The set of all x-values at a distance of 15 or less from the number 6 can be represented in interval notation as (-9, 21).
Interval notation is a way of expressing a set of numbers in a concise and easily readable format. In this case, we are looking for all the x-values that are a distance of 15 or less from the number 6. To find these values, we need to consider the range of numbers that are 15 units away from 6 in both the positive and negative directions.
On the negative side, 6 - 15 = -9, so any x-value that is greater than -9 and less than 6 is within the desired range.On the positive side, 6 + 15 = 21, so any x-value that is greater than 6 and less than 21 is also within the desired range.So, in interval notation, the set of all x-values at a distance of 15 or less from 6 is written as (-9, 21) which means all the values between -9 and 21 (not including -9 and 21)
Key points:
Interval notation uses parentheses to indicate that the endpoint is not included in the interval, and square brackets to indicate that the endpoint is included.The interval is always written in increasing order, with the lower endpoint first and the upper endpoint second.Interval notation is commonly used in mathematics, particularly in calculus and analysis, to describe the domain or range of a function.Learn more about Interval notation here:
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Find c round to the nearest tenth c=
This is the Law of Sines, which is one of the main formulas used in trigonometry to calculate the length of sides and angles of a triangle.
Find c round to the nearest tenth?sin 15° 2 = bc = sin 105° c
2/sin 15° = bc/sin 105°
bc = (2/sin 15°)sin 105°
bc = 2.68 cm
bc ≈ 2.7 cm
It states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.To find the length of side bc, we need to use the Law of Sines and the given information. We know the lengths of sides ac and a, and the angle a. We can plug these into the Law of Sines and solve for b:sin A a/ac = sin B b/bc
sin(15°)2/2 = sin(105°)b/b
b = 2 sin(105°)
b = 2.99 cm
Therefore, side bc is 2.99 cm, rounded to the nearest tenth.To learn more about the Law of Sines refer to:
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two multiplicative sets s and t yield localizations with the same primes then actually they have the same saturation
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Yes, this is true. If two multiplicative sets s and t yield localizations with the same primes, then the two localizations are the same, since the same prime ideals are being used to define the two localizations.
Thus, the two sets s and t have the same saturation since they yield the same localization.
If two multiplicative sets s and t yield localizations with the same primes, then the two sets s and t have the same saturation since they yield the same localization.
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Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2; 5; 7; 2; 2; 10; 20; 15; 0; 7; 0; 20; 5; 12; 15; 12; 4; 5; 10.
Table 1.35 was produced.
a. Fix the errors in Table 1.35. Also, explain how someone might have arrived at the incorrect number(s).
b. Explain what is wrong with this statement: "47 percent of the people surveyed have lived in the U.S. for 5 years."
c. Fix the statement in b to make it correct.
d. What fraction of the people surveyed have lived in the U.S. five or seven years?
e. What fraction of the people surveyed have lived in the U.S. at most 12 years?
f. What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
g. What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?
Someone might have arrived at the incorrect number by incorrectly counting frequencies or not accounting for every data point.
Table 1.35 should be as follows:
Number of Years in US | Frequency
2 | 3
5 | 4
7 | 2
10 | 2
12 | 2
15 | 2
20 | 2
b. This statement is incorrect because 47 percent does not equal the total number of people surveyed.
c. This statement can be fixed by saying "Four out of the nineteen people surveyed have lived in the U.S. for 5 years."
d. The fraction of people surveyed who have lived in the U.S. for five or seven years is 6/19, or 31.58%.
e. The fraction of people surveyed who have lived in the U.S. for at most 12 years is 10/19, or 52.63%.
f. The fraction of people surveyed who have lived in the U.S. for fewer than 12 years is 9/19, or 47.37%.
g. The fraction of people surveyed who have lived in the U.S. from five to 20 years, inclusive, is 12/19, or 63.16%. This can be calculated by subtracting the number of people who have lived in the U.S. fewer than five years (3) from the number of people who have lived in the U.S. 20 or more years (2), and dividing the result (12) by the total number of people surveyed (19).
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Carmen will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $42 and costs an additional 0.18 per mile driven.The second plan has an initial fee of $51 and costs an additional $0.13 per mile driven.
For what amount of driving/miles do the two plans cost the same?
What is the cost when the two plans cost the same?
The two plans cost the same for 550 miles of driving and $113.5 is the total cost.
