The given expression is
[tex]2x+x^2[/tex]
So we can write the general rule for the sequence as
[tex]T_x=2x+x^2[/tex]
Recall that the domain of a sequence is the set of natural numbers.
Let us plug in some first few natural numbers to generate the sequence.
When [tex]x=1[/tex], we obtain,
[tex]T_1=2(1)+(1)^2[/tex]
[tex]\rightarrow T_1=2+1[/tex]
[tex]\rightarrow T_1=3[/tex]
When [tex]x=2[/tex], we obtain,
[tex]T_2=2(2)+(2)^2[/tex]
[tex]\rightarrow T_2=4+4[/tex]
[tex]\rightarrow T_2=8[/tex]
When [tex]x=3[/tex], we obtain,
[tex]T_3=2(3)+(3)^2[/tex]
[tex]T_3=6+9[/tex]
[tex]T_3=15[/tex]
When [tex]x=4[/tex], we obtain,
[tex]T_4=2(4)+(4)^2[/tex]
[tex]T_4=8+16[/tex]
[tex]T_4=24[/tex]
Therefore the number sequence produced by the given expression is,
[tex]\boxed{\bold{3, 8, 15, 24.}}[/tex]
Solve the system of equations.
y = 2 - 6x
1/2y - x = 1
Question 4 options:
(0,-2)
(2,0)
(-2,0)
(0,0)
(1,-4)
Answer:
Step-by-step explanation:
We can start by solving the second equation for y:
1/2y - x = 1
1/2y = x + 1
y = 2x + 2
Now we can substitute this expression for y into the first equation:
y = 2 - 6x
2x + 2 = 2 - 6x
Adding 6x to both sides, we get:
8x + 2 = 2
Subtracting 2 from both sides, we get:
8x = -0
Dividing both sides by 8, we get:
x = 0
Now we can use this value of x to find y:
y = 2x + 2
y = 2(0) + 2
y = 2
Therefore, the solution to the system of equations is x=0 and y=2.
The garment factory plans to make 690 sets of garments. It has been done for 5 days, with an average of 75 sets per day. The rest needs to be completed in 2.5 days, how many sets are done on average per day (step-by-step answer)
The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.
We have,
The number of sets produced in the first 5 days.
= 5 x 75
= 375
The number of sets remaining.
= 690 - 375
= 315
The number of sets to be completed in the next 2.5 days.
= 315
The average number of sets to be completed per day.
= 315 / 2.5
= 126
Therefore,
The garment factory needs to produce an average of 126 sets per day in the next 2.5 days to complete the order of 690 sets.
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A set of data items is normally distributed with a mean of 70 and a standard deviation of 8. Convert 70 to a z-score.
z70=
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
When 70 to a z-score, the resulting z-score is 0
Converting 70 to a z-score.From the question, we have the following parameters that can be used in our computation:
Mean = 70
Standard deviation = 8
Score = 70
To convert 70 to a z-score, we make use of the following equation
z = (score - mean)/Standard deviation
Substitute the known values in the above equation, so, we have the following representation
z = (70 - 70)/8
Evaluate the expression
z = 0
Hence, converting 70 to a z-score. we get 0
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A washer and a dryer cost $949 combined. The washer costs $99 more than the dryer. What is the cost of the dryer?
Step-by-step explanation:
Subtract the 99 from 949 then divide by 2
949-99= 425 dollars = price of dryer
( then washer is 425 + 99 )
It takes Sam 40 minutes to jog 5 kilometers. How far can he jog in 60 minutes?
Answer:
7.5 kilometers
Step-by-step explanation:
[tex]\frac{40}{5}[/tex] = [tex]\frac{60}{x}[/tex]
[tex]\frac{40}{5}[/tex] can be simplified to 8
8 = [tex]\frac{60}{x}[/tex] Multiply both sides by x
8x = 60 Divide both sides by 8
[tex]\frac{8x}{8}[/tex] = [tex]\frac{60}{8}[/tex]
x = 7.5
Helping in the name of Jesus.
