Let
S = 1 + 2 + 3 + … + (n - 2) + (n - 1) + n
Reversing the order of terms, we have
S = n + (n - 1) + (n - 2) + … + 3 + 2 + 1
and we observe that terms in the same position on the right side add up to n + 1.
2S = (1 + n) + (2 + (n - 1)) + (3 + (n - 2)) + … + (n + 1)
There are n terms in the sum, so each the right side is simply n copies of n + 1, and
2S = n (n + 1)
S = n (n + 1)/2
Now,
17 + 18 + 19 + … + 41 + 42 + 43
= (1 + 2 + 3 + … + 41 + 42 + 43) - (1 + 2 + 3 + … + 14 + 15 + 16)
= (S with 43 terms) - (S with 16 terms)
= 43 (43 + 1)/2 - 16 (16 + 1)/2
= 810
I am a two-dimensional shape.
I have two pairs of parallel sides.
I have no axis of symmetry.
What am I?
Answer: Non-rectangular Parallelogram
The opposite sides are parallel, but the figure is not a rectangle. It's also not a square either since those figures have an axis of symmetry.
This figure is composed of a parallelogram and a trapezoid.
32 cm
26 cm
40 cm
T
16 cm
1
What is the area of the figure in square centimeters?
Answer:
944cm²
Step-by-step explanation:
Area = Area of parallelogram + Area of trapezoid
Area of parallelogram= l× b= 16×26= 416cm²
Area of trapezoid= h/2(a+b)
where a=26cm, b=40cm, h=16cm
Area of trapezoid= 16/2(26+40)=8(66)=528cm²
Area= 416+528=944cm²
Give 3 example of real life function with rule of correspondence input and output
1.
2.
3.
Here are the examples of functions in real life.
1. ATM
If you want to withdraw money from your account, the amount of money dispensed by the machine is the amount you request{input}.As a result, the amount requested is a function of the amount distributed{output}. The machine will never give you more or less than what you asked for.
2.Places you can drive with Two Gallons of Fuel
If you still have two gallons of gas in your car's tank, you can visit several locations before running out of gas. As a result, there could be several answers to this question. In this case, the input is two gallons of fuel, and the output is a list of places you can visit with that amount of fuel.
3. Number of Sodas in a Vending Machine
The number of sodas you get from a vending machine is determined by the amount of money you put into it. If you put the same amount in twice and choose the same soda, you will get the same number of cans as you did the first time. In this case, the number is determined by the amount fed into the machine.
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Aaron is helping his uncle plant an apple orchard. After picking up a truckload of trees, they plant 12 of them. The next day, they still have 40 trees left to plant. Which equation can you use to find the total number of trees n in the original truckload?
A new apple orchard is being planted by Aaron's uncle. They plant 12 trees after picking up a truckload of them. They still need to plant 40 trees the following day.
The letter (N) is the symbol used to represent natural numbers. Natural numbers are also known as counting numbers, and they begin with the number 1 and continue to infinity (never ending), which is represented by three dots (...)
900n - 9[tex]n^2[/tex] = A(n) = n(900 - 9n)
For the highest A(n), A'(n) = 0, A'(n) = 900 - 18n = 0, 18n = 900, and n = 900/18 = 50.
50 trees should be planted per acre to produce the most apples possible
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4x+2(x+6)=36 ummm.....what?
Answer:
x = 4
Step-by-step explanation:
4x + 2(x + 6) = 36
4x + 2x + 12 = 36
6x = 36 - 12
6x = 24
x = 24
6
x = 4
What is the value of (2.4)3? 72 18.325 13.824 7.2
The cube of 2.4 is 13.824
What is a cube ?A cube can be described as when a number is multiplied three times. This means a product of the same number three times
From the question we are asked to calculate the cube of 2.4
(2.4)³
= 2.4 × 2.4 × 2.4
= 13.824
Hence the cube of 2.4 is 13.824
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Long division 1,755 divided by 27
Answer:
65
Step-by-step explanation:
What is the simplified value of the expression, below, when x = 4 and y = 6? Leave your an
simplified fraction
Show all steps for full credit. Circle your final answer. (4 points).
3x - y/
2y + x please help
Answer:
2
-
2 - 4 ^ 5
Step-by-step explanation:
I will give brainliest if you explain
Answer:
See below
Step-by-step explanation:
The first one scales UP from 4 to 6 F'G'/FG = factor is 6/4 = 1.5
second one scales DOWN from 4 to 3
F'G' / FG = scale factor is 3/4
Third one is scaled DOWN
F'G' / FG = 2/4 = 1/2
Note when scale is DOWN the factor is less than one
when scale is UP , factor is more than one
Evaluate the function f(x)= |x+4|−5 for
Answer:
f(-1) = |-1+4| - 5 = -2
f(0) = |0+4| -5 = -1
f(2) = |2+4| -5 = 1
Rani is making rice pudding. She uses
cup
cup of white rice for every 2 cups
of milk. How many cups of rice does she need when she uses 3 cups of
milk?
Rani will use 3/2 cups of white rice for 3 cups of milk.