What is linear equations?Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.This problem is about linear equations. We assume Maya drive X miles, and the total cost is $Y, then we can get like, the first plan has an initial fee of $53 and costs an additional $0.11 per mile driven
For plan 1: Y = 53 + 0.11 X
The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven,
For Plan 2: Y= 42 + 0.13 X
When both plans cost the same, then
Plan 1 = Plan 2
53 + 0.11 X = 42 + 0.13 X
0.13 X - 0.11 X = 53 - 42
0.02 X = 11
[tex]$X=\frac{11}{0.02}=550$[/tex] miles
Put the value of X in equation of Plan 1, we get,
Y = 53 + 0.11(550) = 53 + 60.5= $113.5
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the brigham young university statistics department is conducting a series of randomized comparative experiments to compare teaching methods. response variables include students' final-exam scores and a measure of their attitude toward statistics. one study compares two levels of technology for large-group lectures: standard (overhead projectors and chalk) and multimedia. the experimental units in the study are the 8 lecture sections in a basic statistics course. there are four instructors, each of whom teaches two sections. because the lecturers differ, their lectures form four blocks.
Individuals basically use statistics to make decisions in financial planning and budgeting, while organizations are guided by statistics in financial policy decisions.
What exactly do you mean by statistics?
Statistics is the study of data collection, organisation, analysis, interpretation, and presentation. When applying statistics to a scientific, industrial, or social problem, it is customary to begin with a statistical population or a statistical model to be researched.Populations can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal." Every facet of data, including the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.Given data :
Step 1 :
The statistics department at Brigham Young University (BYU) is doing research to contrast various teaching strategies.
For lengthy courses, two technological echelons are contrasted: standard and multimedia. Eight lecture parts with students are present. There are four teachers in all.
Step 2 :
Consider that we randomly select two professors to use standard technology and the other two to use multimedia technology. Various professors will have various teaching philosophies, which will eventually influence final grades. We won't be able to tell a teaching method from a piece of technology in this way. Regarding technological disparities, there is no assurance.
Step 3 :
The ideal plan would be to divide each teacher's lectures into two sections, one utilising normal technology and the other multimedia.
There are four blocks as a result, one for each teacher.
Variability would be reduced because they are all being taught by the same person.
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Help me please I don’t know how to do it
The slope equals the rise divided by the run: . You can determine the slope of a line from its graph by looking at the rise and run.
How do you find slope of a line?A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.
The definition of slope in mathematics is pretty close to how we normally define it. Slope is a mathematical term used to indicate a line's steepness and direction. A line's slope can be inferred from its graph alone, especially in relation to other lines plotted on the same coordinate plane.
slope=rise/run.
The ratio of the change in the y-value to the change in the x-value can also be used to determine slope. For instance: Given two points on the line, P = (0, -1) and Q = (4,1), we may compute
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Please hurry
Which of these graphs best illustrates
how the velocity of the free-falling rock
changes during the first four seconds?
J) Has a box that has a line at an angle. Inside the box from the bottom left corner to the top right corner is the angled line like |_ and inside the box is a line angled like this /
K) Same as “J” except the angle is a curved half circle angled from the bottom left corner going to the top of the box. Therefore the curved/bent line isn’t exactly going to the top right corner.
L) Same as “J” except the line is going from top left corner to bottom right corner.
M) same as “K” except the bent/curved line is going from left bottom corner to right side of box like in the middle.
The graph which represents the velocity of the free-falling rock that changes during the first four seconds is option L: Same as “J” except the line is going from top left corner to bottom right corner.
What is velocity?
The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction.
The velocity of a free-falling rock can depicted by equation of motion.
The first equation of motion, v = u + it is referred to as the velocity-time relation. On the other hand, the second equation of motion is s = ut + 1 / 2at² can be called the position-time relation. Likewise, we call the third equation of motion, v² = u²+ 2as, position – velocity relation.
The laws are: (1) Every object moves in a straight line unless acted upon by a force. (2) The acceleration of an object is directly proportional to the net force exerted and inversely proportional to the object's mass. (3) For every action, there is an equal and opposite reaction.
Since, the rock is falling freely it will form a straight line (first equation of motion) on the graph and not curved.
The rock will start to fall at an increasing speed with respect to time.
Therefore, option L is the correct answer.
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If $8000 is deposited into an account earning simple interest at an annual interest rate of 4% for 10 years, how
much interest was earned? Show you work.
