a) General solution of the system is (x, y, z) = (2, 0, 1).
b) There are no multiple solutions, and we cannot find two specific solutions.
How to evaluate each part of the question?The given system of linear equations is:
1) x - y + z = 3
2) 3x + 2z = 7
3) x - 4y + 2z = 5
The reduced matrix for this system is:
1 0 1
0 1 0
0 0 1
Using the reduced matrix, we can rewrite the system of linear equations as:
1) x + z = 3
2) y = 0
3) z = 1
Now we can solve the system step by step:
From equation (3), we know that z = 1.
Next, we can use the value of z in equation (1) to find x:
x + 1 = 3
x = 3 - 1
x = 2
Finally, from equation (2), we know that y = 0.
So, the general solution of the system is (x, y, z) = (2, 0, 1).
(b) Since there is only one solution to this system, there are no multiple solutions, and we cannot find two specific solutions.
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suppose you have a set of normally distribution data where the mean is 120 and the standard deviation is 15. what score is located at -3sx?
The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.
To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.
Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.
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show your work below
70 POINTS PLEASE SOMEONE
Therefore , the solution of the given problem of arithmetic mean comes out to be A(n) = 130 + (n - 1)13 = 286 inches.
Arithmetic mean : What is it?The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.
Here,
We can use the explicit formula for an arithmetic sequence to symbolize the height of the bamboo plant after "n" days:
=> A(n) = a + (n - 1)d
Therefore, the following explicit method can be used to determine the height of the bamboo plant after "n" days:
=> A(n) = 130 + (n - 1)13
Adding "n = 13" to the calculation will yield the height of the bamboo plant after 13 days:
=> A(13) = 130 + (13 - 1)13
=> A(13) = 130 + 12(13)
=> A(13) = 286
As a result, the bamboo growth will reach a height of 286 inches after 13 days.
The right response is thus:
=> A(n) = 130 + (n - 1)13 , or 286 inches.
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what is the measure of angle 1 in degrees?
A long straight cylindrical shell has an inner radius R, and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r Ro). We conclude that the wire:A) is on the cylinder axis and carries current i in the same direction as the current in the shell 4 B) may be anywhere in the hollow region but must be carrying current į in the direction opposite to that of the current in the shell « C) may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell< D) is on the cylinder axis and carries current i in the direction opposite to that of the current in the shelle E) does not carry any current Ans: D Difficulty: Section: 29-3- Learning Objective 29.3.4
Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.
we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.
Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.
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What is the radius of a sphere if its volume is 7,234.56 ft3 please answer it,Show work.
Answer:
11.52 feet
Step-by-step explanation:
The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.
We can rearrange the formula to solve for the radius:
r = (3V/4π)^(1/3)
Substituting the given volume V = 7,234.56 ft³, we get:
r = (3(7,234.56)/(4π))^(1/3) ≈ 11.52 ft
Therefore, the radius of the sphere is approximately 11.52 feet.
The following are the ages of 12 history teachers in a school district.
36, 38 ,39 ,40 ,42 ,50 ,51 ,52 ,53 ,53 ,56 ,57
Notice that the ages are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.
How does interquartile range work?Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.
According to the given information:To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.
Step 1: Find the median (Q2)
When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:
Median (Q2) = (50 + 51)/2 = 50.5
Step 2: Find the lower quartile (Q1)
The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:
Q1 = (38 + 39)/2 = 38.5
Step 3: Find the upper quartile (Q3)
The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:
Q3 = (53 + 53)/2 = 53
Now we have all the information we need to construct the five-number summary and interquartile range:
Minimum: 36
Lower quartile (Q1): 38.5
Median (Q2): 50.5
Upper quartile (Q3): 53
Maximum: 57
Interquartile range (IQR) = Q3 - Q1 = 53 - 38.5 = 14.5
the five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.
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Solve for x,
using the secant lines.
4 cm
20 cm
x = [?] cm
X
6 cm
Remember: a b = c.d
Enter
Answer:
x = 118.5°
Step-by-step explanation:
the measure of the chord- chord angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
x = [tex]\frac{1}{2}[/tex] (27 + 210)° = [tex]\frac{1}{2}[/tex] × 237° = 118.5°
The value of x in the given circle by secant lines is 118.5 degrees.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
A straight line that intersects a circle in two points is called a secant line
A chord is in a unique secant line and every secant line defines a unique chord.