What is termed as unitary method?"It is a method in which we obtain the value of a single unit by subtracting the value of multiple units and thus the value of multiple units by subtracting the value of a single unit."
The value of several things is given in the unitary method, and we must either figure out the significance of more or lesser things. To do so, we must first determine the value of one item by division and then determine the value of ever more or fewer items by multiplication.Now, for the given question;
1 cup of white rice is required for every 2 cups of milk by Rani.
Thus,
2 cups of milk ------> 1 cup of white rice.
So, using unitary method. Divide both side by 2.
1 cups of milk ------> 1/2 cup of white rice.
Now, calculate for the 3 cups of milk.
multiplying both side by 3.
3 cups of milk ------> 3/2 cup of white rice.
Therefore, the 3/2 cups of white rice required for the 3 cups of milk.
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6/5 Given that and k are roots of the quadratic equation = h(x-2), where h is a constant. Find the values (5x-6)(x+2) of h and k.
What price do farmers get for their watermelon crops? in the third week of july, a random sample of 40 farming regions gave a sample mean of x bar = $6.88 per 100 pounds of watermelon. assume that is known to be $2.00 per 100 pounds.
We have given a sample size of n=40
Sample mean ¯x=$6.88 per 100 pounds
Population standard deviation= 1.96 per 100 pounds
First, we need to find the value of z α /2 =z (1−0.90/2)
Z (α/2) =z0.05
Z (α/2) =1.645
(a)The required 90% confidence interval is;
¯x ± margin of error
¯x ± z (α/2) * σ/sqrt 40
6.88 ± 1.645 * 1.96/sqrt 40
6.88±0.5097
(6.38,7.38)
Therefore, the lower limit is $6.38 per 100 pounds.
The upper limit is $7.38 per 100 pounds.
The margin of error is 0.50 per 100 pounds.
(b) to have the maximum of E, we use the formula;
n= (z (α/2)×σ/E) ^2
n= (1.645× (1.96/0.41)) ^2
n=61.84≈62
Therefore, the required farming region will be 62.
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Find the magnitude of the net electric field at the origin (created by charges q1 and q2).
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
How to find the magnitude?[tex]q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)[/tex]
[tex]$q_2=6 \mathrm{nC}$[/tex] at (0.6,0)
[tex]$r_1=$[/tex]Distance of [tex]$q_1$[/tex] from origin[tex]$=\sqrt{0.6^2+0.8^2}$[/tex]
[tex]$r_2=$[/tex] Distance of [tex]$q_2$[/tex] from origin [tex]$=0.6$[/tex]
[tex]$\mathrm{k}=$[/tex] Coulomb constant[tex]$=9[/tex]times [tex]10^9 \mathrm{Nm}^2 / \mathrm{C}^2$[/tex]
Electric field is given by
[tex]&E_1=\frac{k q_1}{r_1^2} \\[/tex]
[tex]&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\[/tex]
[tex]&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}[/tex]
[tex]&\theta=\tan ^{-1} \frac{0.8}{0.6} \\[/tex]
[tex]&\Rightarrow \theta=53.13^{\circ} \\[/tex]
[tex]&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\[/tex]
[tex]&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}[/tex]
[tex]&E_2=\frac{k q_2}{r_2^2} \\[/tex]
[tex]&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\[/tex]
[tex]&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}[/tex]
The charge [tex]$q_2$[/tex] is on the [tex]$\mathrm{x}$[/tex] axis itself and it is pointing towards the origin (left side) so the sign will be negative
[tex]E_2=-150 \hat{i}[/tex]
Resultant electric field
[tex]&E=E_1+E_2 \\[/tex]
[tex]&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\[/tex]
[tex]&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}[/tex]
Magnitude of electric field is given by
[tex]&|E|=\sqrt{(-128.4)^2+28.8^2} \\[/tex]
[tex]&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}[/tex]
Magnitude of the net electric field is [tex]$121.6 \mathrm{~N} / \mathrm{C}$[/tex]
Direction is given by
[tex]\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}[/tex]
From the -x axis
[tex](90+77.36)^{\circ}=167.36^{\circ}[/tex]
The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]
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Consider sets a = { x | x is a prime number less than 7} and b = { y | y is perfect square of an integer and y is less than 29}. what is the cardinality of the cartesian product of a and b ?
The cardinality of the cartesian product of A and B is 18.
Cartesian Product of two sets A and B is defined as the set of all ordered pairs (a,b) where a∈A & b∈B.
Cardinality of a set is defined as the number of elements in that particular set.
For example, for a set A={2,6,4} , the cardinality is 3.
Given set A= { x | x is a prime number less than 7}
A={2,3,5}
set B = { y | y is perfect square of an integer and y is less than 29}
B={0,1,4,9,16,25}
The cartesian product of A and B denoted by AxB will be
AxB={(2,0),(2,1),(2,4),(2,9),(2,16),(2,25),(3,0),(3,1),(3,4),(3,9),(3,16),(3,25),(5,0),(5,1),(5,4),(5,9),(5,16),(5,25)}
The number of elements in AxB is 18.
Therefore , the cardinality of the cartesian product of A and B is 18.
