1) the expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
How to write the expression in words1) The expression (23,000-789) × 19 can be written in words using the following steps:
The expression inside the parentheses is the difference between 23,000 and 789, which is 22,211.
The expression is then multiplied by 19, which means it is being increased by 19 times.
So the final expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."
2) The expression 2.6+(88×7) can be read in words using the following steps:
The expression inside the parentheses, 88×7, means 88 multiplied by 7.
The result of the multiplication is 616.
The expression then becomes 2.6 added to 616.
So the final expression in words can be read as "Two point six plus six hundred and sixteen."
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Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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On January 1, Year 2, Kincaid Company's Accounts Receivable and the Allowance for Doubtful Accounts carried balances of $74,600 and $3,700, respectively. During Year 2, Kincaid reported $208,000 of credit sales, wrote off $2,000 of receivables as uncollectible, and collected cash from receivables amounting to $258,900. Kincaid estimates that it will be unable to collect one percent (1%) of credit sales.
What effect will recognizing the uncollectible accounts expense for Year 2 have on the elements of the financial statements?
Multiple Choice
Decrease total assets and net income
Decrease total assets and increase retained earnings
Increase total assets and decrease net income
Increase total assets and retained earnings
The correct answer is: Decrease total assets and net income.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.
When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.
Therefore, the correct answer is: Decrease total assets and net income.
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please help meeeee. What is the value of k?
Answer:
k = 10
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ MYZ is an exterior angle of the triangle , then
4k + 5 + 6k + 10 = 115
10k + 15 = 115 ( subtract 15 from both sides )
10k = 100 ( divide both sides by 10 )
k = 10
Answer:
k = 10----------------------
Exterior angle of a triangle is equal to the sum of remote interior angles.
In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.
Set up equation and solve for k:
4k + 5 + 6k + 10 = 11510k + 15 = 11510k = 100k = 10Therefore the value of k is 10.
Jason bought 91.5 pounds of fruit for a class party. The class ate 0.2 pounds of the fruit. How much fruit is left?
91.3 pounds of fruit are left
Jason bought = 91.5 pounds
class ate = 0.2 pounds
You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.
91.5 - 0.2 = 91.3 pounds
ZA =
Round your answer to the nearest hundredth.
Angle A equals 41.81°
c:
Tentor, Inc., purchases disposable coffee cups on which to print logos for sporting events, proms, birthdays, and other special occasions. The owner received a large shipment of 861 cups this afternoon, and to ensure the quality of the shipment, he selected a random sample of 410 cups and identified 353 as defective.
What is the estimated proportion of defectives in the population? (Round the final answer to 3 decimal places.)
Answer
What is the standard error of the sample proportion? (Round your answer to 3 decimal places.)
Answer
What are the upper and lower bounds for a 98% confidence level? (Round the final answers to 3 decimal places.)
Upper bound is Answer
Lower bound is Answer
It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to√(0.861(1.0.861)/410) = 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?
The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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Amy and Zack each have 24 feet of fencing for their rectangular gardens. Amy makes her fence 6 feet long. Zack makes his fence 8 feet long. Whose garden has the better area? How much greater?
Answer:
The answer is Zack garden
The ratio of union members to nonunion members working for a company is 4 to 5. If there are 140 nonunion members working for the company,
what is the total number of employees?
The total number of employees is 112.
Explain numbers
Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.
According to the given information
Let's use x to represent the total number of employees.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.
So, we can set up the following proportion:
4/9 = x/(x - 140)
To solve for x, we can cross-multiply and simplify:
4(x - 140) = 9x
4x - 560 = 9x
560 = 5x
x = 112
Therefore, the total number of employees is 112.
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A certain test has a population mean (mu) of
285 with a population standard deviation
(sigma) or 125. You take an SRS of size 400
find that the sample mean (x-bar) is 288. The
sampling distribution of x-bar is approximately
Normal with mean:
Answer:
124
Step-by-step explanation:
You'll need a calculator for this one
The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 62 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of 1-mile long roadways with potholes numbering between 51 and 84?
50 Points! Write the expression x^4+5x^2-8 in quadratic form, if possible. Photo attached. Thank you!
The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)
How to solve the expressionIt should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.
One possible substitution is to let u = x^2, so that we can write:
x^4 + 5x^2 - 8 = u^2 + 5u - 8
We can then factor this quadratic expression as:
u^2 + 5u - 8 = (u + 8)(u - 1)
Substituting back u = x^2, we get:
x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)
Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:
(x^2 + 8)(x^2 - 1)
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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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Answer:
B
Step-by-step explanation:
Compute the following
(a) Calculate the scalar projection and projection of (5,3) onto (7,-2)
(b) Interpret this projection graphically
The scalar projection and projection vector of vector (5,3) onto vector (7,-2) can be calculated by using the appropriate formulas and then interpreted graphically.
