Answer:
the answer is d
Step-by-step explanation:
before the increase the range is three with the lowest number being four and the highest 7
where as after the increase the lowest value is 5 and the highest nine giving us a range of four
four minis three is one therefore the range increases by one mile
Answer: D: The range will increase by 1 mile.
Step-by-step explanation:
The current range is solved by doing the highest number minus the lowest number, so 7-4. The current range would therefore be 3.
The miles on Monday and Tuesday have been increased by 1 mile, from 4 miles to 5 miles.
The miles on Friday, Saturday and Sunday have been increased by 2 miles, from 7 miles to 9 miles.
You subtract the new values: 9 miles - 5 miles = 4 miles
And subtract your new values from your old range: 4 miles - 3 miles = 1 mile
The range would therefore increase by 1 mile.
An airplane cruises at an altitude of 35,000 feet. It begins its descent at a rate of 1,200 feet per minute. Find a linear model
in the form h(t) = mt+b where h represents the altitude of the plane, in feet, after t minutes into its descent.
It costs $3.50 for 25 fl. oz. of detergent. Which graph models a relationship with the same unit rate? 10 POINTS
The 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
What are arithmetic operations?Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.
The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.
To determine which is a better buy, we need to compare the cost per fl. oz. of detergent for both options.
For the first option, the cost is $3.99 for 25 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $3.99 / 25 fl. oz. ≈ $0.16/fl. oz.
For the second option, the cost is $6.99 for 90 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $6.99 / 90 fl. oz. ≈ $0.08/fl. oz.
Since the cost per fl. oz. is lower for the second option, it is a better buy. Therefore, the 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
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The complete question is:
It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
Here are three similar cuboids, A, B and C.
A has length 6 cm, width 2 cm
and height 5 cm
B has length 12 cm
C has length x cm
b) Volume of A x 343/8 = Volume of C
Work out the value of x in cm.
Your final line must be, x = ...cm
The required value of x is approximately [tex]x = 257.25[/tex] cm.
How to find the volume of cuboid?The volume of cuboid A can be found by multiplying its length, width, and height:
[tex]$V_A = 6\text{ cm} \times 2\text{ cm} \times 5\text{ cm} = 60\text{ cm}^3$[/tex]
To find the volume of cuboid C, we can use the given information that the volume of A multiplied by 343/8 is equal to the volume of C:
[tex]$V_C = V_A \times \frac{343}{8} = 60\text{ cm}^3 \times \frac{343}{8} =2572.5[/tex]
Now, we can use the formula for the volume of a cuboid to find the length of C:
[tex]$V_C = \text{length} \times \text{width} \times \text{height}$[/tex]
[tex]$2572.5}\text{ cm}^3 = x\text{ cm} \times 2\text{ cm} \times 5\text{ cm}$[/tex]
[tex]{2572.5}\text{ cm}^3 = 10x\text{ cm}^3$[/tex]
[tex]x = 257.25[/tex]
Therefore, the value of x is approximately [tex]x = 257.25[/tex] cm.
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Discount questions…..
Mr Leonard will receive a discount of £45.84 on his oil purchase.
How is discount calculated?We must first determine the entire amount of oil Mr. Leonard intends to buy in order to determine the discount he will receive.
There are currently 450 liters in the tank, which has a capacity of 1200 liters. Therefore, Mr. Leonard needs to buy an extra 750 liters (1200 - 450 = 750).
The total cost of the oil before the discount must then be determined.
With a litre costing 81.5p, the price for 750 liters of oil would be:
750 liters x 81.5 pence per liter = £611.25.
We must multiply the entire cost of the oil by the discount rate (7.5 percent, or 0.075), in order to determine the discount:
£611.25 x 0.075 = £45.84
Therefore, Mr Leonard will receive a discount of £45.84 on his oil purchase.
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The total amount of oil that can be added to the tank is 1200 liters, and there are already 450 liters in the tank. Therefore, the tank can hold an additional 750 liters of oil.
Mr. Leonard will get a discount of [tex]£45.84[/tex] on this purchase.
The price of oil is 81.5p per litre. So, the cost of 750 liters of oil would be:
[tex]750 * 81.5p = £ 611.25[/tex]
As Mr. Leonard is a loyal customer and gets a discount of 7.5% on the price of oil, he will get a discount of:
[tex]7.5% of £611.25 = £45.84[/tex]
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A sample of size n=77 is drawn from a population whose standard deviation is σ=50.
Find the margin of error for a 90% confidence interval for μ.
If we take multiple samples of the same size and calculate their means, 90% of the resulting sample which is 69.3 means will fall within 9.02 units of the true population mean for standard deviation.
The following formula must be used to determine the margin of error for a 90% confidence interval for the population mean ():
Margin of error = [tex]z * (/n)[/tex].
where is the population standard deviation, n is the sample size, and z is the critical value from the standard normal distribution with a 90% confidence level.
The matching z-value is 1.645 because a 90% confidence interval is what we are looking for. Thus, the margin of error can be determined as follows:
Margin of error: (50 / 77) / 1.645 = 9.02
This indicates that 90% of the sample means obtained when calculating the means of several samples of equal size will be within 9.02 units of the actual population mean.
It is significant to remember that the margin of error lowers with sample size and rises with confidence level. A bigger sample size in this situation would lead to a smaller margin of error, whereas a greater confidence level would lead to a larger margin of error.
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While riding "The Screamer" (an unreliable ferris wheel with a radius of 100 feet) you start getting nervous about how
high in the air you are...you estimate you're about 95 feet high in the air... how much could The Screamer have rotated
(round to the nearest whole degree). There are 2 answers
The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.
What is circumference?Circumference is the distance around the edge of a closed curve or a circle. It is the length of the boundary of a circular object or shape. In other words, it is the total length of the circular shape.
According to question:We can use trigonometry to determine the rotation's angle. The rider's height above the ground is equal to the ferris wheel's radius plus the distance travelled around its circle. Let's call the angle of rotation we're trying to find θ.
The distance traveled along the circumference of the wheel can be calculated as follows:
distance = θ/360 * 2πr
where r is the radius of the wheel. Substituting the given values, we get:
95 = 100 + θ/360 * 2π(100)
Simplifying the equation:
θ/360 = (95-100)/(2π(100))
θ/360 = -0.007957747
θ = -2.8661 degrees or 357.1339 degrees
So there are two possible answers: The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.
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A friend is curious what the probability of it snowing today is. What would the complement of this event be? explain how you would calculate the complement of an event. 
Answer:
Step-by-step explanation:
compliment of an event A is probability of not happening A
Hope the picture helps :)
A graph of a function f(x) undergoes a sequence of transformations to form a new function f(x)= -2f(x+6)-8, which transformation are part of the sequence?
Chose all that apply
A.) f(x) reflected over x-axis
B.) f(x) reflected over y-axis
C.) f(x) stretched vertically
D.) f(x) stretched horizontally
E.) f(x) shifted right 6 units
F.) f(x) shifted down 8 units
Find the values of m and b
The values of m and be for the line given, can be found to be:
m - 3 / 5b - 5How to find the values of m and b on a line ?First, we need to pick two points from the line which would be ( 0, 5 ) and ( -5, 2 ).
To find the values of m (slope) and b (y-intercept) for a line with the given coordinates (0, 5) and (-5, 2), we can use the slope formula and the point-slope form of a linear equation.
Calculate the slope (m) using the slope formula:
m = (y2 - y1) / (x2 - x1)
m = (2 - 5) / (-5 - 0)
m = (-3) / (-5)
m = 3/5
Find the y-intercept (b) using the point-slope form. The y - intercept is the point where the line crosses the y axis. This means that the value of x at this point would be 0.
The y - intercept can therefore be seen from the point ( 0, 5 ) which means that 5 is the y - intercept or b.
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Question 20 options: The time a student sleeps per night has a distribution with mean 6.1 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night. Answer: (round to 4 decimal places)
The probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.
Describe Probability?Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. It is used to quantify uncertainty and make predictions based on incomplete information. In general, probability is defined as a number between 0 and 1, where 0 represents an event that is impossible, and 1 represents an event that is certain to occur.
The basic concept of probability is based on the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 or 0.5, since there is one favorable outcome (heads) out of two possible outcomes (heads or tails).
We can use the central limit theorem to approximate the distribution of the sample mean, assuming that the sample size is large enough. Since the sample size is n=36, we can assume that the sample mean has a normal distribution with mean μ=6.1 and standard deviation σ/√n=0.6/√36=0.1.
Let X be the sample mean sleeping time per night. Then we need to find the probability P(X > 6), which can be transformed into a standard normal distribution using the formula:
Z = (X - μ) / (σ/√n)
where Z is the standard normal variable.
Substituting the given values, we get:
Z = (6 - 6.1) / (0.1) = -1
Now we need to find the probability that Z is greater than -1. Using a standard normal distribution table or calculator, we can find that the probability is approximately 0.8413.
Therefore, the probability that the average sleeping time for a randomly selected sample of 36 students is more than 6 hours per night is 0.8413.
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You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
1) The cost of both bands would be equal for 100 students. 2) the fixed cost for the caterer is $150 and the rate per student served is $3. 3) Ticket Price = $4.75 4) you can afford a maximum of 3 bouquets of roses.
Let x be the total number of students in Part 1A.
Band A costs $500.
Band B costs $350 plus $1.50 times.
Part B: By graphing the equations, we can determine the location where the price of the two bands is equal.
$500 = $350 + $1.50x \s$150 = $1.50x \sx = 100
As a result, the price for both bands for 100 students would be the same.
Part 2: Let's solve for the fixed cost and rate per student served using the information provided:
50f + 50r = $450
150f + 150r = $1050
When we deduct the first equation from the second, we obtain:
100f + 100r = $600
F plus R equals $6 when we divide by 100.
The result of replacing the value of f in the first equation is:
50($6 - r) + 50r = $450
$300 - 50r + 50r = $450 \sr = $3
As a result, the caterer's fixed fee is $150, and the cost each student served is $3.
Part 3: For 100 pupils, Band A would cost $500, and Band B would cost $350 plus $1.50 (100) for a total of $500.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(100)).
Final price: $950
Total Cost / Number of Students x Ticket Price equals $9.50
Band A would cost $500 for 200 pupils, and Band B would cost $350 + $1.50 (200) = $650.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(200)).
Final price: $950
Total Cost / Number of Students x Ticket Price is $4.75
Let d be the total number of daisy bouquets and r be the total number of rose bouquets in part 4A.
[tex]25d + 35r \leq $500[/tex]
B. You would have spent $375 if you purchased 15 bouquets of daisies at a cost of 15 ($25).
When we deduct this from the overall budget, we get:
$500 - $375 = $125
The result of dividing by the price of one bunch of roses is: $125/$35 3.57.
Thus, you can buy no more than three rose bouquets.
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what is the missing polynomial?
The missing polynomial is 40 - 4x - 12x²
How to find the missing polynomialThe missing polynomial is solved by comparing the polynomials as done below
? - (20 - 4x - 5x²) = 20 - 7x²
? = 20 - 7x² + (20 - 4x - 5x²)
comparing the terms
constant terms: 20 + 20 = 40
x terms : -4x
x² terms : -7x² - 5x² = -12x²
This can be combined as 40 - 4x - 12x²
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Dana had an equal number of red beads and yellow beads. After using 500 red beads to make necklaces, she had 3 times as many yellow beads as red beads. How many yellow beads does she have?
Answer:2000
Step-by-step explanation:
Dana has 1500 yellow beads when Dana had an equal number of red beads and yellow beads.
Dana had an equal number of red beads and yellow beads, so let's say she had x red beads and x yellow beads.
After using 500 red beads to make necklaces, she was left with x - 500 red beads.
Since she now had 3 times as many yellow beads as red beads, she had a total of 3 * (x - 500) = 3x - 1500 yellow beads.
We know that the total number of yellow beads is x, so we can set the two expressions equal to each other:
x = 3x - 1500
Solving for x, we get:
2x = 1500
x = 750
Therefore, Dana had x = 750 yellow beads.
Since she now has 3 times as many yellow beads as red beads, she has a total of 3 * 750 = 1500 yellow beads.
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12a+14=302
♀️♀️♀️♀️♀️♀️
Answer
a=24
Step-by-step explanation:
12 times 24 equals 288 plus 14 equals 302
False False Exercise 4 The steps to draw a pentagonal prism are listed below. Identify the missing step. response - correct Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1: Draw identical pentagonal bases. Step 2: 1 Step 3: Change any hidden lines to dashed lines.
You could shade in the faces of the prism or add labels to identify different parts of the drawing.
What is Pentagonal ?
"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.
To draw a pentagonal prism, you'll need to follow these steps:
Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.
Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.
Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.
Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.
Therefore, You could shade in the faces of the prism or add labels to identify different parts of the drawing.
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What scale factor was used to produce figure 1 from figure 2?
two triangles labeled figure 1 and figure 2, where figure 1 has legs that are 3 units long and figure 2 has legs that are 6 units long
one half
2
one sixth
6
Answer:
Since the legs of figure 2 are twice as long as those of figure 1, the scale factor to produce figure 1 from figure 2 would be 1/2. This means that every length in figure 1 is half the length of the corresponding length in figure 2.
Answer:
Option A. 1/2
Step-by-step explanation:
100 on the test!
simplify 22 - (-24) + (-32)
Simplify
22 - (-24)
Swap since they are both negatives.
22-(-24) =
22+(24)
22+24
= 46
Which now add in the negative 32 to the problem
46 + (-32)
Recreate the problem to make it more simple:
46 - 32
= 14
In the slope-intercept form y = m x + b, what does the m and the b stand for? a. m = slope, b = y-intercept c. m = variable, b = slope b. m = y-intercept, b = slope d. m = slope, b = variable Please select the best answer from the choices provided
Answer: Choice A
Step-by-step explanation:
M= slope
B= y-intercept
PLEASE IM FAILING AND IM GONNA GET HELD BACK PLEASEPLEASE...Which two ordered pairs represent a proportional relationship? A. (3, 2) and (6, 6) B. (4, 2) and (6, 4) C. (5, 3) and (6, 4) D. (3, 2) and (6, 4)
Answer:
D
Step-by-step explanation:
If you flip the X and Y axis you get the same answer
Write a quadratic function in standard form that models the table. X -5 -3 -1 13 y 0 12 12 16 12 0
Answer:
First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b
Order the following from least to greatest: -1,0.25, 0.15,-0.10.
-1, -0.10, 0.15, 0.25
So, the answer is the way we do it
-1 , -0.1(or 0.10) , 0.15 , and 0.25
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The weight of 1000 children's an average of 50 kilograms and the standard deviation is 5 kilograms how many children weigh between 40 kilograms and 55 kilograms
There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
What is Standard deviation ?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.
To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.
We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.
We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:
z = (x - μ) ÷ σ
where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.
For x = 40 kilograms:
z = (40 - 50) ÷ 5 = -2
For x = 55 kilograms:
z = (55 - 50) ÷ 5 = 1
Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.
Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.
Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:
0.8186 * 1000 = 818.6 children
Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.
Therefore, there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
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The distribution of weights of pumpkins from a harvest is approximately normal with a mean of 8.3 pounds and a standard deviation of 1.68 pounds. Find the value of the interquartile range (IQR) for the mean of 15 pumpkins. Express the answer as a decimal value rounded to the nearest thousandth.
The value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.
What is mean?
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To find the IQR for the mean of 15 pumpkins, we need to first find the standard error of the mean, which can be calculated using the formula:
SEM = σ / sqrt
where SEM is the standard error of the mean, σ is the standard deviation, and n is the sample size.
Substituting the given values, we get:
SEM = 1.68 / sqrt(15) = 0.433
The interquartile range (IQR) for the mean can be calculated as:
IQR = 1.35 * SEM
where 1.35 is the multiplier for the IQR based on the normal distribution.
Substituting the value of SEM, we get:
IQR = 1.35 * 0.433 = 0.585
Rounding to the nearest thousandth, we get the final answer as:
IQR ≈ 0.585
Therefore, the value of the interquartile range (IQR) for the mean of 15 pumpkins is approximately 0.585 pounds.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear function.
Explain about the linear or non linear function:A linear function is one whose graph on a Cartesian plane is a straight line. The line is always straight even though it can travel in any direction.