The interest earned by the investment of $8,000 at an annual simple interest rate of 4% for 10 years is $3,200.
What is the simple interest?The simple interest method is a system that does not accumulate interest on interest.d
The simple interest system is unlike the compound interest system.
The formula for computing the simple interest is principal x rate x time.
Initial deposit = $8,000
Interest rate = 4%
Investment period = 10 years
Interest system = simple interest
Simple interest = P x R x T
= $8,000 x 4% x 10
= $3,200
Thus, the investment will earn a total interest of $3,200.
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Please help with this ewuation
Answer: 57°
Step-by-step explanation:
Because the angle has a bisector ON, we should be able to add the angles together to collectively equal 106. This will help us to find c, so then we can solve <LOM.
(10c-23) + (-3c+73) = 106
Now combine like terms of the left side of the equation
7c + 50 = 106
get the variables alone on one side of the equation
7c = 56
c = 8
Now, plug in c to the equation for the degree of <LOM to solve
10(8) -23 = 80 - 23 = 57°
Hope this helps!
It seems these days that students have to work more and more each week to be able to afford the costs of college. For a recent labor survey conducted by the
government, there were 78 respondents who were working while attending college. The frequency distribution below summarizes the number of hours worked
per week as reported by the respondents.
Number of hours
worked per week Frequency
(hours per week)
26 to 30
31 to 35
36 to 40
41 to 45
46 to 50
51 to 55
10
24
20
13
7
4
Based on the frequency distribution, using the midpoint of each data class, estimate the mean number of hours worked per week by the respondents. For your
intermediate computations, use four or more decimal places, and round your answer to one decimal place.
hours per week
The mean number of hours worked per week by the respondents will be 37.68.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
Number of hours worked per week Frequency
26 to 30 10
31 to 35 24
36 to 40 20
41 to 45 13
46 to 50 7
51 to 55 4
The mean is given as,
Mean = [28 x 10 + 33 x 24 + 38 x 20 + 43 x 13 + 48 x 7 + 53 x 4]
(10 + 24 + 20 + 13 + 7 + 4)
Mean = 2939 / 78
Mean = 37.68
The mean number of hours worked per week by the respondents will be 37.68.
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Determine the friction force on the 40 kg crate, and the resultant normal force and its position x, measured from point A, if the force P = 300 N. Take μs=0.5 and μk=0.2
The friction force on the 40 kg crate is the product of the coefficient of static friction, μs, and the normal force on the crate. Therefore, the friction force is 40 kg ×0.5 = 20 N.
The resultant normal force on the crate is the sum of the force P and the friction force, which is
300 N + 20 N = 320 N.
The position x, measured from point A, is determined by the direction of the force P. If the force P is acting to the right, then the normal force will have a position x that is to the right of point A. If the force P is acting to the left, then the normal force will have a position x that is to the left of point A.
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the histogram below shows the distances (in meters) of all qualifying throws for the women's javelin event at the 2004 summer olympics.Which of the following terms apply to this histogram? (Select all that apply.)positively skewedsymmetricuniformunimodalbimodalnegatively skewed
Positively Skewed: A positively skewed distribution is one that has a long tail in the positive direction (to the right).
The mean is usually greater than the median, and the data points are concentrated on the left side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is greater than the median, and the skewness is therefore positive.
Symmetric: A symmetric distribution is one that is perfectly centered around the mean and has equal amounts of data points on either side of the mean. In the histogram, the data points are not perfectly centered around the mean, so this term does not apply.
Uniform: A uniform distribution is one that has all the data points clustered around the same value. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Unimodal: A unimodal distribution is one that has a single peak. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Bimodal: A bimodal distribution is one that has two peaks. In the case of the histogram, the data points are spread out across a wide range, so this term does not apply.
Negatively Skewed: A negatively skewed distribution is one that has a long tail in the negative direction (to the left). The mean is usually less than the median, and the data points are concentrated on the right side of the graph. To calculate the skewness of a distribution, we use the formula: skewness = (mean – median) / standard deviation. In the case of the histogram, the mean is less than the median, and the skewness is therefore negative.
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-1 2. Solve the pair of equations: 2a-1-3b-¹ = 4; 4a-¹ + b¯¹ = 1 3.
Hope it helps.
If you have any query, feel free to ask.