The measure of the angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle
x=1/2(210+27)
x=1/2(237)
Divide two hundred thirty seven by two
x=118.5
Hence, the value of x in the given circle by secant lines is 118.5 degrees.
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the number of students who seek assistance with their statistics assignments is poisson distributed with a mean of 0.24 per day. what is the probability that at least three students seek assistance in 10 days?
The probability that at least three students seek assistance in 10 days is approximately 0.117.
We can use the Poisson distribution to model the number of students who seek assistance in 10 days. Let X be the number of students who seek assistance in 10 days.
Then X follows a Poisson distribution with parameter λ=2.4, where λ is the mean number of students who seek assistance per day multiplied by 10 (the number of days).
Using the Poisson probability formula, we can calculate the probability of at least three students seeking assistance:
P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]
We can find that:
P(X ≥ 3) = 0.117
Therefore, the probability that at least three students seek assistance in 10 days is approximately 0.117.
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The image shows the graph of the circle
Image of prob below:
Answer:
The line y = 2 - 5/20 can be simplified to y = 2 - 1/4 = 7/4.
Substituting y = 7/4 into the equation of the circle, we get:
(x - 5)² + (7/4 + 1)² = 25
(x - 5)² + (15/4)² = 25
(x - 5)² = 25 - (15/4)²
x - 5 = ±√(25 - (15/4)²)
x = 5 ± √(25 - (15/4)²)
Simplifying, we get:
x = 5 ± √(400/16 - 225/16)
x = 5 ± √(175/16)
x = 5 ± (√175)/4
Therefore, the two intersection points are:
Left point: (5 - (√175)/4, 7/4)
Right point: (5 + (√175)/4, 7/4)
Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. If she spends 3x-7 dollars on rent, how much does she spend on electricity? Use pencil and paper. For which
value(s) of x is the amount the shopkeeper spends on electricity less than $100? Explain how you found the value(s)
She spends
(Simplify your answer.)
dollars on electricity.
The values of x is [tex]x < 39.5[/tex].
Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]
Spending of shopkeeper on rent [tex]= 3x-7[/tex]
So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]
Given that amount the shopkeeper spends on electricity less than 100.
So suitable inequality,
[tex]2x+21 < 100[/tex]
[tex]2x < 100-21[/tex]
[tex]2x < 79[/tex]
[tex]x < 39.5[/tex]
All the values of [tex]x < 39.5[/tex].
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a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?
A total of 5 glove prices meet the condition of having an absolute deviation from the mean of $8 or less.
To find the mean price, we need to sum up all the glove prices and divide by the total number of gloves.
Sum of glove prices = $55 + $42 + $28 + $39 + $82 + $25 + $40 + $32 + $45 + $38 + $52 + $34 = $512
Total number of gloves = 12
Mean price = Sum of glove prices / Total number of gloves = $512 / 12 = $42.67
To find the absolute deviation of each glove price from the mean, we subtract the mean from each price and take the absolute value.
Absolute deviation from mean for each glove = |Price - Mean price|
For example, for the first glove price of $55, the absolute deviation from the mean is |$55 - $42.67| = $12.33
We want the absolute deviation to be at most $8, so we need to find how many glove prices have an absolute deviation from the mean of $8 or less.
We can calculate the absolute deviation for each glove price and count how many are less than or equal to $8.
First row:
|$55 - $42.67| = $12.33
|$42 - $42.67| = $0.67
|$28 - $42.67| = $14.67
|$39 - $42.67| = $3.67
|$82 - $42.67| = $39.33
|$25 - $42.67| = $17.67
Out of the 6 glove prices in the first row, 2 have an absolute deviation from the mean of $8 or less.
Second row:
|$40 - $42.67| = $2.67
|$32 - $42.67| = $10.67
|$45 - $42.67| = $2.33
|$38 - $42.67| = $4.67
|$52 - $42.67| = $9.33
|$34 - $42.67| = $8.67
Out of the 6 glove prices in the second row, 3 have an absolute deviation from the mean of $8 or less.
Therefore, a total of 5 glove prices meet the condition
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The given condition is incomplete, the complete question is:
a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?
2.) In the coordinate plane, the line with equation y = 5x - 10 crosses the x-axis at the point with coordinates (a, b) What is the value of a? Explain or show your work.