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d= 163t
D. d= 81.50t
Answer:
C. d= 163t represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours. This is because Rajindri earns $163 for every two hours that she works, which means she earns $81.50 for each hour that she works. Therefore, the equation that relates the number of dollars earned to the number of hours worked is d = 163t.
Step-by-step explanation:
Eulerize this graph in the most efficient way possible, considering the weights of the edges.
We can eulerize this graph in the most efficient way possible by making these vertices have even degree through adding an edge between them.
How do we Eulerize a graph?We can Eulerize a graph by ensuring to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.
A good method to do this is by adding edges between pairs of vertices that have odd degree until all vertices have even degree.
In the scenario above, all the vertices have odd degree except for the first and last vertices. To make these vertices have even degree, we go ahead and add an edge between them.
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What meaning of the statement this?
The meaning of the given statement is concept of a cyclic subgroup in group theory.
What is cyclic group?
In group theory, a cyclic group is a group that can be generated by a single element. That is, it is a group that is generated by a single element a, where any element of the group can be expressed as a power of a.
The order of a cyclic group is equal to the order of its generator. If the generator has order n, then the cyclic group has n elements. The group operation in a cyclic group can be either additive or multiplicative, depending on the notation used.
The statement defines a cyclic subgroup is a subgroup of a group that is generated by a single element. The element used to generate the subgroup is called the generator of the cyclic subgroup. The set of all powers of the generator, including the inverse powers and the identity element, forms the cyclic subgroup.
In other words, the cyclic subgroup generated by an element a of a group is the smallest subgroup that contains a. It consists of all possible combinations of a and its inverse under the group operation.
A group or subgroup is called cyclic when it can be generated by a single element. In other words, if every element of the group can be expressed as a power of a single element, then the group is cyclic.
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Phil owns a ranch business and uses four-wheelers to do much of his work. Occasionally, though, he and his boys will go for a ride together as a family activity. During year 1, Phil put 1,124 miles on the four-wheeler that he bought on January 15 for $12,800. Of the miles driven, only 274 miles were for personal use. Assume four-wheelers qualify to be depreciated according to the five-year MACRS schedule and the four-wheeler was the only asset Phil purchased this year. (Use MACRS Table 1, Table 2, Table 3, Table 4 and Table 5.) (Do not round intermediate calculations. Round your final answers to the nearest whole dollar amount.) b. Calculate the allowable depreciation for year 2 if total miles were 1,610 and personal-use miles were 760 (ignore the §179 expense and bonus depreciation).
Phil owns a ranch business and uses four-wheelers to do much of his work the allowable depreciation for year 2 is $4,096.
To calculate the allowable depreciation for year 2, we need to determine the depreciation basis of the four-wheeler and then apply the appropriate MACRS depreciation rate.
The depreciation basis is the original cost of the asset minus any Section 179 expense deduction and any bonus depreciation claimed.
Since we are ignoring these deductions in this case, the depreciation basis is simply the original cost of the four-wheeler:
Depreciation Basis = $12,800
To determine the MACRS depreciation rate for year 2, we need to consult Table 2 from the MACRS tables, which gives the percentage rates for assets in the 5-year class for each year of the recovery period. According to Table 2, the depreciation rate for year 2 is 32%.
Using this information, we can calculate the allowable depreciation for year 2 as follows:
Depreciation for Year 2 = Depreciation Basis × MACRS Depreciation Rate for Year 2
Depreciation for Year 2 = $12,800 × 32%
Depreciation for Year 2 = $4,096
Therefore, the allowable depreciation for year 2 is $4,096.
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Solve the right triangle using the information given. Round answers to two decimal places, if necessary. a = 4, b = 6; Find c, α, and β.