Find the Volume for the following cylinder.
a. 527.5 ft2
b. 342.7 ft2
c. 373.7 ft2
d. 307.7 ft2
The volume of the cylinder is 769.3 cubic feet.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given a cylinder,
radius = 7 feet
height = 5 feet
volume of cylinder = πr²h
V = πr²h
V = 3.14*(7²)*5
V = 769.3 cubic feet
Hence the volume of a cylinder is 769.3 cubic feet.
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Find the vectors u and v whose initial and terminal points are given. Initial Point Terminal Point u: (4,2) (5, 6) v: (2, 4) (3,8) U = V =
The vector is given by (1,4) and (1,4) for the given 2 conditons
what is vector?A vector is a mathematical object that has both magnitude and direction. In physics, vectors are used to represent quantities such as velocity, force, and acceleration. In mathematics, vectors can be represented by an ordered list of numbers (also known as components or coordinates) that specify the magnitudes of the vector in different directions. Vectors can be added, subtracted and multiplied by scalars. They also have properties such as dot and cross product. Vectors can be represented graphically as directed line segments. They are used in various fields like physics, engineering, computer science etc.
Part 1:
The vector is given by (final -initial)
=> (5-4 , 6-2)
=> (1 , 4)
Part : 2
The 2nd vector is given by (final - initial)
=> (3-2 , 8-4)
=> (1 , 4)
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before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. he randomly selects 1000 households from all households in the area and mails a questionnaire to them. of the 1000 surveys mailed, he receives 150 back. which of the following is the most obvious concern with how this information is gathered?
The most obvious concern is those who chose to respond to the survey may have different eating habits from those who did not respond.
One of the major worries when conducting a survey is that people who choose to reply can differ from those who choose not to. The term for this is nonresponse bias. The representativeness of the sample may be impacted by the traits, opinions, or actions of respondents that differ from those of non-respondents.
In this given case, the chef issued a survey to 1000 families, but only 150 of them responded, or 15% of the households. It's probable that those who are very interested in food or cooking will respond to the poll more frequently than others who aren't. Due to the possibility that the eating patterns of individuals who replied may not be typical of the total population, this could cause the sample to be skewed. Thus, the chef would need to consider the nonresponse bias when interpreting the results of the survey.
Complete Question:
Before opening a new restaurant, a chef wants to gather information about the eating habits of the local residents. He randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, 150 are returned. Which of the following is the most obvious concern with how this information is gathered?
(A)Mailing questionnaires instead of conducting in-person interviews produce a convenience sample.
(B)Those who chose to respond to the survey may have different eating habits from those who did not respond.
(C)Only residents from the local area were polled.
(D)The chef must conduct a census in order to avoid all sources of bias.
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7 milimeter = 5 meter scale factor
The scale factor for 7 millimeters to 5 meters is 0.0014.
What is the scale factor?The scale factor is the ratio between the scale of an original object, drawing, map, model, or blueprint compared to its representation as a larger or smaller object.
We can compute the scale factor (scaled-down) using the following formula:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape
1 meter = 1,000 millimeters
5 meters = 5,000 millimeters (1,000 x 5)
The scale-down factor of 7 millimeters to 5,000 millimeters = 0.0014 (7/5,000)
The scale-up factor of 7 millimeters to 5,000 millimeters = 714.286 (5,000/7)
Thus, the scale factor is 0.0014.
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Question Completion:What is the scale factor?
How many times dose 13 go into 26
Answer:
2
Step-by-step explanation:
26/13=2
Answer:
2
Step-by-step explanation:
26-13=13-13=0
Christmas lights are produced in a large quantity and as a result one-fifth are faulty. If
individual lights are taken out one by one from this large quantity, find the probability
that when the first three lights are taken out
a there is one faulty light
b there are two faulty lights
c there is at least one faulty light.
The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
What is probability?The likelihood that an event will occur is measured by probability. It is difficult to make a complete prediction for many events. By using it, we are only able to forecast the likelihood of an event, or how likely it is, to occur. Between 0 and 1, where 1 denotes a certain event and 0 denotes an impossibility, is the range of probability. For students in class 10, probability is a crucial subject because it clarifies all of the fundamental ideas. In a sample space, there is a probability of 1 for each event.
a. Let there be 100 lights, 1/5th are faulty = 20
There is one faulty in first three, P = 3/100 × 20/100
= 0.006
= 0.60%
b. There are two faulty lights, P = 3/100 × 20/100 × 20/100
= 0.0012
= 0.12%
c. There is at least one faulty light = 3/100 ×1/5
= 0.006
= 0.60%
Thus, The probability of there is one faulty light is 0.60%, There are two faulty lights is 0.12% and There is at least one faulty light is 0.60%.