The form of a non-linear function is not a straight line.There are no exponents higher than one for the linear functions. Some of them only have the single variable x, which would be equal to x to the first power, if they have any variables at all.In its most basic form, a linear function is stated as y = a + bx, where this one and b are both constants.Given table:
x y
-2 -7
-1 -4
0 -1
1 2
2 5
Plot the coordinates on graph:
(-2, -7), (-1, -4),(0,-1),(1,2),(2,5)
The graph of the given values of x and y coordinates shows the straight line. Thus, the function is said to be linear.
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Complete question:
Explain, if the given table shows linear or non linear function?
x y
-2 -7
-1 -4
-0 -1
1 2
2 5
Which measurement is not equal to one mile
Thus, the parking space is longer than length of the truck by 42 inches.
Explain about the unit conversion:The same attribute is expressed using a unit conversion, but in a different measurement equivalent. For instance, time can always be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or another type of measurement unit instead of miles.
Using conversion factors, existing units, and or the fact that a unit of measure cancels out another unit of measure, a unit cancellation table is created.
Given data:
Length of the parking space = 60 feet
Length of truck = 6 yard.
Convert yards in feet
1 yard = 3 feet
Multiply both side by 6.
6*1 yard = 6*3 feet
6 yard = 18 feet
Difference = 60 - 18 = 42 feet.
The parking space is longer than length of the truck by 42 inches.
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3. The ASHI Standard of Practice requires a home inspector to inspect
Safety glazing
Porches and railings
Children's play structures
Fences and gates around pools
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice. So, B is the right answer.
Explain ASHI?The American Society of Home Inspectors is known as ASHI. It is a non-profit company with its main office in Des Plaines, Illinois, and it was established in 1976.
ASHI's major objective is to advance professionalism in the home inspection industry by establishing and upholding high standards for its members. Home inspectors can get education, training, and certification from ASHI. Members are also obliged to abide by the organisation's Code of Ethics and Standards of Practice. The minimal requirements for a house inspection are outlined in the Standards of Practice, along with the inspector's obligations to the client.
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice.
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Help guys small math problem PLEASE ASAP !!
Step-by-step explanation:
F'(x) = f(x + h)² - 5(x + h) + 3 - (x² - 5x + 3)
---------------------------------------------------
h
F'(x) = x² + 2xh + h² - 5x - 5h + 3 - x² + 5x - 3
--------------------------------------------------------
h
F'(x) = 2xh + h² - 5h
-----------------------
h
F'(x) = h(2x + h - 5)
----------------------
h
F'(x) = 2x + h - 5
Lim
h---0
= 2x + 0 - 5
= 2x - 5
A poll of 1075 Americans showed that46.8 % of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
By using the P-value method, we conclude that, fewer than half of Americans prefer to watch the news rather than read or listen to it.
What is p-value?
In statistics, the p-value is a probability value that measures the evidence against a null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the actual test statistic, assuming that the null hypothesis is true.
In this problem, we want to test the claim that fewer than half of Americans prefer to watch the news, based on a poll of 1075 Americans where 46.8% of the respondents said they prefer to watch the news.
Let p be the true proportion of Americans who prefer to watch the news. Then the null hypothesis is:
H0: p ≥ 0.5 (more than or equal to half of Americans prefer to watch the news)
The alternative hypothesis is:
Ha: p < 0.5 (fewer than half of Americans prefer to watch the news)
We will use the normal distribution as an approximation to the binomial distribution, since n = 1075 is large and the success-failure condition is satisfied. The expected number of respondents who prefer to watch the news is:
E = np = 1075 × 0.468 = 503.1
The standard deviation of the sampling distribution of p is:
σ = sqrt[(p(1-p))/n] = sqrt[(0.5×0.5)/1075] ≈ 0.015
We can now calculate the z-score for the sample proportion:
z = (x - E) / σ = (1075 × 0.468 - 503.1) / 0.015 ≈ -4.28
where x is the observed number of respondents who prefer to watch the news, which is 1075 × 0.468 ≈ 503.
The P-value for this test is the probability of getting a z-score less than or equal to -4.28 under the standard normal distribution. Using a standard normal table or calculator, we find that this probability is very close to 0. Therefore, the P-value is less than 0.10, the chosen significance level.
Since the P-value is less than the significance level, we reject the null hypothesis. We have sufficient evidence to conclude that fewer than half of Americans prefer to watch the news rather than read or listen to it.
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