The scalar projection of (5,3) onto (7,-2) was found to be 29/53, and the projection vector was found to be (203/53, -58/53). This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
What is graph?Graph is a data structure that consists of nodes and edges, which are used to represent relationships between different objects. A graph is often used to represent the real-world relationships between objects such as cities, towns, and roads. Graphs can also represent abstract relationships such as between two people or mathematical formulas. Graphs are widely used in computer science, networking, and mathematics.
(a) Scalar Projection:
The scalar projection of vector A onto vector B can be calculated by using the following formula:
Projection = (A⋅B)/|B|
In this case, the scalar projection of (5,3) onto (7,-2) is:
Projection = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2))
= (35 - 6)/53
= 29/53
Projection Vector:
The projection vector of vector A onto vector B can be calculated by using the following formula:
Projection Vector = (A⋅B/|B|²)B
In this case, the projection vector of (5,3) onto (7,-2) is:
Projection Vector = (5⋅7 + 3⋅(-2))/(7⋅7 + (-2)⋅(-2)) ⋅ (7,-2)
= (35 - 6)/53 ⋅ (7,-2)
= (29/53)⋅(7,-2)
= (203/53, -58/53)
(b) Interpretation Graphically:
The projection of vector (5,3) onto vector (7,-2) can be interpreted graphically as follows:
First, draw the two vectors (5,3) and (7,-2) on a graph. Then draw a line from the origin to the tip of vector (7,-2). This line will represent vector (7,-2). Next, draw a line from the origin to the tip of vector (5,3). This line will represent vector (5,3).
Finally, draw a line from the tip of vector (7,-2) to the tip of vector (5,3). This line will represent the projection vector of (5,3) onto (7,-2). The length of this line will be the scalar projection of (5,3) onto (7,-2).
This graphical representation illustrates the projection of vector (5,3) onto vector (7,-2).
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x=10 3x+5y=20 in the system of equations, what is the value of x
John is making his pasta dish. his mom eats 1/12 of pasta and his brother eats 1/6 of pasta. How much of pasta is left over?
Answer:
1/4 of the pot is left.
Step-by-step explanation:
Let x be the total amount of pasta in the pot.
Then the amount of pasta her mother got= 1x/12
The amount of pasta her brother got= 1x/6
The total amount of pasta he serve= 1x/12 + 1x/6
First, convert them into like fractions, then
The total amount of pasta he serve= 1x/12 + 2x/12 = (x+2x)/12 = 3x/12 = 1x/4
Hence, 1/4 of the pot is left over.
Step-by-step explanation:
Mom: 1/12
Brother: 1/6
1/6 × 2/2 = 2/12
2/12 + 1/12 = 3/12
12/12 (= 1 whole) - 3/12 = 9/12 of pasta is left
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.
What is angle?Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary by angles
m∠4=180°-m∠3 ----> equation B
substitute the equation- B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
therefore
Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary to angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
therefore
This option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of any of tAnswer:
Step-by-step explanation:
he interior angles that of a triangle must be equal to 180 degrees
therefore
This option is true for sure
case E) we have
m∠2+m∠3+m∠5=180°.
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
Describe Volume?In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).
In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.
For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.
In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.
The formula for calculating the volume of air passing through a filter is:
Volume = Filter Area x Airflow Velocity
Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:
Filter Area = Length x Width
Filter Area = 4 ft x 2 ft
Filter Area = 8 square feet
Now we can substitute the values into the formula:
Volume = Filter Area x Airflow Velocity
Volume = 8 sq ft x 100 ft/min
Volume = 800 cubic feet per minute (CFM)
Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
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Given f(x)=3x2−2 and g(x)=7−1/2x2, find the following expressions.
(a) (f◦g)(4) (b) (g◦f)(2) (c) (f◦f)(1) (d) (g◦g)(0)
Answer:
To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.
(a) (f◦g)(4):
To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):
g(4) = 7 - 1/2(4)^2
= 7 - 8
= -1
Now we substitute g(4) = -1 into f(x):
(f◦g)(4) = f(g(4))
= f(-1)
= 3(-1)^2 - 2
= 1
Therefore, (f◦g)(4) = 1.
(b) (g◦f)(2):
To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):
f(2) = 3(2)^2 - 2
= 10
Now we substitute f(2) = 10 into g(x):
(g◦f)(2) = g(f(2))
= g(10)
= 7 - 1/2(10)^2
= -43
Therefore, (g◦f)(2) = -43.
(c) (f◦f)(1):
To find (f◦f)(1), we need to find f(f(1)):
f(1) = 3(1)^2 - 2
= 1
Now we substitute f(1) = 1 into f(x):
(f◦f)(1) = f(f(1))
= f(1)
= 1
Therefore, (f◦f)(1) = 1.