Answer:
6y
Step-by-step explanation:
because if u divde
Answer:
(2,0). First use a graphing calculator called demos. graph the y=5x-10
Once you graph the equation. Look for the cooordinates of the graph. One the coordinates are 2,0
Step-by-step explanation: Hope this helps!! Mark me brainliest!! Have a great spring break!! :))
what percentage of fat are in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories?
The percentage of fat in a 200 calorie peanut butter sandwich is 40%.
To find the percentage of fat in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories, we need to use the formula:
Percentage of fat = (Calories of fat / Total calories) x 100
Let's substitute the given values in the above formula:
Calories of fat = 80
Total calories = 200
Percentage of fat = (80/200) x 100 = 40%
Therefore, the percentage of fat in a 200 calorie peanut butter sandwich is 40%.
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Pls help ASAP. Will mark BRAINLIEST if answered CORRECTLY!
Diameter = 16 mm
Radius = Diameter/2
= 16/2
= 8 mm
Total height of figure = 32 mm
Height of cylinder = 19 mm
Height of cone = 32 - 19
= 13 mm
Volume of cylinder = πr²h
Substituting the values of r and h in above formula,,
[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]
Hence, Volume of cylinder is 3820.17 mm³
Now,
Volume of cone = 1/3 πr²h
[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]
Hence, Volume of the cone is 871.26 mm³
Volume of composite figure = Volume of cylinder + Volume of cone.
= 3820.17 + 871.26
= 4691.43 mm³
Therefore, Volume of the composite figure is 4691.43 mm³.
what is the future value of 6000 earning 18% interest, compounded monthly for 8 years
Answer:
To calculate the future value of an investment earning compound interest, we can use the formula:
FV = P(1 + r/n)^(nt)
where:
FV is the future value
P is the principal (starting amount)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, we have:
P = 6000
r = 0.18 (18% annual interest rate)
n = 12 (compounded monthly)
t = 8
Substituting these values into the formula, we get:
FV = 6000(1 + 0.18/12)^(12*8)
FV = 6000(1.015)^96
FV = 6000(3.045)
FV = 18270
Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.
What is 50. 7 / 7 bc im not sure I understand
The value of 50.7 / 7 is approximately equal to 7.24285714.
The given expression is 50.7 / 7.
Creating equal groupings or determining how many individuals are in each group after a fair distribution is the basic objective of division.
To simplify the expression, we need to perform the division operation.
In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
To solve this, we can perform the following steps:
First, we can write the given expression as:
50.7 ÷ 7
Then, we can perform the division operation as shown below:
50.7 ÷ 7
= 7.24285714 (rounded to 8 decimal places)
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t-test is used when you have two samples or data coming from 2 groups, and you want to compare whether or not they're distinct (in other words, is the data coming from 2 separate populations, or not?)
The result is the t-statistic, which is used to compare the two samples.
The t-test is used to compare the means of two independent samples. The formula for the t-test is:
[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],
where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.
To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.
Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).
Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.
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Select the correct location on the image.
Marta simplified this expression.
4 logs z logs 22
log, 3x
In which step did she incorrectly apply a property of logarithms?
-
Step 1
Step 2
Step 3
Step 4
=
4 log5 x + log5 2x - log, 3x
log, 4x + logs 2x - log5 3x
log, 8x²- log5 3x
= logs (3x)
logs (3x)
||
log5 x∧4 + log5 2x - log5 3x - correct. The property of logarithms to be used a log b = log a∧b.
What is logarithm?A logarithm is a mathematical function that represents the relationship between the logarithm of a number and its actual value. In simpler terms, a logarithm is the exponent to which a base must be raised to get a certain value.
According to question:4 log5 x + log5 2x - log5 3x
log5 4x + log5 2x - log5 3xlog5 8x²- log5 3x log5 (8x²/3x)log5(8/3 x)Marta incorrectly applied a property of logarithms at step 1:
log5 4x + log5 2x - log5 3x - incorrect
log5 x∧4 + log5 2x - log5 3x - correct
The property of logarithms to be used:
a log b = log a∧b.
Therefore at step 1 she incorrectly applied.
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which number is absent in the first 31 digits of π
The number which is absent in the first 31 digits of the pi is 9
The digit that is absent in the first 31 digits of pi is the digit 9. Pi is an irrational number with an infinite number of decimal places, and it is believed to be a random sequence of digits. However, the absence of the digit 9 in the first 31 digits of pi is just a coincidence and has no special mathematical significance.
