The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3
What is an absolute value equation?
An absolute value equation can be written as |expression| = value
To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.
We can write,
|x + 5| = 3
To solve for x, we have two cases,
Case 1: x + 5 is positive
If x + 5 is positive, then the equation becomes x + 5 = 3
Solving for x,
x = -2
This matches one of the solutions we want.
Case 2: x + 5 is negative
If x + 5 is negative, then the equation becomes -(x + 5) = 3
Solving for x,
x = -8
This also matches the other solution we want.
Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.
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The following data values represent a population. What is the variance of the population? u = 12. Use the information in the table to help you.
A. 18 B. 41 O C. 12 OD. 80
x 3 11 13 21
(x-μ)² 81 1 1 81
The variance of the population according to the given table is option B 41.
What is variance?The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.
The variance is given by the formula:
variance = (sum of squared deviations from the mean) / (number of observations)
Using the table we have sum of squared deviations from the mean:
81 + 1 + 1 + 81 = 164
variance = 164 / 4 = 41
Hence, the variance of the population according to the given table is option B 41.
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the area of Rectangle is 112 in sq. if the height is 8 in, what is the base length
Answer:
14cm
Step-by-step explanation:
112÷8=14
base length=14cm
Answer:
To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:
Area = Length x Width
In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.
So, the equation for the area of the rectangle becomes:
112 = x * 8
To solve for "x", you can divide both sides of the equation by 8:
112 / 8 = x
x = 14
Therefore, the base length of the rectangle is 14 inches.
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A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) (2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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An average newspaper contains at least 9 pages and at most 46 pages. How many newspapers must be collected to be certain that at least two newspapers have the same number of pages?
We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.
What is the minimum number of newspapers needed to guarantee that two newspapers have the same number of pages?According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.
In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.
However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.
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A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slope of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x)
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
Where do the X and Y axes intersect on the coordinate plane, at position 0 0?The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.
We can use the slope formula to get the slopes of the lines f(x) and g(x):
slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3
slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2
The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
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what’s the surface area of this figure ?
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
Explain about the pentagonal prism:A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.
The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.
Given data:
base area B = 84.3 sq. ftLength of rectangular side L = 7 ftwidth of rectangular side w = 4 ftsurface area of pentagonal prism = 2* base area + 5*rectangle area
surface area of pentagonal prism = 2* B + 5*L*w
surface area of pentagonal prism = 2* 84.3 + 5*7*4
surface area of pentagonal prism = 168.6 + 140
surface area of pentagonal prism = 308.6 sq. ft
Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.
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Suppose you have $1600 in your savings account at the end of a certain period of time. You invested $1500
at a 6.49% simple annual interest rate. How long, in years, was your money invested?
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
Explain about the simple interest:Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.
Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).
Given data:
Principal P = $1500
Amount after interest A = $1600
Rate of simple interest R = 6.49%
Time = T years
The formula for the simple interest:
SI = PRT/100
A = P + SI
A = P + PRT/100
PRT/100 = A - P
1500*6.49*T/100 = 1600 - 1500
1500*6.49*T = 100 *100
T = 10000 / 9735
T = 1.027 years
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
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1 1/4 - 1 1/5
Pls answer it today!
Answer:
fraction form: 1/20
decimal form:0.05
Which of these expressions could Alex and Taylor use to calculate the square footage of the tile Dining area? Find only the tile floor, and not the cabinets shown in black. Select all that apply.
A 34 foot by 13 foot grid. The kitchen is flush left. It has an 18 foot by 2 foot horizontal rectangle in the top left of the grid. Under the far left and right sides of the rectangle are two 6 foot by 2 foot vertical rectangles. There are two other horizontal rectangles on the bottom left of the grid that are 2 foot by 6 foot. There is a 4 foot gap between them. The dining room is on the right with a 12 foot by 2 foot rectangle in the top right of the grid.
Select answers
(16 x 13) - (12 x 2)
(4 x 13) + (12 x 2) + (12 x 11)
(17 x 11) + (4 x 2)
(4 x 13) + (12 x 11)
Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)
How to calculate the area of rectangle?The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,
[tex]Area=length*width[/tex]
Now, Solving given problem,
The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft
Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft
The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft
Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft
To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:
(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft
So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft
The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft
Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft
The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft
Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft
Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:
Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft
So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft
Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.
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The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once all growth plates fuse, growth stops, and an individual is considered a biological adult. The age at which growth plates fuse for males is approximately normally distributed with a mean of 18.8 years and a standard deviation of 15.1months. Complete parts (a) through (d).
The answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?
