The 17 th term of each sequence a₁₈ = -5, d=12 is [tex]a_{17}[/tex] = 187.
What is a sequence?
a₁₈ = -5, d=12
[tex]a_{17}[/tex] = a + (n-1)d
[tex]a_{17}[/tex] = -5 + (16)12
[tex]a_{17}[/tex] = 187
succession: the doing of one thing after another. A list of books is presented in alphabetical order. a succession of sonnets that is continuous or connected. a later event, outcome, or repercussion; something that happens after.
A series of numbers is an ordered list. The three dots signify moving forward in the set pattern. Each digit in the sequence is referred to as a word. The first term in the list is 1, followed by the second by 3, the third by 5, and so on.
Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.
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Joseph bought a pair of pants and a t shirt. the pair of pants costs 1,250.00 and the t shirt costs 350.00 less 'than the pair of pants. if 'he gave the cashier three 1,000 peso bill, how much did he change did he receive? please answer correctly
The entrance fee to the fair is $15. You pay $2.50 for each ride you ride. Create a table and graph to represent the total paid as a function of the number of rides you ride.
The cost for x rides is modeled by the linear function:
c(x) = $15 + $2.50*x
A table and a graph for that function are provided below.
How to create a table and graph that represents the amount you pay?Here we know that the entrance fee to the fair is $15, and the cost of each ride on the fair is $2.50
So, if you go to the fair and enter in x rides, the total cost for that will be modeled by the linear function:
c(x) = $15 + $2.50*x
Now let's find a table, to do that we just need to evaluate the function in some values of x, I will use x = 0, x = 1 and x = 2, we will get:
C(0) = $15 + $2.50*0 = $15
C(1) = $15 + $2.50*1 = $17.50
c(2) = $15 + $2.50*2 = $20.00
Then we can write the table:
Number of rides ||| Cost
0 $15
1 $17.50
2 $20.00
Now that we have the table, we just need to graph these 3 points on a coordinate axis, and connect them with a line.
The graph can be seen below.
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BRAINLIEST EXPLAIN HOW U GOT ANSWER
Complete the following:
Write an exponential expression: Let 10 be the base and an even number between 1 and 10 be the exponent.
Then write the exponential expression in expanded form and standard form.
Answer:
10^2 . . . . see below for additional information or versions of the answer(s)
Step-by-step explanation:
You seem to want 10^exponent, where exponent is an even single digit, not zero.
We choose exponent = 2, so your expression is ...
10^2
__
There are several versions of expanded form. One uses exponents. In that form, the expression above is the expanded form.
Another uses multipliers of 1, 10, 100, 1000, and so on. In that form, the expression expands as ...
10^2 = 1×100
Another expanded form uses individual digits of the expanded form with others set to zero
10^2 = 100
The standard form is ...
10^2 = 100.
_____
We suppose your exponential expression might have another multiplier, such as 2.98:
exponential expression: 2.98×10^2
standard form: 298
expanded form 1: 2×10^2 + 9×10^1 +8×10^0
expanded form 2: 2×100 +9×10 +8×1
expanded form 3: 200 + 90 + 8
The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the length.
Answer:
W=12cm
L=36cm
Step-by-step explanation:
We are told L=3W
and P=96
so 96=2⋅W+2⋅3⋅W
8W=96
so W=968=12cm
and L=3⋅12=36cm
hope this helps :)
Write each equation in y intercept form x+2y=10
Answer:
y
=
1
2
x
−
5
Step-by-step explanation:
Answer:
y=x+5
Step-by-step explanation:
divide by 2 on each side
12. Determine whether the cost of renting equipment is sometimes, always, or never proportional. Explain.
The cost of renting equipment is sometimes, always, or never proportional based on the prices attached.
How to illustrate the information?It should be noted tha two sequences of numbers are proportional or directly proportional when their corresponding elements have a constant ratio. It should be noted that this is the coefficient of proportionality.
In this case, the reasoning here is that if all the items have different prices it won't be, however, if the items you are ordering all have the same price they will be proportional.
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how would you limit the domain for it to be one to one f(x)= x^4
Limit the domain to x > 0 for it to be one to one
How to limit the domain for it to be one to one?The function is given as:
f(x)= x^4
The above function is an even function
This means that
f(x) = f(-x)
So, for the function to be one to one, we have to limit the function to only the positive x values
Hence, limit the domain to x > 0 for it to be one to one
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The height of a binary search tree is given as h. what is the maximum number of nodes in the tree?
The greatest number of comparisons each operation in the method add needs, given a binary search tree with n nodes and height h, is O. (h).
What is a binary search?Computer scientists utilize the search method known as binary search to locate a target value within a sorted array. Binary chop, logarithmic search, and half-interval search are other names for it. The binary search compares the target value to the array's center member. If not, the half where the target cannot lie is eliminated, and the search is then carried out on the remaining half while once again comparing the center element's value to the target value. Up till the goal value is found, this process is repeated. if, at the end of the search, the remaining half is empty.