It is important to note that the digits of pi are not random in the strict sense of the word, but they appear to be so, and they follow a pattern that has yet to be fully understood by mathematicians. The quest to discover the properties of pi has been ongoing for centuries, and it continues to be a fascinating and important area of research in mathematics.
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The given question is incomplete, the complete question is:
Which number is absent in the first 31 digits of pi
Whats the highest degree x^4-3x^2+9x
Answer:
4th degree
Step-by-step explanation:
When you are looking for the degree of an expression or equation, you just look for the biggest exponent.
Here, there is an
"x to the 4th power",
a "minus3 to the second power" and
a "9x" (which is a power of 1)
So the biggest exponent is 4...4th degree. That's it!
which factors could be part of the function so that the function has a decreasing end behavior on the right? select all that apply. f(x)
The function f(x) has a decreasing end behaviour on the right when its leading coefficient is negative and its degree is greater than or equal to 2.
This means that the terms in the function must be decreasing from left to right and the last term must be negative. To illustrate, an example of a function with a decreasing end behaviour on the right could be
f(x) = -2x2 + 3x + 4.
The leading coefficient is -2, which is negative, and the degree is 2, which is greater than or equal to 2. The terms decrease from left to right, and the last term is negative, which both fulfil the requirements for the function to have a decreasing end behaviour on the right.
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The factors that could be part of the function so that the function has a decreasing end behavior on the right are as follows: - A negative coefficient of the highest degree term.
- An odd degree of the highest degree term and a negative coefficient.
- An even degree of the highest degree term and a negative coefficient.
Explanation:
A function's end behavior refers to what happens to the function's values as x approaches positive or negative infinity. A function's end behavior is said to be decreasing if the values of the function decrease as x approaches infinity, and increasing if the values of the function increase as x approaches infinity.
There are three cases when the function has a decreasing end behavior on the right:
1. If the highest degree term has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -2x³ - 4x² + 3x + 6 will have a decreasing end behavior on the right.
2. If the highest degree term is odd and has a negative coefficient, the function will have a decreasing end behavior on the right.
For example, the function f(x) = -x⁵ + 2x³ - x will have a decreasing end behavior on the right.
3. If the highest degree term is even and has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -4x⁶ + 3x⁴ - 2x² + 1 will have a decreasing end behavior on the right.
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Geometry textbook has a mass of 59 grams. The textbook is in the shape of a restangular prism with dimensions.
5 cm
16 cm
10 cm
Find the density of the terkbook. Round your answer to the nearest ten-thousandth.
The density of the textbook which is in the rectangular prism with dimensions is 0.0738 grams per cubic centimeter.
Define density.
Density is the mass of a component per unit volume.
→d = M/V,
where d is density, M is mass, and V is volume, is the expression for density. Grams per cubic centimeter are a standard unit of measurement for density.
The volume of a component = length*breadth*height
Given:
length = 16cm; breadth = 10cm; height = 5cm; Mass = 59grams
The volume of the book = 16 * 10 * 5
= 800 cm³
The density of the textbook = Mass/volume
= 59/800
Density = 0.07375 g/cm³
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hi what is 2x -9x =5x so x = ?
Answer:
-3x
Step-by-step explanation:
FIrst you subract 2 from both sides then eliminate the x's
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral tris are all 9 feet long, and the height of the equilateral triangle is 7.8 feet. The pyramid's slant heigh feet. What is its surface area?
If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.
How to find the surface area?To solve this problem, we can use the formula for the surface area of a pyramid:
Surface area = base area + (1/2) x perimeter of base x slant height
First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:
Area = (square root of 3) / 4 x (side length)^2
Substituting the given values, we get:
Area = (square root of 3) / 4 x 9^2
Area = (square root of 3) x 20.25
Area = 11.06 (rounded to two decimal places)
Next, we need to find the perimeter of the base, which is simply 3 times the side length:
Perimeter = 3 x 9
Perimeter = 27
Finally, we can use the given slant height to find the surface area:
Surface area = 11.06 + (1/2) x 27 x 8.1
Surface area = 11.06 + 109.35
Surface area = 120.41 square feet (rounded to two decimal places)
Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.
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Which value represents |-50|?