Step-by-step explanation:
first, remember Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle).
a and b are the legs.
so, in our case
c² = 4² + 6² = 16 + 36 = 52
c = sqrt(52) = 7.211102551... ≈ 7.21
and then remember the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides, A, B, C are the corresponding opposite angles (here also called alpha, beta. gamma would be the 90° angle).
so,
4/sin(alpha) = c/sin(90) = c
4 = c×sin(alpha)
sin(alpha) = 4/c = 4/7.211102551... = 0.554700196...
alpha = 33.69006753...° ≈ 33.69°
we don't need to do that much calculation for the third angle beta, as we know the sum of all angles in a triangle is always 180°.
so,
180 = alpha + beta + 90 = 33.69 + beta + 90
90 = 33.69 + beta
56.30993247... = beta ≈ 56.31°
is 400% of 2 less than 10, greater than 10 but less than 100, or greater than 100?
Answer:
400% of 2 is 8, so it would be less than 10
Step-by-step explanation:
different equation dy÷dx+ytanx=secx
Answer:
First, we rearrange the equation to isolate the y-term on one side:
dy/dx + ytanx = secx
Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1
Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1
Integrating both sides with respect to x, we get: y |secx| = x + C
where C is the constant of integration. Solving for y, we have:
y = (x + C)/|secx|
Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined
Which of the following equations represents a line that is perpendicular to the line that passes through the points below?
(-3,10) (3,8)
The equation of the line that is perpendicular to the line passing through the points (-3, 10) and (3, 8) is y = 3x + 9.
To find a line that is perpendicular to another line, we need to use the fact that the slopes of the two lines are negative reciprocals of each other.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:
slope = (y₂ - y₁)/(x₂ - x₁)
Therefore, the slope of the line passing through the points (-3, 10) and (3, 8) can be found as follows:
slope = (8 - 10)/(3 - (-3)) = -1/3
Now, to find the equation of a line perpendicular to this line, we need to find the negative reciprocal of the slope -1/3, which is 3.
Therefore, the slope of the line perpendicular to the given line is 3.
Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form of a linear equation is:
y - y₁ = m(x - x₁)
where m is the slope of the line, and (x₁, y₁) is any point on the line.
We know the slope of the perpendicular line is 3, and we can choose any point on the line. Let's choose the midpoint of the given points (-3, 10) and (3, 8), which is
=> ((-3+3)/2, (10+8)/2) = (0, 9).
So, using the point-slope form of the equation with m = 3 and (x1, y1) = (0, 9), we get:
y - 9 = 3(x - 0)
Simplifying this equation, we get:
y = 3x + 9
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If a = 3 and b = -2, what is the value of a2 + 3ab ”“ b2?
Lauren over-filled the homemade pecan pie that she was baking for Thanksgiving, so the pie needed additional cooking time. Lauren decided to place a strip of aluminum foil around the edge of the crust so that it would not burn. If Lauren used a pie pan with a 12-inch diameter, how long, to the nearest inch, should the strip of foil be?
A. 19 inches
B. 24 inches
C. 113 inches
D. 38 inches
Applying the circumference formula, the strip of aluminum foil should be about 38 inches long, which corresponds to answer choice D.
How to Calculate Circumference?To determine the length of the aluminum foil strip, we need to find the circumference of the pie pan, which is the distance around the edge of the pan.
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (which is half the diameter).
Since the pie pan has a diameter of 12 inches, the radius is 6 inches. Therefore:
C = 2π(6)
C ≈ 37.7 inches
This is approximately, D. 38 inches.
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Compare the numbers with
>, <, =.
69
-0.43
- 4
-2.3
Answer:
-4 < -2.3 < -0.43 < 69
Step-by-step explanation:
If you look at a number line,
-4 is the first to come and as we approach 0, it's -2.3 and then -0.43. After 0 is only 69 leftover.