To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,
Z = (X - mean) / standard deviation
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.
(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?
We need to standardize the values of 16 and 18 using the mean and standard deviation provided.
Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03
Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53
Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.
Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.
(c) What is the age at which growth plates fuse for the top 5% of males?
We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).
Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.
Then, we can solve for X using the formula:
Z = (X - mean) / standard deviation
1.645 = (X - 18.8) / (15.1/12)
Simplifying the equation, we get:
X = 18.8 + (1.645)(15.1/12) = 20.24
Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.
(d) What percentage of males have growth plates that fuse before the age of 16?
We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).
Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.
Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.
hence, the answers to each question are:
(a) 0.351.
(b) 0.317.
(c) 20.24 years.
(d) 16.
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Name one right angle.
Name one straight angle.
Please help with this math question!
The exponential function of the population is P(x) = 15000 * 1.046^x
Calculating the exponential function of the populationFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 15000
Rate, r = 4.6%
The equation of the function is represented as
P(x) = a * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
P(x) = 15000 * (1 + 4.6%)^x
Evaluate
P(x) = 15000 * 1.046^x
Hence, the function is P(x) = 15000 * 1.046^x
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Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.
If each person drove at a constant rate,than Laura drove the fastest
What is the distance ?Displacement is the measurement of the how far an object is out of place,therefore distance refers to the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.
What is the speed?The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.
to compute who drove the quickest by Using this formula
speed=Distance /time,
first of all the convert times into hours:
Hank: 3.2 hours x 3 hours and 12 minutes.
Laura: 2.5 hours is 2 hours and 30 minutes.
Nathan: 2.25 hours is 2 hours and 15 minutes.
Raquel: 4 hours plus 24 minutes equals 4.4 hours.
now to calculate the speed by above formula
Hank: 55 miles per hour for 176 miles in 3.2 hours.
Laura: 60 miles per hour equals 150 miles in 2.5 hours.
Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.
Raquel: 65 miles for 286 miles in 4.4 hours.
As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.
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Find the area
(Please do not guess )
Answer:
A = 50.24 m²
Step-by-step explanation:
A = π r²
d = 8 m
r = d/2
r = 8/2
r = 4 m
A = 3.14 × (4)² m
A = 3.14 × 16 m
A = 50.24 m²
Answer:
50.24 m²
Step-by-step explanation:
Diameter = 8 m
Formula
Radius ( r ) = Diameter/2
r = 8/2
r = 4 m
Formula
Area of circle = π r²
Note
The value of π is 3.14 ( approximately )
Area of circle
= 3.14 × 4²
= 3.14 × 4 × 4
= 3.14 × 16
= 50.24 m²
Hence,
The area of circle is 50.24 m².
Help me this is a Screensho
t
Answer:
21.8 - 0.1 = 21.7
21.7 is 0.1 less than 21.8
Answer:
The answer is 21.7
Step explanation
21.8 - 0.1 = 21.7
I hope it helped you.
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A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.
What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent.
63% of people Surveyed shop at a local grocery store.
What is percentage ?A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.
For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.
In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.
What are proportions ?The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;
it is frequently stated as a fraction.
For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.
An assertion of equality between two ratios is a proportion.
For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,
hence the sentence "3/5 = 6/10" is a proportion.
Analysis: -
people surveyed at store = 45
total no. of people = 72
the
Percent of peopla = 45/72 x100
= 0.625 × 100
= 62.5 %
= 63 %
63% of people Surveyed shop at a local grocery store.
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Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
HELP FAST PLEASEEE!!!!
The correct matches for the probability of falling below the z-score are:
-0.08: 0.4681
0.63: 0.7357
-2.7: 0.0035
1.95: 0.9744
Explain probability
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.
According to the given information
To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:
For a z-score of -0.08, the probability of falling below it is 0.4681.For a z-score of 0.63, the probability of falling below it is 0.7357.For a z-score of -2.7, the probability of falling below it is 0.0035.For a z-score of 1.95, the probability of falling below it is 0.9744.To know more about probability visit
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In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. What is the likelihood of a yellow marble being selected on the first draw?
likely
unlikely
even chance
certain
Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.
What is Probability?Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.
In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.
The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:
likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles
So, in this case, the likelihood of selecting a yellow marble on the first draw is:
likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3
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A rectangle has an area of 108 square
centimeters. Its width is 9 centimeters.
What is the perimeter of the
rectangle?
Therefore, the perimeter of the rectangle is 42 centimeters.
What is area?The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.
Here,
To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.