Answer:50
Step-by-step
Answer:
Answer is D
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50
(+8) - (+3) = (+8) + (-3)
pls help i need this today
Answer:
In a circle, an exterior angle is formed when a side of a triangle is extended. The measure of the exterior angle is equal to the sum of the measures of the two intercepted arcs.
Let x be the measure of the exterior angle. Then we have:
x = 84° + 108°
x = 192°
Therefore, the measure of the exterior angle is 192°.
People of different ages were asked the question "Do you listen to audiobooks?” The bar chart displays the percentage of "yes” responses in each age group.
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).
What is percentage?Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol “%” and is used to compare values or express change. It can be used to compare two or more numbers, to show how much one number is a percentage of another, or to indicate the rate of change. In mathematics, percentages are often used to compare the size of one number to the size of another number.
The bar chart shows that the percentage of people who responded “yes” to listening to audiobooks increases with age. Only 18% of people aged 18-24 said they listen to audiobooks, while 30% of people aged 25-34 and 44% of people aged 35-44 responded positively. The percentage continues to increase with age, with the highest percentage of people aged 45-54 saying they listen to audiobooks (54%).
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).
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No, since the ratios do not constitute a whole. Option(a) is the required response to the posed query.
What is a bar chart and pie chart?A collection of categorical data can be summarised using a bar chart, and continuous data can be made categorical using auto-binning. The bar chart uses several bars to show data, with each bar denoting a distinct category.
A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarise a collection of nominal data. This kind of chart consists of a circle with numerous parts. A specific group is represented by each segment. A pie chart is useful for organising and displaying data by proportion of the total.
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The rest of the question is,
Would it be appropriate to display the data with a pie chart?
a). No, because the proportions are not parts of a whole.
b). No, because the data categories are too broad.
c). Yes, because the data are grouped into categories.
d). Yes, because the data can be represented by a relative frequency compared to the whole.
1. consider the sequence defined for positive integers n. which elements of this sequence are divisible by 5? what
The elements of the sequence that are divisible by 5 occur every third term, while the elements divisible by 13 occur every fourth term. There are no elements of the sequence that are divisible by 65, since there are no elements that are divisible by both 5 and 13.
To find which elements of the sequence are divisible by 5, we need to find the remainder of each element when divided by 5. Using the first few terms of the sequence, we get:
a₁ = -1, a₂ = 0, a₃ = 5, a₄ = 13, a₅ = 29, a₆ = 61, a₇ = 125, a₈ = 253, ...
To check if an element is divisible by 5, we only need to look at the units digit of the number, since any multiple of 5 ends in 5 or 0. From the sequence, we can see that the units digit of a₃ is 5, so a₃ is divisible by 5. To find any other elements that are divisible by 5, we can look for a pattern in the units digits of the terms. We can see that the units digits of the terms cycle through 5, 3, 1, and 9. Since 5 appears in the cycle, every third term of the sequence will be divisible by 5. Therefore, the only elements of the sequence that are divisible by 5 are a₃, a₆, a₉, a₁₂, and so on.
To find which elements of the sequence are divisible by 13, we can use a similar approach. We need to find the remainder of each element when divided by 13. From the sequence, we can see that the units digit of a₄ is 3, so a₄ is not divisible by 13. To find any other elements that are divisible by 13, we can look for a pattern in the remainders of the terms. We can see that the remainders cycle through 3, 8, 6, and 10. Since 10 appears in the cycle, every fourth term of the sequence will be divisible by 13. Therefore, the only elements of the sequence that are divisible by 13 are a₄, a₈, a₁₂, a₁₆, and so on.
To find if any elements of the sequence are divisible by 65=5.13, we need to find elements that are divisible by both 5 and 13. From our analysis above, we can see that a₃ is the only element of the sequence that is divisible by 5, and a₄ is the only element that is divisible by 13. Therefore, there are no elements of the sequence that are divisible by 65, since the only way a number can be divisible by 65 is if it is divisible by both 5 and 13.
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Complete question:
Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5? What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?
10 more than the product of 2 and a number value
Answer:
10 + 2x
also,
2x + 10
Step-by-step explanation:
"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)
"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.
"product" means multiplying. So the "product of 2 and a number" is 2x.
So to translate this word phrase into an algebraic expression, you get:
10 + 2x
but also 2x + 10 is the same thing.