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Select all the angles of rotation that produce symmetry for this flower.
Flower on polar grid.
A: 45 degrees
B: 90 degrees
C: 135 degrees
D: 180 degrees
E: 225 degrees
F: 270 degrees
The angles of rotation symmetry for the flower are:
B. 90 degrees
D. 180 degrees
F. 270 degrees
A shape with a rotation symmetry will look the same, after the rotation also.
The order of symmetry is the number of rotations that can be applied to a figure while maintaining its original appearance.
From the image of the flower (image attached at the end of solution), we can see that the lines that pass through the origin of the flower are perpendicular.
The perpendicular lines will form the degrees of 90.
This means that 90 degrees of rotation will produce symmetry for the flower.
Other angles that produce symmetry must be multiples [tex]90^{\circ}[/tex].
These angles are:
[tex]\theta=90^{\circ}, 180^{\circ}, 270^{\circ}, 360^{\circ}[/tex].
Here we have [tex]90^{\circ}, 180^{\circ}, 270^{\circ}[/tex] options
Hence, (B), (D), and (F) are the correct options.
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Jeremy has two pieces of wood: one is 90 inches and the other is 72 inches. He wants to cut both pieces into smaller pieces of the same length. What is the longest possible length he can cut and not have any lumber left over?
answer choices
O 9
O 2
O 18
O 72
The longest piece of same size that can be cut from 90 inches and 72 inches pieces of wood using HCF is of length 18 inches.
So, the correct option is (c) 18.
Given that,
Jeremy has two pieces of 90 inches and the other is 72 inches wood. He wants to cut both pieces of wood into smaller pieces of same length and length as long as possible.
Therefore, the Highest Common Factor (H.C.F.) of both the lengths will gives the highest possible length i.e between both the wooden pieces.
To find Highest Common factor,
Prime factorizations of 90 and 72 :
90 = (2 x 3 x 3) x 5
72 = 2 x 2 x (2 x 3 x 3)
2 x 3 x 3 is common factor between 90 and 72
∴ The Highest Common Factor of 90 and 72 = 2 x 3 x 3 = 18
The longest possible length that can be cut out from both the pieces are of length = 18 inches
Number of pieces that can be cut from 90 inches long piece = 90/18 = 5
Number of pieces that can be cut from 72 inches long piece = 72/18 = 4
Therefore, the total number of pieces of lumber = 5+4 = 9 pieces
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Como saber cuánto creció
The seedlings grew by 7/6 inches in the first 2 weeks.
What is LCM ?
The abbreviation LCM stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.
Let' assume the growth of seedling was 'nil' at the beginning.
According to the situation,
In the first week it grew by 1/3 inches and,
In the next week it grew by 5/6 inches.
So, we can say that the total growth will be the sum of growth in the first and second week.
Hence, total growth would be 7/6 inches (i.e. 1/3 + 5/6).
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a circle is formed when a plane slices through a cone. which of the following describes the relationship between the plane and the cone? the plane is parallel to the base of the cone. the plane is perpendicular to the base of the cone. the plane is parallel to the slant edge of the cone and intersects the base of the cone. the plane is at a slight angle with respect to the base of the cone, but does not intersect it.
The relationship between the plane and the cone is expressed by the statement that it is parallel to the base of the cone.
Given,
A circle is a closed, curved shape with two dimensions in geometry, alternatively we might say that a circle is a spherical form without borders or edges.
When a cone is cut by a plane that is parallel to the cone's base, a circle is the resultant cross-section.
The form that results from a plane cutting a cone at an angle such that it misses the base or the vertex is called an ellipse. (As in the figure.)
Hence When a plane cuts through a cone and the plane is parallel to the base of the cone, the result is a circle.
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givin the sequence
19,13,7,1
what is the 18 term of the sequence
A-71
B-77
C-83
D-89
The 18th term of the sequence is -83, the correct option is C.
What is arithmetic sequence?An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.
If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:
a, a + d, a + 2d, ... , a + (n-1)d, ...