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"one-third of a number is 12 less than the number itself"
translate as an equation not solved
Answer:
1/3 n = n - 12 Cross multiply
n = 3(n - 12)
n = 3n -36
2n = 36
n = 36/2
n = 18
Check:
1/3 (18) = 18 - 12
6 = 6
Hope this helps
Find the center and the radius of each circle. x²+(y-4)²=11
The equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, x^2 + (y - 4)^2 = 11, is in standard form, then
h = 0
k = 4
r = √11
Hence, the equation of the circle x^2 + (y - 4)^2 = 11 has a radius of √11 and a center located at (0 , 4).
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Farmer ed has meters of fencing, and wants to enclose a rectangular plot that borders on a river. If farmer ed does not fence the side along the river, what is the largest area that can be enclosed?.
The largest area that can be enclosed will be 2812.5 square meters.
The perimeter of a rectangle is given as:
2L + 2W ∴ L = length and W = width
As the farmer does not want to fence the side along the river, then the formula will be:
P = L + 2w
Now
150 = L + 2w
L = 150 - 2w
Here the area is LW
Area = (150 - 2W)(W)
After solving we get
150 - 2W = 0 or W = 0
150 - 2W = 0
2W = 150
W = 75
Now, there are two solutions whether 0 or 75
Let's find their average 0+75 / 2 = 37.5
Now L = 150 - 2(37.5)
L = 150 - 75
L = 75
As the dimensions are L = 75 and W = 37.5
Area = L x W = 75 x 37.5 = 2812.5 square meters
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The complete question is:
Farmer Ed has 150 meters of fencing and wants to enclose a rectangular play that borders a river. If farmer Ed does not fence in the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?
Write each arithmetic series in summation notation. 100+90+80+ . . . . . . +10
The algebraic expression or sigma (summation) notation is given by:
∑ = 10(100 + 10)/2
And its value is ∑ = 550
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
100+90+80+ . . . . . . +10
a1 =100an = 10n = 10∑ = 10(100 + 10)/2
∑ = 10(110)/2 = 5(110)
∑ = 550
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You make $7.25/hr and your boss
promises at least 3 hours but no
more than 18 hours per week.
Payroll (FICA) taxes of 7.65% are
withheld from your paycheck.
Be sure to deduct your tax
The question's payroll (FICA) taxes total 0.2295.
Considering the information provided,
7.65% of payroll (FICA) taxes
Boss promises a minimum of 3 hours each week and not more than 18 hours.
We have, 3 × 0.0765
= 0.2295
Amount of payroll taxes that will be taken out of your paycheck.
= 0.2295
FICA Taxes: The Federal Income Contributions Act, also known as FICA, is the name of the payroll tax deduction used in the United States to pay for Social Security and Medicare. Tens of millions of seniors, Americans with disabilities, and children receive financial and medical benefits from those well-known government programs. Both employees and the employers they work for are jointly liable for FICA taxes.
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Element X decays radioactively with a half life of 15 minutes. If there are 420 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 4 grams?
If there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
Given that the element X decays radioactively with a half life of 15 minutes.
We are required to find the time that would take the 420 grams of element X would take the element to decay to 4 grams.
Radioactive decay is basically the emission of energy in the form of ionizing radiation.
4=420*[tex](1/2)^{x/15}[/tex]
x=15* [tex]log_{2}[/tex] (105)
x=15*log (105)/log (2)
x=15*2.0212/0.3010
x=30.318/0.3010
x=100.72
After rounding it will be 100.7 of a minute.
Hence if there are 420 grams of Element X, then it would take 100.7 of a minute to take the element to decay to 4 grams.
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I really need help with how to do this . I am confused . Thank you
Answer:
You could measure the distance from both of the lasers and divide by 2 to know the middle of the line. Then draw a straight line from the middle of the line joining the lasers, to you.
Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-6=3x+2x
-6=5x
x=-6/5
Answer:
x = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
- 2x = 3x + 6 ( subtract 3x from both sides )
- 5x = 6 ( divide both sides by - 5 )
x = - [tex]\frac{6}{5}[/tex]
What is the next fraction in this sequence? Simplify your answer.
4/5, 13/20, 1/2, 7/20,....
The next fraction in this sequence is 1/5
Arithmetic sequenceArithmetic sequence are sequence that are separated by a common difference.
Given the sequence below:
4/5, 13/20, 1/2, 7/20,....
The fractions expressed as percentage is given as:
80, 65, 50, 35...
The nth term of the sequence is Tn = a+(n-1)d
T5 = 80+(5-1)(-15)
T5 = 80+(4)(-15)
T5 = 80 - 60
T5 = 20
Express 20% as a fraction
20% = 20/100 = 1/5
Hence the next fraction in this sequence is 1/5
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Sanjay's dad has asked sanjay and his little brothers to rake the leaves in their yard. they rake all afternoon and fill a number of bags with leaves. then, when sanjay isn't looking, his brothers empty 4 of the bags to make a giant leaf pile! sanjay is frustrated that only 6 bags of leaves remain. which equation can you use to find the total number of bags b that sanjay and his brothers fill with leaves?