We can use the formula for the area of a rectangle:
Area of rectangle = length x width
Plugging in the values we have:
108cm² = length x 9cm
Solving for the length, we can divide both sides by 9cm:
length = 108cm² / 9cm
length = 12cm
So, the length of the rectangle is 12 centimeters.
To find the perimeter of the rectangle, we can use the formula:
Perimeter of rectangle = 2 x (length + width)
Plugging in the values we have:
Perimeter of rectangle = 2 x (12cm + 9cm)
Perimeter of rectangle = 2 x 21cm
Perimeter of rectangle = 42cm
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Which one is the correct choice?
Therefore, the correct response From these integral is option D is.
``` 10 + ∫₅¹ R(t) dt
What is an integral?An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.
Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.
The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.
``` 10 + ∫₅¹ R(t) dt
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3+4x greater than 27
subtract 3 from both sides to get
4x > 27
divide both sides by 4 to get
x > 27/4 or 6 3/4
Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison. Which design is the most appropriate for this experiment
- Randomly number each item with 1, 2, or 3. Assign the items labeled 1 to the process 1 group, assign the items labeled 2 to the process 2 group, and assign the items labeled 3 to the process 3 group.
- Number each item from 1 to 1,200.
Reading from left to right from a table of random digits, identify 800 unique numbers from 1 to 1,200. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Number each item from 0000 to 1199.
Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Select an item, and identify the first digit reading from left to right on a random number table. If the first digit is a 1, 2, or 3, assign the item to the process 1 group.
If the first digit is a 4, 5, or 6, assign the item to the process 2 group. If the first digit is a 7, 8, or 9, assign the item to the process 3 group. If the first digit is a 0, skip that digit and move to the next one to assign the item to a group. Repeat this process for each item.
Answer: The most appropriate design for this experiment is the third option:
- Number each item from 0000 to 1199.
- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.
Step-by-step explanation:
Alex scored 7/20 of the points in a basketball game. How many of the team's 120 points did Alex score?
Answer:
Step-by-step explanation:
I think its 42 because 7/20ths of 120 is 42
7/20 x 120 =42
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.
Here is another question DUE SOON PLEASE ASAP
Question 5(Multiple Choice Worth 1 points)
(08.07 MC)
The table describes the quadratic function p(x).
x p(x)
−1 10
0 1
1 −2
2 1
3 10
4 25
5 46
What is the equation of p(x) in vertex form?
p(x) = 2(x − 1)2 − 2
p(x) = 2(x + 1)2 − 2
p(x) = 3(x − 1)2 − 2
p(x) = 3(x + 1)2 − 2
The equation of p(x) in vertex form is;
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
What is vertex?In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.
To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.
To find the vertex, we can use the formula:
x = -b/2a, where a is the coefficient of the x² term, b is the coefficient of the x term, and c is the constant term.
Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.
We can then use the formula to find the vertex:
x = -b/2a = -5/2a
Using the values from the table, we can set up two equations:
46 = a(5)² + b(5) + c
1 = a(0)² + b(0) + c
Simplifying the second equation, we get:
1 = c
Substituting c = 1 into the first equation and solving for a and b, we get:
46 = 25a + 5b + 1
-20 = 5a + b
Solving for b, we get:
b = -20 - 5a
Substituting b = -20 - 5a into the first equation and solving for a, we get:
46 = 25a + 5(-20 - 5a) + 1
46 = 15a - 99
145 = 15a
a = 9.67
Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:
b = -20 - 5(9.67) = -71.35
Therefore, the equation of p(x) in vertex form is:
p(x) = 9.67(x - 5)² + 1
Simplifying, we get:
p(x) = 9.67(x² - 10x + 25) + 1
p(x) = 9.67x² - 96.7x + 250.85 + 1
p(x) = 9.67x² - 96.7x + 251.85
Rounding to the nearest hundredth, we get:
p(x) = 9.67(x - 5² + 1 = 9.67(x + 1.04)² - 10.25
Therefore, the answer is:
p(x) = 9.67(x + 1.04)² - 10.25
The closest answer choice is:
p(x) = 3(x - 1)² - 2, which is not correct.
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4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
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Part of the proceeds from a garage sale was $290 worth of $5 and $20 bills. If there were 8 more $5 bills than $20 bills, find the number of each denomination.
Answer:
18 5-dollar bills
10 20-dollar bills
Find the value of x from the given figure.
The value of x from the given figure is given as follows:
144º.
What is a straight angle?An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.
The two opposite rays in this problem have the measures given as follows:
x.x/4.Hence the equation to find the value of x is given as follows:
x + x/4 = 180
x + 0.25x = 180
1.25x = 180
x = 180/1.25
x = 144º.
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Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776