Its nth term is
T_n = a + (n-1)d
(for all positive integer values of n)
And thus, the common difference is
T_{n+1} - T_n
for all positive integer values of n
Given:
The sequence=19,13,7,1...
n=18
D= 13-19
D= 6, a= 19
Now,
=a + (n+1)d
=19+(18-1)x-6
=-83
Therefore, the 18th term of the sequence will be -83
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A rectangular landing strip for an airplane has a perimeter of 8876 feet. If the length is 10 feet longer than 35 times the width, what is the length of the air strip?
The length of the air strip is 451feet.
What is perimeter?Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthened n sides).
Given in question;
Perimeter= 8876feet
Let the length be x;
and the width be y;
Now, length will be x= 10+35y
Perimeter of rectangle= 2l+2b
8876=2(10+35y)+y
8876=20+700y+y
y=12.6
x=10+35y
x=451;
Hence, the answer by the given perimeter will be 451feet.
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Surface area of rectangular prism length 12ft width 3ft height 8ft
The surface area of the rectangular prism is: 312 ft².
How to Find the Surface Area of a Rectangular Prism?The surface area of rectangular prism can be calculated using the formula that is given as:
Surface area (SA) = 2(w * l + h * l + h * w), where l is the length, w is the width, and h is the height of the rectangular prism.
Given the following dimensions of the rectangular prism as:
length (l) = 12 ft
width (w) = 3 ft
height (h) = 8 ft
Therefore:
Surface area of the rectangular prism = 2*(3 * 12 + 8 * 12 + 8 * 3) = 312 ft²
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HELP ASAP !! WHATS THE END BEHAVIOR ?
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
What is end behaviour ?When referring to a function, "end behaviour" refers to the character of the value as the function parameter becomes closer to +∞ and -∞.
In the given table for f(x), we see that for every value of x, function f(x) is decreasing.
f(-2) = 48
f(0) = 12
f(2) = 3
f(3) = 1.5
In other words as the value of x increases, f(x) is approaching towards 0.
Now we take another function g(x) =
Now we plug in the values of x to get the values of g(x)
g(-1) =2^-1-5
= 1-10/2
= -9/2
= -4.5
g(0) = 2^0-5
= 1 - 5 = -4
g(2) = 2^2-5
= 4 - 5 = -1
g(3) = 2^3-5
= 8 - 5= 3
Now we find that g(x) is increasing with the values of x.
Now we take third function h(x).
By analyzing the given graph we find
h(-4) = 2
h(0) = 3
h(1) = 5
So when we are increasing the value of x function h(x) is increasing.
Finally we conclude by the options given that f(x) is the only function which tends to 0 with the increase in the values of x.
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a convex pentagon has exterior angles with measures 75°, 62°, 68°, and 101°. the measures of the last exterior angle is?
Answer:
x=54°
Explanation step by step
The sum of angles of a Pentagon is 5
from the question Pentagon is given an angles of
75°, 62°, 68°, and 101°
Let the other angle of Pentagon be x.
The measures of the last exterior
=x+75° +62° +68° +101° = 360°.
Note: the sum of exterior angle add up to 360°
306° + x = 360°
x = 360° - 306°
x = 54°.
Calculate the amount of interest that will be charged on $8500.00 borrowed for 6 months at 5.25%.
Answer:
A = $8,725.58
P (principal) = $8,500.00
I (interest) = $225.58
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 5.25/100
r = 0.0525 rates per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,500.00(1 + 0.0525/12)(12)(0.5)
A = 8,500.00(1 + 0.004375)(6)
A = $8,725.58
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $8,500.00 at a rate of 5.25% per year compounded 12 times per year over 0.5 years is $8,725.58.
A building surmounted is in the form of a cylinder by a cone of height 24.m. If the base diameter and total height of the building are 14m and 34 m respectively, find the outer surface area of the building.
Answer: The building is in the form of a cylinder surmounted by a cone. To find the outer surface area of the building, we need to find the total surface area of the cylinder and the cone and add them together.
The total surface area of the cylinder = 2πr^2 + 2πrh = 2π(7^2) + 2π(7)(24) = 2π(49) + 2π(168) = 98π + 336π = 434π square meters
The total surface area of the cone = πr^2 + πr√(r^2 + h^2) = π(7^2) + π(7)(√(7^2 + 24^2)) = 49π + 49π(√(625)) = 49π + 49π(25) = 49π + 1225π = 1274π square meters
The outer surface area of the building is the sum of the total surface area of the cylinder and the cone, which is 434π + 1274π = 1708π square meters.
Step-by-step explanation:
