Answer:
see below
Step-by-step explanation:
1. study hard and go to a good college and then find a good job.
2. be intelligent on spending and save money to invest in the financial markets
3. buy a few life insurance policies with living benefits.
4. find a niche on social media and create contents to attract followers, and then invest the earnings in stock market or bond market.
5. invest in real estate
6. start a small business and then grow into franchise.
Translate these statements into English, where the domain for each variable consists of all real numbers.
a) ∀x∃y(x < y)
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
c) ∀x∀y∃z(xy = z)
a) ∀x∃y(x < y): For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0)) : For any numbers x and y if x is greater tha or equal to 0 and y is greater than or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z) : For any numbers x and y there exist number z such that the product of x and y is equal to z.
We know that a mathematical statement is nothing but a sentence which is either true or false.
We need to translate these statements into English.
The meaning of some mathematical symbols:
∀ : for all
∃ : there exists exactly one
∧ : and
Here, x, y, z are real numbers.
Consider given mathematical statements.
a) ∀x∃y(x < y)
For all values of x there exist number y such that all x are less than y.
b) ∀x∀y(((x ≥ 0) ∧ (y ≥ 0)) → (xy ≥ 0))
For any numbers x and y if x is greater tha or equal to 0 and y is greater tha or equal to 0 then their product is greater than or equal to 0.
c) ∀x∀y∃z(xy = z)
For any numbers x and y there exist number z such that the product of x and y is equal to z.
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What fraction is not greater than 1/2? 7/8 4/6 3/5 2/5
Answer:this is so ez
Step-by-step explanation: 2/5
A blood test indicates the presence of a particular disease 96% of the time when the disease is actually present. The same test indicates the presence of the disease 0.8% of the time when the disease is not present. Two percent of the population actually has the disease. Calculate the probability that a person has the disease, given that the test indicates the presence of the disease.
The probability of a person that has the disease and indication of the test also shows the presence of the disease is given by 0.92.
Let us consider 'A' represents the test indicate the presence of disease when it was actually present
A = 96%
= 0.96
And 'B' represents the population percent actually has the disease
B = 2%
= 0.02
A' represents the population who represents the disease when actually disease is not present.
A' = 0.08
Probability of a person that has the disease when test also indicates its presence is given by :
P ( A/ B) = P( A∩B) / [ P(A∩B) + P(A'∩B) ]
= ( 0.02 × 0.96 ) / [ ( 0.02 × 0.96 ) + ( 0.02 × 0.08 ) ]
= 0.0192 / 0.0208
= 0.92
Therefore, the required probability of a person having disease when test also indicates it is equal to 0.92.
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a norman window has the shape of a rectangle surmounted by a semicircle. if the perimeter of the window is 30 ft, express the area a of the window as a function of the width x of the window.
The area a of the window as a function of the width x of the window 12x -(4 + π)x2/8
Let y be the height of the window's rectangular part, and let P represent the window's perimeter.
P then equals x plus 2y plus the length of the semicircular part. The radius of the semicircular part is x/2.
So, P = x + 2y + (1/2)(circumference)
P = x + 2y + (1/2)(2)π(x/2)
P = x + 2y +πx/2 = 24
2y = 24 - x - πx/2
y = 12 - x/2 - πx/4 = 12 - (2 + π)x/4
A = xy + (1/2)π(x/2)2
= x(12 - (2 + π)x/4) + πx2/8
= 12x -(2 + π)x2/4 + πx2/8
= 12x - (4 + 2π)x2/8 + πx2/8
= 12x - 4x2/8 - πx2/8
= 12x -(4 + π)x2/8
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Which inequality is graphed below?
-6
-5
Ox≤-2
Ο x > - 2
Stry
x < -2
Ox>-2
The inequality that is graphed on the number line is:
x > -2
Which inequality is graphed below?Here we can see the graph of an inequality on a number line, on it, we can see a blue line that starts with a open circle (which means that we need to use the symbols < or >) at x = -2
Then the line extends to the right of that number, so the allowed values of x are larger than -2, then the inequality graphed is:
x > -2
Thus the correct option is the fourt one.
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Which expressions are equivalent to -4(-25y + 4 + 50y - 8)? Select all
that apply.
A - 100y - 4
B -2(23y - 5 + 27y - 3)
C (100y + 32) - (200y + 16)
D -16 - 100y
E -(-100y + 16 + 200y - 32)
F
- 300y - 48
The two equivalent expressions to the given one are the ones in options C and E.
C (100y + 32) - (200y + 16)
E -(-100y + 16 + 200y - 32)
Which expressions are equivalent to the given one?We want to see which expressions are equivalent to:
-4*(-25y + 4 + 50y - 8)
Let's distribute that product so we will get:
-4*(-25)*y - 4*4 - 4*50y - 4*-8
100y - 16 - 200y + 32 = -(-100y + 16 + 200y - 32)
Then option E is a correct option
And also is C: (100y + 32) - (200y + 16)
If we keep simplifying this we wil get:
100y - 16 - 200y + 32 = -100y + 16
And here we end.
The only two equivalent expressions are E and C.
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Abby was cycling to her school from home .on her way she meets her friend Betty who says that the roads were blocked and the shool was closed.Abby goes back home .
Abby"S distance from home is given with the function : s= 100t 2 +400 t
t is time in minutes .Find after how many minutes , after leaving from home , did Abby meet Betty ?
After 2 minutes of leaving home, Abby meet Betty.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Abby's distance from home is given with the function :
S{t} = 100t² + 400t, where {t} is time in minutes.
The given function is -
S{t} = 100t² + 400t
dS{t}/dt = 0
200t = 400
t = 2
Therefore, after 2 minutes of leaving home, Abby meet Betty.
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There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. 6Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science.
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
Finding the number of teachers:To find the number of teachers that teach only Science we can subtract the number of teachers who teach both subjects from the number of teachers that teach science.
Similarly, to find the number of teachers that teach only Humanities we can subtract the number of teachers who teach both subjects from the number of teachers that teach Humanities.
To find the number of teachers who teach Humanities or science we use the elementary set formula,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)Here we have
Total number of teachers = 100
No of teachers who teach Humanities, n(H)= 25
No of teachers who teach Science, n(S) = 60
No of teachers who teach both Science and Humanities, n(H ∩ S) = 15
The number of teachers who teach science but not humanities
= No of teachers who teach Science - No of teachers who teach both
= 60 - 15 = 45
The number of teachers who teach Humanities but not science
= No of teachers who teach Humanities - No of teachers who teach both
= 25 - 15 = 10
The number of teachers who teach Humanities or Science
As we know n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
The number of teachers who teach Humanities or Science
= n(S) + n(H) - n(S ∩ H)
= 60 + 25 - 15
= 70
Therefore,
The number of teachers who teach:
(a) science but not humanities = 45
(b) Humanities but not science = 10
(c) Humanities or science = 70
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i need to know what it is written out
I think you want to know what written out means? If yes it means when someone writes something down on a book or paper.
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 2 sin Ït + 4 cos Ït, where t is measured in seconds. (Round your answers to two decimal places.)(a) Find the average velocity during each time period.i. [1,2]ii. [1,1.1]iii. [1.1.01]iv. [1.1.001]
The average speed throughout the given time was [1,2] = -2.00 cm/sii. -0.26 cm/siii for [1,1.1]. [1.1,1.01] = 0.17 cm/siv. [1.1,1.001] = 0.02 cm/s
The particle's displacement divided by the passage of time represents its average velocity at each time interval. The displacement of the particle for the above motion equation is given by s = 2 sint + 4 cost. By subtracting the displacement at the beginning and end of the period and dividing it by the change in time, we can determine the average velocity for each time period. As an illustration, the displacement for the time period [1,2] is 2 sin + 4 cos at the beginning of the period and 2 sin + 4 cos at the end of the period. These two figures differ by -4, and one second has passed between them.
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Solve the equation for N
The value of N would be N = q/(9 + 4uz).
What is algebraic manipulation?
Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.
Given:
q - 4Nuz = 9N
To find the value of N, we can use algebraic manipulation.
9N + 4Nuz = q
N(9 + 4uz) = q
N = q/(9 + 4uz)
Hence, the value of N would be N = q/(9 + 4uz).
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Which expression is equivalent to -63y² + 27y?
O-9y(7y-3)
O9y(7y-3)
O-9y(7y + 3)
O9y(7y + 3)
HELP ASAP
Answer:
[tex]9y\left(-7y+3\right)[/tex]Step-by-step explanation:
[tex]-63y^2+27y[/tex]
[tex]-63yy+27y[/tex]
[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]
[tex]9y\left(-7y+3\right)[/tex]
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function:
y = (pie)x Power Function
y = xy Exponential Function
y = x2(2-x3) Polynomial (degree of 2)
y = tan t â cos t Trigonometric
y = s / 1+s Algebraic Function
y = sqrt(x3 â 1) / 1+ 3sqrt(x) Root Function
Not sure on these. Thanks!
A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.
The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.
Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.
Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.
Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.
Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.
Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.
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Type the correct answer in each box. Lmk!
There were 0-5 Listeners when the song was released.
The approximate number of listeners who had heard the song after the hour 5 was 15- below 50
The number of listeners was about 29,458 after hour 5842.62/
How can I explain?Alternative forms
Y= 4,637(1.26)ˣ
292131/50,5842,31/50,5.84262 =10³
5842.62
Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.
Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.
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Select <,>, or = from the drop-down box to compare the two fractions 4/5 and 2/6
Answer:
4/5 < 2/6
Step-by-step explanation:
Hope it helps! =D
umb
1 MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/8 pounds of soil
and a box with 1 3/4pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
No, she does not have enough soil as she needs 4 pounds of soil.
What is meant by soil?
A mixture of organic material, minerals, gases, liquids, and living things make up soil, often known as earth or dirt, and they work together to support life. Certain scientific definitions separate dirt from soil by limiting the former term to just displaced soil.The field of edaphology investigates how soils affect living beings.The study of how soils are formed, described (morphology), and categorized in their natural environments is known as pedology.In engineering, the term "soil" is used to refer to loose material that is present on the Moon and other celestial bodies, as well as other loose material that is found above the bedrock.she as = 2 1/8 + 1 3/4
= 17/8 + 7/4
= 17+ 7 × 2 / 8
= 17 + 14 / 8
= 31/8
= 3 7/8 pounds
≤ 4 pounds.
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4/7 x 3/8 then simplify
Answer:
0.2142857143
Step-by-step explanation:
4/7 × 3/8
=12/56
=0.2142857143.
Which is a better deal 5 tickets for $12.50 or 8 tickets for $20.60
Answer:
5 tickets for $12.50
Step-by-step explanation:
because in that deal the ticket only costs $2.05
and in the second deal which is 8 tickets for $20.60 the ticket costs 2.57
Express the answers to the following operations with the
proper number of significant figures.
(a) (1.600 × 10-¹)(2.1 × 10³)
(b) (1.33)³
(c) 1.93.x 2.651
(d) 4.4/2.200
I don’t understand what it is asking for, help please!
Expressed the answers to the given operations with the proper number of significant figures:
(a) (1.600 × 10-¹)(2.1 × 10³) = 336
(b) (1.33)³ = 2.352637
(c) 1.93.x 2.651 = 5.11643
(d) 4.4/2.200 = 2
What's meant by integers?In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.
A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.
When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.
They're unfit to begin with zero since it'll also be regarded as a single- number .
Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.
a) (1.600 × 10-¹)(2.1 × 10³)
= 1.6 × 2.1 × 10⁻¹⁺³
= 3.36 × 10²
= 336
b) (1.33)³
= 2.352637
c) 1.93 × 2.651
= 5.11643
d) 4.4/2.200
= 2.0
= 2
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6. Insert < >, or = to make the sentence true. (1 point)
3/4 ? 4/7
O>
O<
O=
Answer:
3/4 > 4/7
Step-by-step explanation:
1. Find the LCM of 4 and 7, which is 28
2. Take 3/4 and multiply the numerator and the denominator by 7 (because 7x4=28)
You will end up with 21/28
3. Take 4/7 and multiply the numerator and the denominator by 4 (because 4x7=28)
You will end up with 16/28
Now that the denominators are the same, the fraction with the bigger numerator is the greater fraction. Therefore, 3/4 is the greater than 4/7.
How to solve this problem
Answer:
656 cm sq
Step-by-step explanation:
2 x 10 x 2 x 10 = 400
8 x 2 x 8 x 2 =256
256+400 = 656
Find the measure of a single exterior angle of the regular polygon shown below. If necessary, round to the nearest tenth.
The measure of an exterior angle of the regular polygon shown in the figure is 60°.
What are exterior angle?The angle between a side of a polygon and an extended adjacent side is called its exterior angle.
Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,
We know that, the sum of interior angles of regular hexagon is 720°
Therefore, one interior angle = 720 / 6 = 120°
If we extend a side of the hexagon, (refer to figure attached in solution)
Then, the interior angle and an exterior angle "A" will make a linear pair,
Therefore,
120° + A = 180°
A = 60°
Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.
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Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Applying the Midsegment Theorem, the length of BC is: 10.
What is the Midsegment Theorem?The Triangle Midsegment Theorem states that in a triangle, a line segment connecting the midpoints of two sides is parallel to the third side and is half as long.
From the information given we know that:
E is the midpoint of BC and D is the midpoint of AC.