The given situation presents a word problem and can be solved by converting the word problem into an equation.
Word problem is a few sentences representing a real-life scenario where a problem needs to be solved by method of a mathematical calculation.
According to the given situation:
Total number of bags – number of bags emptied=number of bags left
Total number of bags filled= b
Number of bags emptied=4
Number of bags left=6
Hence,
b-4=6
Solving the equation,
b=6+4
b=10
Note: The provided question does not include the options of equation. Possible options are:
4b=6; b+4=6; b/4=6; b-4=6
Hence, the equation used to determine the numbers of bags initially filled is b-4=6 and number of bags are 10 bags.
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write 1/16 as a power of 2
Answer:
256
Step-by-step explanation:
According to the rule of exponents: 16 to the power of 2 can be written as 162.
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
Rotation symmetry is also called mirror symmetry.
false, reflection
Rotation symmetry is also called mirror symmetry.
false, reflection
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated at 90°, however, the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles, and other spheroids
Rotational symmetry is symmetry with respect to some or all rotations in m-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation.
Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations.
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Please please please help please asap!!!
........................................................................................
Answer:
Options 3 and 6
[tex]3i\sqrt{3} \\-3i\sqrt{3}[/tex]
Step-by-step explanation:
hope this helps
Pls help me this is due Monday 9/12/22
It’s about statements in geometry and I’m confused
Answer:
what are the given options? :)
(6x³)² I need answer asap please and thank you
URGENNTTT !!! ITS EASY BUT I NEED CLARIFICATION
You can solve this by isolating the variable.
1.
30 + a = 40
You can isolate a by subtracting 30 from each side
30 + a - 30 = 40 - 30
a = 10
2.
500 + b = 200
Subtract 500 from each side
500 + b - 500 = 200 - 500
b = -300
3.
-1 + c = -2
Add 1 to each side
-1 + c + 1 = -2 + 1
c = -1
4.
d + 3567 = 0
Subtract 3567 from each side
d + 3567 - 3567 = -3567
d = -3567
Consider the U.S. Shirts function, C(s) = 8s + 15. Explain me how to solve it please.What number would be S and what would be C
( - ∞ , + ∞) is the possible domain and range for this situation.
What is the domain function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Because C(s) = 8s + 15 one off function.
So, s ∈ R
80 the domain is defined as ( - ∞ , + ∞)
b) because s ∈ R
So , C(s) ∈ ( - ∞ , + ∞)
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The complete question is -
Consider the U.S. Shirts function, C(s) = 8s + 15. What expression in the function equation represents: a. the domain of the function? b. the range of the function? 5. Describe the possible domain and range for this situation.
Find the value of a. The diagram is not to scale.
21°-
129
(2q+6)°
9°
Answer:
−2322q−6945
Step-by-step explanation:
Simplify 129(2q+6) * 9 to 1161(2q + 6)
Expand by Distributing terms
21 - (2322q + 6966)
Remove parentheses.
21 - 2322q - 6966
Collect like terms.
-2322q + (21−6966)
Simplify
-2322q - 6945
Done
The cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit. For how many hours is the cost of renting a pool the same for both plans?
If the cost of renting a pool at an aquatic center is either 30 per hour or 20 per hour with a 40 non-refundable deposit, then the cost of renting the pool is the same for both plans for 4 hours.
The number of hours for which the cost of renting the pool will be the same for both plans can be calculated by using an algebraic expression.
An algebraic expression is a type of equation that consists of both numbers and letters.
An algebraic expression for this problem can be given as,
30(x) = 20(x) + 40
Where x is equal to the number of hours.
The value of x can be calculated by rearranging the equation,
30(x) - 20(x) = 40
10(x) = 40
x = 40 ÷ 10
x = 4
Thus, the number of hours for which the cost of renting the pool same for both plans is 4 hours.
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question is in the picture
Answer:
after 4 years her salary would be $48,000
salary after t years: y=2000t+40000
can someone please help me
Answer:mhmm cool b
Step-by-step explanation:
|||
Finding the average rate of change of a function given its...
Find the average rate of change of g (x) = -2x²-x from x = 1 to x = 6.
Simplify your answer as much as possible.
0
18 08
X
k
Answer:
Mind you that the average rate of change is the gradient. Commonly we get it by using the formula that requires us to have also the y coordinates.
we can find them by plugging in the x-values in the function g(x)
x=1
[tex]g(1)=-2(1^{2} )-1\\g(1)=-3\\\\g(6)=-2(6^{2})-1\\ g(6)=-73[/tex]
now we have the points (1,-3) and (6,-73)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
that is the formula we will use
[tex]=\frac{-73-(-3)}{6-1} \\=\frac{-70}{5} \\=-14[/tex]
