 2 is -8/3 meters.
What is function?A function is a mathematical concept that describes a relationship between two sets of values, called the domain and the range. It is a rule or a set of rules that assigns a unique output value for every input value in the domain. In other words, it is a process that takes one or more inputs and produces a corresponding output. Functions are commonly represented using equations, graphs, or tables. They are used in various branches of mathematics, science, engineering, and technology to model real-world phenomena, make predictions, and solve problems.
Here,
(a) To find the acceleration, we need to take the derivative of the velocity function with respect to time:
a = dv/dt
= d/dt (t³ - 4t² + 5t + 1)
= 3t² - 8t + 5
(b) To find the values of t for which the magnitude of the acceleration is instantaneously zero, we need to solve the equation:
|a| = |3t² - 8t + 5|
= 0
This occurs when 3t² - 8t + 5 = 0, which factors as (3t - 5)(t - 1) = 0. Therefore, the magnitude of the acceleration is instantaneously zero at t = 5/3 and t = 1.
(c) To find the displacement of P from the origin when t = 2, we need to integrate the velocity function from t = 0 to t = 2:
s = ∫(v dt)
= ∫(t³ - 4t² + 5t + 1 dt)
= (1/4)t⁴ - (4/3)t³ + (5/2)t² + t + C
We know that s(0) = 3, so we can solve for C:
3 = (1/4)(0)⁴ - (4/3)(0)³ + (5/2)(0)² + 0 + C
C = 3
Therefore, the displacement of P from the origin when t = 2 is:
s(2) = (1/4)(2)⁴ - (4/3)(2)³ + (5/2)(2)² + 2 + 3
= -8/3 meters
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A ramp is being made in the shape of a right triangular prism with dimensions shown below. It is to be made from concete that weighs 150 pounds per cubic foot.
1.5 ft, 15 ft, and 6ft is the demensions
In the given problem, the ramp weighs 10,125 pounds.
How to Solve the Problem?To calculate the weight of the ramp, first, determine its volume and then multiply it by the weight of concrete per cubic foot.
The ramp is shaped like a right triangle prism, with a triangular base and three rectangular faces. The ramp's measurements are as follows:1.5 feet in height15 feet is the length of the base (b).6 feet in length (l).
The area of the triangular base can be determined using the triangle area formula: A = 0.5 * b * h A = 0.5 * 15 * 1.5A = 11.25 ft^2
The volume of the ramp can be estimated by multiplying the base area by the ramp length: V = A * l V = 11.25 feet 2 feet 6 feet
V = 67.5 ft^3
Finally, the weight of the ramp can be calculated by multiplying the volume by the weight of concrete per cubic foot:W = V * 150 lbs/ft3 W = 67.5 feet * 150 lbs/ft3 W = 10,125 pounds
As a result, the ramp weighs 10,125 pounds.
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What is the measure of angle B?
Answer:
36°
Step-by-step explanation:
angle a= 180-117
angle a=63°. because angles on straight line add to 180°
angle b= 180-81-63
angle b=36°. because angles in triangle add to 180°
Claim: than 4.5% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 14,031 homes 5.78% had landline phones without wireless phones.
When the original claim is expressed in symbolic form, we have p < 0.045.
How to express in symbolic form ?To symbolize the initial claim adequately, we must assign a value to parameter p.
Let us designate p as the ratio of households possessing solely landline telephones without wireless communication devices.
The original statement denotes that indisputably below 4.5% of households are equipped with exclusively traditional telephone dialers, and absent from contemporary wireless communication alternatives; this assertion can be formulated symbolically as:
p < 0.045
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The question is:
Express the original claim in symbolic form. Let the parameter represent a value with respect to homes that have only a landline telephone and no wireless phone.
Please help! (the question on the picture)
Answer:
-23
Step-by-step explanation:
15(-3)/9 + 4(-3)-6
-45/9 + (-12)-6
-5 + (-18)
-23
(missed the -6 sorry)
Answer:
-23
Step-by-step explanation:
15(-3)/9 +4(-3) -6 = -5 -12 -6 = -23
You are deciding between two different levels of auto insurance. Please make your choice based off of the value of your vehicle and financial situation. While justifying the plan you have choosen be sure to demonstrate your knowledge on the vocabulary terms like bodily injury liability, property damage liability, collision insurance, comprehenisve insurance, uninsured/underinsured motorist coverage, annual premium, coverage and deductible.
Plan 1:
Bodily injury: $25/50,000 (Annual Premium $20.58)
Property Damage: $25,000 (Annual Premium $135.80)
Collision: $100 deductible (Annual Premium $466.53)
Comprehensive: $50 deductible (Annual Premium $126.62)
Plan 2:
Bodily injury: $50/100,000 (Annual Premium $30.88)
Property Damage: $50,000 (Annual Premium $161.67)
Collision: $500 deductible (Annual Premium $202.59)
Comprehensive: $100 deductible (Annual Premium $91.32)
The choice of auto insurance plan depends on the value of the vehicle and financial situation. Plan 2 with higher coverage and deductibles is better for expensive vehicles and those with higher financial stability.