Thus, applying the Midsegment Theorem, we have:
ED = 1/2(BA)
Substituting the values not expressive, we would get:
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BE = x = 5
Therefore, BC = 2(5) = 10.
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Jamie buys p bags of pears for $8 each and m melons for $6 each.
Write an expression to represent how much Jamie spends in all.
The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y is 8, 0.30x + 0.30y is 6
What is an expression to represent?Set variables to represent the amounts we wish to identify.
Let x = the quantity of p bagsLet y=the quantity of m melonsThen, using these variables, we create equations that fully capture the narrative.Since the overall cost is $8 and $6 the cost of each bags variety varies, we may state0.40x + 0.40y = 8.0.30x + 0.30y =6The total amount of bags purchased together will be represented by the other equation, as Mark said. Once you have those equations, you may solve the problem for the variables x and y by utilising substitution and elimination techniques.The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y = 8, 0.30x + 0.30yTo learn more about expression refer to:
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A bag of m & m is dumped on the table and you count 82 blue pieces.approximately how many m&ms do you expect to be in the entire bag based on the entire class. Round to the nearest whole m&m
Answer: Based on the information provided, we can use the proportion of blue m&ms found in the sample (82 out of some larger total number of m&ms) to estimate the total number of m&ms in the entire bag.
If we let x be the total number of m&ms in the bag, we can set up the proportion:
82/x = blue m&ms / total m&ms
To solve for x, we can cross-multiply and divide by 82:
x = 82 * total m&ms / blue m&ms
x = 82 * 1
x ≈ 82
Therefore, based on the sample, we expect there to be approximately 82 m&ms in the entire bag, rounded to the nearest whole m&m.
It's worth noting that this is an estimation, and the actual number of m&ms in the bag may be different.
Step-by-step explanation:
based on the information in the table, what quantity of reserves would the federal reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.
Now, According to the question:
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
We know that:
Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).
The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.
It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.
So the answer is $0.30 billion + $0.36 billion = $0.66 billion.
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The given question is incomplete, complete question is :
Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?
December 1921
-Currency held by public: $4.59
-Reserve Deposit ratio: 0.095
-Bank reserves: $3.11
-Money supply: $37.3
December 1932
-Currency held by public: $4.82
-Reserve Deposit ratio: 0.109
-Bank reserves: $3.18
-Money supply: $34.0
3xcube+x-200 divide by x-4
When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
What is division?Division is the process of splitting a number or an amount into equal parts.
Given is an expression, 3x³+x-200 which is divided by x-4,
Therefore,
(3x³+x-200) / (x-4)
Step 1)Divide the leading term of the dividend by the leading term of the divisor:
3x³/x = 3x²
Multiply it by the divisor: 3x²(x−4)=3x³−12x²
Subtract the dividend from the obtained result:
(3x³+x−200)−(3x³−12x2) = 12x²+x−200
Step 2)Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x
Multiply it by the divisor: 12x(x−4) = 12x²−48x
Subtract the remainder from the obtained result:
(12x²+x−200)−(12x²−48x) = 49x−200
Step 3)Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49
Multiply it by the divisor: 49(x−4) = 49x−196
Subtract the remainder from the obtained result:
(49x−200)−(49x−196) = −4
Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.
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One side of triangle is 6 more than 2 times the shortest side. The third side is 8 feet more than the shortest side. The perimeter is 54 . Find all three sides.
Answer:
Shortest = 10ft
Middle = 18 ft
Longest = 26ft
Step-by-step explanation:
(btw u can make a diagram to make it easier to visualise)
Let shortest side of triangle be x
So:
1st side = 2x+6
2nd side = x
3rd side = x+8
These sides all equal to 54 ft (perimeter)
2x+6 + x + x+8 = 54
4x + 14 = 54
4x = 40
x = 10
Now that we know the shortest side just sub it back into the equations!
The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
Group of answer choices
68
33
47
40
Number of shingles in the 6th row is 110.
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;
Each row has 7 fewer shingles than the row below it
First row has 75 shingles
Now,
a=75
D=7
n=6
a_{n}=a_{1}+(n-1)d
a6=75+(6-1)7
a6=75+35
a6=110
Therefore, the answer of arithmetic sequence will be 110.
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. (75 -7) On the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
if interest is compounded monthly, then the actual amount you would owe in the situation of part (b)is given by $7000 ✕ 1.01612. What is the actual amount you would owe at the end of the year? (Round your answer to the nearest cent.
If you look at this rationally I believe it will be 7.0 with the odd number.