(d) (g◦g)(0):
To find (g◦g)(0), we need to find g(g(0)):
g(0) = 7 - 1/2(0)^2
= 7
Now we substitute g(0) = 7 into g(x):
(g◦g)(0) = g(g(0))
= g(7)
= 7 - 1/2(7)^2
= -17/2
Therefore, (g◦g)(0) = -17/2.
8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
Solve by using matrices.
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
X
= -66, y = [?], z =
Enter
Solving the system of equations using matrices is : = -66, y = 163, and z = 11.
Solving the system of equations using matrices ?To solve this system of equations using matrices, we can write it in the form AX = B, where:
A = coefficient matrix
X = variable matrix (containing x, y, and z)
B = constant matrix (containing the constants on the right-hand side of each equation)
So, we have:
| 2 -1 3 | | x | | 180 |
| -4 2 3 | x | y | = | 225 |
| 3 -4 0 | | z | | 270 |
We can solve for X by multiplying both sides of the equation by the inverse of A:
X = A^-1 * B
First, we need to find the inverse of A. We can do this by using the formula:
A^-1 = (1 / det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
The cofactor matrix is:
| 2 9 6 |
| 12 0 -2 |
| 13 -9 8 |
Taking the transpose of the cofactor matrix gives us the adjugate of A:
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
So, we have:
A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
Multiplying A^-1 by B gives us:
| x | | -66 |
| y | = | 163 |
| z | | 11 |
Therefore, x = -66, y = 163, and z = 11.
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What is the equation of the circle with centre
(1/2, 0)and radius 2?
Responses (attached)
The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.
How to calculate the equationThe equation of a circle with center (a,b) and radius r is given by the equation:
(x - a)^2 + (y - b)^2 = r^2
Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:
(x - 1/2)^2 + (y - 0)^2 = 2^2
Expanding and simplifying, we get:
(x - 1/2)^2 + y^2 = 4 - 1/4
Therefore, the equation of the circle is:
(x - 1/2)^2 + y^2 = 15/4
So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.
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What is a formula for the nth term of the given sequence? 18 , 21 , 24
Answer:
3n+15
Step-by-step explanation:
18, 21, 24
+3. +3
3n
18-3=15
3n+15
Find the inradius of triangle ABC.
Find the circumradius of triangle ABC.
The sides of the triangle are 5, 29, and 42.
Is the graph increasing, decreasing, or constant?
-8 -6 4
A. Decreasing
B. Increasing
C. Constant
-2
4-
2
-2
AY
2
4
6
8
SUBMIT
Is the graph increasing, decreasing, or constant: C. Constant.
What is a graph?In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.
In conclusion, the above is constant, rather than increasing or decreasing.
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is trigonometry hard?
Answer:
yes it is pretty hard but I believe I. you
Workout 461÷4 give your answer as a whole number and a reminder
Step-by-step explanation:
the answer is 115 remainder 1
2 only can you solve associative, identity and inverse of this
The set 2Z is associative under the operation *, has an identity element of 2, and every element (except for 0) has an inverse element.
Solving the associative, identity and inverse of this the setThe set 2Z is defined as follows:
2Z = {2n | n ∈ Z, a * b = a + b}
Associative element:
There exists an associative element in 2Z if, for all a, b, and c in 2Z, the equation a*(bc) = (ab)*c holds.
Let a, b, and c be arbitrary elements of 2Z:
a = 2n₁
b = 2n₂
c = 2n₃
Then we have:
a*(bc) = a(2n₂2n₃) = a(4n₂n₃) = 2n₁ + 4n₂n₃ = 2(n₁ + 2n₂n₃)
(a*b)c = (2n₁2n₂)*2n₃ = (4n₁n₂)*2n₃ = 8n₁n₂n₃ = 2(2n₁n₂n₃)
Therefore, a*(bc) = (ab)*c, and 2Z is associative under the operation *.
Identity element:
There exists an identity element in 2Z if there exists an element e in 2Z such that, for all a in 2Z, the equation ae = ea = a holds.
Let e be an arbitrary element of 2Z:
e = 2n
Then we have:
ae = a2n = a + 2n = 2m, where m = n + (a/2) ∈ Z
ea = 2na = a + 2n = 2m', where m' = n + (a/2) ∈ Z
Therefore, e = 2n is an identity element in 2Z.
Inverse element:
There exists an inverse element in 2Z if, for all a in 2Z, there exists an element b in 2Z such that ab = ba = e, where e is the identity element.
Let a be an arbitrary element of 2Z:
a = 2n
Then we need to find an element b in 2Z such that ab = ba = e = 2.
We have:
ab = ba = 2n*b = 2
Therefore, b = 1/(2n) is the inverse of a in 2Z if n ≠ 0.
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4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years