What is insurance?Insurance is a contract between an individual or an entity and an insurance company. The individual or entity pays a premium, and in return, the insurance company agrees to pay for losses or damages that occur, as per the terms of the policy.
What is financial stability?Financial stability refers to a situation where an individual, household, company, or economy can manage their financial resources and obligations in a sustainable manner, without facing significant risks or uncertainty.
According to the given information:
Based on my vehicle's value and my financial situation, I have decided to choose Plan 1.
Bodily injury liability coverage provides protection if I were to injure someone while driving, and the amount of coverage in Plan 1 ($25,000 per person up to $50,000 per accident) is adequate for my needs. Property damage liability coverage provides protection for any damage I might cause to someone else's property while driving, and the $25,000 coverage in Plan 1 is also sufficient.
Collision insurance provides coverage for any damage to my own vehicle in the event of an accident, regardless of who is at fault. The $100 deductible in Plan 1 means that I would have to pay the first $100 of any repair costs, but the lower annual premium makes this plan more affordable for me.
Comprehensive insurance provides coverage for non-collision events, such as theft, fire, and natural disasters. Again, the lower annual premium of Plan 1 with a $50 deductible makes it more cost-effective for me.
Uninsured/underinsured motorist coverage is not included in either plan, so I would need to decide if I want to add this coverage as an additional policy or not.
Overall, based on the value of my vehicle and my financial situation, Plan 1 provides adequate coverage at a more affordable price. However, it is important to note that everyone's situation is unique and insurance needs may vary. It is always a good idea to shop around and compare different policies before making a final decision.
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Will using name-brand microwave popcorn result in a greater
percentage of popped kernels than store- brand microwave popcorn?
To find out, Briana and Maggie randomly selected 10 bags of name-
brand microwave popcorn and 10 bags of store-brand microwave
popcorn. The chosen bags were arranged in random order. Then each
bag was popped for 3.5 minutes, and the percentage of popped kernels
was calculated. The data are displayed in the table.
Name brand 95 88
95 88 84 94 81 90 97
93 91 86
Store brand 91 89 82 82 77 78 84 86 86 90
1. Make parallel boxplots of the data. Write a few sentences
comparing the distributions of the percent of popped kernels in the
two samples.
2. Do the data provide convincing evidence at the 0.05 significance
level that using name-brand microwave popcorn will result in a
greater mean percentage of popped kernels?
Since the calculated t-value (2.26) is greater than the critical t-value (1.734), we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim that using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn at the 0.05 level of significance.
What is test statistic?In statistics, a test statistic is a numerical summary of a sample that is used to assess the evidence provided by data in favor of some conjecture about the population from which the sample was drawn. A test statistic compares the observed data to what is expected under the null hypothesis, and measures how many standard errors the observed data deviates from the expected value. Test statistics are used in hypothesis testing to determine the likelihood that an observed effect or difference between groups is due to chance, or whether it is statistically significant.
Here,
To determine if using name-brand microwave popcorn results in a greater percentage of popped kernels than store-brand microwave popcorn, we can compare the mean percentage of popped kernels between the two groups using a hypothesis test.
Let μ1 be the mean percentage of popped kernels for name-brand microwave popcorn and μ2 be the mean percentage of popped kernels for store-brand microwave popcorn.
The null hypothesis is that there is no difference in the mean percentage of popped kernels between name-brand and store-brand microwave popcorn:
H0: μ1 - μ2 = 0
The alternative hypothesis is that the mean percentage of popped kernels for name-brand microwave popcorn is greater than the mean percentage of popped kernels for store-brand microwave popcorn:
Ha: μ1 - μ2 > 0
We can use a two-sample t-test with unequal variances to test this hypothesis. Assuming a significance level of 0.05, the critical t-value for a one-tailed test with 18 degrees of freedom is 1.734.
Using the given data, we find that the sample mean percentage of popped kernels for name-brand microwave popcorn is 90.9% with a sample standard deviation of 5.09%, and the sample mean percentage of popped kernels for store-brand microwave popcorn is 85.9% with a sample standard deviation of 4.67%.
We can calculate the test statistic as follows:
t = (x1 - x2 - 0) / √(s1²/n1 + s2²/n2)
t = (90.9 - 85.9) / √((5.09²/10) + (4.67²/10))
t = 2.26
Therefore, based on this study, using name-brand microwave popcorn is likely to result in a greater percentage of popped kernels than store-brand microwave popcorn.
To know more about test statistic,
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1.
Find the area of the kite.
253.92 m²
380.88 m²
126.96 m²
190.44 m²
6.9 m
9.2 m
9.2 m
13.8 m
Step-by-step explanation:
Area of a kite = D1 × D2/2
D1 = 6.9 + 13.8 = 20.7m
D2 = 9.2 + 9.2 = 18.4m
Area =. 20.7 × 18.4
------------------
2
= 190.44m²