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Which graph shows the image of ABC after a rotation about the origin
Answer:
I need the rotation in degrees around the origin (flip around x axis, 90 degrees counter clockwise) or send all of the graph options
Step-by-step explanation:
It's illegal to bet on political races in the United States, but overseas betting on American elections is common. As of this writing, Hillary Clinton is the favorite to win the presidency in 2016, with odds listed as 8/11. Explain what that means, including relating it to probability.
Answer:
57.89%
Step-by-step explanation:
Implied probability = (1 / (odds + 1)) x 100%
Using the odds of 8/11 for Hillary Clinton:
Implied probability = (1 / (8/11 + 1)) x 100% = 57.89%
There is a 57.89% chance that Hillary Clinton will win the presidency.
Given the demand function D(p) = 400-4p².
Find the Elasticity of Demand at a price of $8.
At this price, we would say the demand is:
-Inelastic
-Elastic
-Unitary
Based on this, to increase revenue we should:
-Keep Prices Unchanged
-Lower Prices
-Raise Prices
The Elasticity of Demand at a price of $8 is 0.056.
Given the demand function,
D(p) = 400 - 4p²
The formula to find the elasticity of demand is,
e = p/D
Here p is the price and D is the quantity demanded.
When p = $8,
D = 400 - (4 × 8²) = 144
Elasticity of demand = 8 / 144 = 0.056
Hence the elasticity of demand is 0.056.
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The length of a rectangle is 2x+ 5 units and the width is 7x+ 1 units. Find the area of the rectangle.
FIND THE SUM OF GEOMETRIC SERIES 3+2.55+2.1675+1.842375+...
The sum of geometric series 3+2.55+2.1675+1.842375+...
Hence, the correct option is B.
To find the sum of a geometric series, we can use the formula
S = a(1 - [tex]r^{n}[/tex]) / (1 - r)
Where
S = sum of the geometric series
a = first term of the series
r = common ratio of the series
n = number of terms in the series
In this case, we can see that the first term is 3 and the common ratio is 2.55/3 = 0.85. We can also see that there are an infinite number of terms in the series.
Using the formula for an infinite geometric series, we can simplify the formula to
S = a / (1 - r)
By putting these values we have, we get
S = 3 / (1 - 0.85) = 20.
Hence, the sum of the geometric series is 20.
Hence, the correct option is B.
The question is incomplete and the complete question is '' FIND THE SUM OF GEOMETRIC SERIES 3+2.55+2.1675+1.842375+...
A. 8
B. 20
C. 12
D. 4 ''
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I’m stuckkkk please helpppp
The hiking trial at the state park that is the longest would be D. Hilltop
How to find the longest hiking trail?To find the hiking trail that is longest, convert the lengths shown to one form so as to see which is the longest.
Mammoth = 8.005 kilometers
Brookside = 8. 7 kilometers
Wild Rose = 8, 080 meters = 8. 08 kilometers
Hilltop = 8 kilometers 800 meters = 8. 8 kilometers
This then shows that the hiking trail that is the longest in the state park is the Hilltop trail which goes for 8. 8 kilometers.
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a. ¿Cuál es el pago mensual de la hipoteca a 25 años, de $200,000 al 4% al primer centavo?
1. 7/8 + 1 1/4
2. 1 2/6 + 2 3/8
3. 2 3/4 + 1 1/6
4. 2 2/7 - 1
Answer:
1. 17/8 2. 89/24 3. 47/12 4. 9/7
Answer:
1) 29
2) 57
3) 91
4) 15
Step-by-step explanation:
1) 7/8 + 11/4
find lcm
lcm=8
multiply through by 8
8×7/8+8×11/4
Gives: 7 + 22
=29
2) 12/6+ 11/4
lcm=12
multiply through by 12
12× 12/6 + 12× 11/4
24 + 33
=57
3) 23/4 + 11/6
lcm=12
multiply through by 12
12× 23/4 + 12× 11/6
=69 +22
=91
4) 22/7 - 1
lcm=7
multiply through by 7
7 ×22/7 - 7 ×1
22-7
=15
Each of P, Q and R had a certain amount of money. P gave some money to Q and R in such a way that the amounts with them were doubled. Now Q gave some money to P and R such that the amounts with them were doubled. Finally R also gave some money with him to P and Q such that the amounts with them were doubled. At this stage, each of them had 240.What was the initial amount with P?
The initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
What is amount?Amount is the sum of money or quantity of something. It is usually measured in numerical values such as dollars, pounds, or euros. It is used to describe the total of something, such as how much money is in a bank account or the total cost of a purchase. Amount can also be used to describe a quantity of something such as the amount of time spent on a project or the amount of people present at an event.
Let us denote the initial amount of money with P, Q and R as P0, Q0 and R0 respectively. We know that P gave some money to Q and R such that their amounts were doubled, which implies that P0 = 2(Q0 + R0). Similarly, Q gave some money to P and R such that their amounts were doubled, which implies that Q0 = 2(P0 + R0). Finally, R gave some money to P and Q such that their amounts were doubled, which implies that R0 = 2(P0 + Q0). Substituting the value of P0 from the first equation in the third equation, we get:
2(Q0 + R0) = 2(P0 + Q0)
2Q0 + 2R0 = 2P0 + 2Q0
R0 = P0
Substituting the value of R0 in the first equation, we get:
P0 = 2(Q0 + R0)
P0 = 2(Q0 + P0)
P0 = 2Q0 + P0
P0 = 2Q0
Finally, substituting the value of P0 in the second equation, we get:
Q0 = 2(P0 + R0)
Q0 = 2(2Q0 + R0)
Q0 = 4Q0 + R0
R0 = 3Q0
Therefore, the initial amount of money with P, Q and R can be calculated as follows:
P0 = 2Q0
Q0 = 3Q0
R0 = 3Q0
Therefore, the initial amount of money with P was 2Q0 = 2 * 3Q0 = 6Q0.
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Which of the following is true for the traditional economy?
Answer:
They barter, or trade (without using money). Economic systems are based on customs, traditions, and beliefs of the past.
Step-by-step explanation: -
A company needs to deliver product to each of their 5 stores around the Dallas, TX area. Driving distances between the stores are shown below. Find a route for the driver to follow, returning to the distribution center in Fort Worth:
a. Using Nearest Neighbor starting in Fort Worth
b. Using Repeated Nearest Neighbor
Using Nearest Neighbor starting in Fort Worth, the route will have a total path length of 183.
How to calculate the valueUsing Nearest Neighbor starting in
Foethliceth:
We take the cheapest way to travel,
19 38 41 D42 F
d+ F A 43 M
Total path length = 19 +43 +38 +41 +42 = 183
Using Repeated Nearest. Neighbor:
The repetitive nearest algorithm says. to tey each veetex as starting point I then choose the best answer.
Feam Fort Worth:
F 19 A 43 M 38 p 4D 42 F
Total path length. = 183
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A wave is traveling at a speed of 3.4m/s has a length of 1.3m. what is its frequency?
The frequency of the wave is 2.62 Hz
Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is to be $500. What is your expected net winnings?
Answer:
Expected Value = -1(999/1000) + 499(1/1000) = -500/1000 = -50 cents
Step-by-step explanation:
The measurements of the angles of a triangle have a ratio of 4:5:6. What are the three angle measurements? Classify the triangle by its sides and its angles.
please help with 21-24
The three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.
The three angles of the triangle 4x, 5x, and 6x, where x is a constant of proportionality.
We know that the sum of the angles of a triangle is always 180 degrees, so we can set up an equation:
4x + 5x + 6x = 180
Simplifying, we get:
15x = 180
Dividing both sides by 15, we get:
x = 12
So the three angles of the triangle are:
4x = 4(12) = 48 degrees
5x = 5(12) = 60 degrees
6x = 6(12) = 72 degrees
all three angles are less than 90 degrees, the triangle is an acute triangle.
Therefore, the three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees and it is a acute triangle.
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