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HELP PLEASEEEI’ll
Make you brainlist
Answer:
Step-by-step explanation:
0,5 0.6 and 0.5 again? sorry i might be wrong if i am my apologies
please help me out with 2, 5, 8, 9, 7, and 10!
Considering the condition for a relation to be a function, we have that:
These items represent functions: 2, 5, 9, 10B.These items do not represent functions: 7, 8, 10A.When does a relation represents a function?A graph represents a function if each value of the input is mapped to only one value of the output.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
Hence:
The table in item 2 represents a function, as each value of x is mapped to only one value of y.The relation in item 5 represents a function, as each value of x is mapped to only one value of y.The table in item 7 does not represent a function, as the input -4 is mapped to two outputs, -2 and 2.The relation in item 8 does not represent a function, as the input 1 is mapped to two outputs, -1 and 1.The graph in item 9 represents a function, as it has no vertically aligned points.The table A in item 10 does not represent a function, as the input -9 is mapped to multiple(four) outputs.The table B in item 10 represents a function, as each value of x is mapped to only one value of y.More can be learned about relations and functions at https://brainly.com/question/12463448
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When analyzing three linear functions, Bill noticed that they all intersect at the point (10,10). What conclusion can Bill come to about the linear function with the largest slope?
a. It has the highest y-intercept.
b. It has the middle y-intercept.
c. It has the lowest y-intercept.
d. Bill cannot conclude anything.
A printing service charges a set-up fee of $10.00 for each order and 8 cents more for each copy. The total cost, C (in dollars), for an order of x copies is given
by the following function.
C(x) = 10.00 +0.08x
What is the total cost for an order of 50 copies?
Answer:
$14 for 50 copies.
Step-by-step explanation:
Given that,
→ C(x) = 10.00 + 0.08x
Then the cost for 50 copies will be,
→ C(50) = 10.00 + (0.08 × 50)
→ C(50) = 10.00 + 4
→ [ C(50) = $14 ]
Hence, the total cost of $14.
Briana wrote an integer. The opposite of her integer is -53. Which of these statements about Briana’s integer must be true?
Select two answers.
Group of answer choices
The integer is 53
The integer has an absolute value of -53
The integer is -53
The integer has an absolute value of 53.
Answer:
The integer is 53The integer has an absolute value of 53.Step-by-step explanation:
The opposite of an integer is the negative of that integer.
The absolute value of an integer is its distance from 0
Describe maysa's error. explain how you would use a model or place-value concepts to help maysa build understanding. give the correct answer in your explanation.
2/3 would use a model or place-value concepts.
What is probability?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.The possible rolls are 1,2,3,4,5,6 total of 6
2 or less than 5 rolls are 1,2,3,4 total of 4
P (2 or less than 5) = total number of choices of 2 or less than 5 / total
=4/6
=2/3
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#15: m∠NST = ____°
need answer
Answer:
∠ NST = 59°
Step-by-step explanation:
∠ NST and ∠ LSN form a right angle , that is
∠ NST + ∠ LSN = 90
3x - 1 + 2x - 9 = 90
5x - 10 = 90 ( add 10 to both sides )
5x = 100 ( divide both sides by 5 )
x = 20
Then
∠ NST = 3x - 1 = 3(20) - 1 = 60 - 1 = 59°
Find a₁for each arithmetic series. Sa₃₀=240 and d=-2
As a reminder, an arithmetic sequence or arithmetic progression (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the progression is constant.
Therefore, the expression for the nth term is
an = a₁ + (n − 1) d
and in general
an = am + (n - m) d.
where d is the difference.
For an arithmetic series with initial term a₁ and difference between terms of d
an = a₁ + (n − 1) d
We are told
d = -2 and
S8 = 240
So,
a1 = 240 = a1 + ( 30 - 1) * ( -2 ) = a1 - 58
a1 = 240+58 =298
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A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected. Everyone on the junior varsity swim team is either a freshman or sophomore. What fraction of the swim team are sophomores?
Using the probability concept, it is found that 60% of the swim team are sophomores.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The sum of the probabilities of all outcomes of an event is of 1, hence:
P(freshman) + P(sophomore) = 1.
The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected, hence:
x + 3/2x = 1.
5/2x = 1
5x = 2
x = 0.4.
Thus:
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Find the coordinates of the point 7/10 of the way from A to B.
(-1/5, 37/70) are the coordinates of a point 7/10 of the way between A and B.
What exactly is the section formula?In coordinate geometry, the Section formula is used to obtain the ratio of a line segment separated by a point, whether in internally or externally.It finds the triangle's centroid, incenter, and excenter.Let P be the point 7/10 of the way from A to B. This implies that it partitions P in the 7:10 ratio (AP/PB = 7/10).
Should use section formula to find the coordinates, which is given as:
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Where,
(x₁, y₁) = A(-4, -7)
(x₂, y₂) = B(11, 5)
m = 7 and n = 10.
Put the values to obtain the x and y coordinates of point P.
y = (7×5 + 10(-7))/(7 +10)
On solving;
y = -1/2
Solve for x coordinates;
x = (7(11) + 10(-4))/(7 +10)
on solving;
x = 37/70
Therefore, the coordinates of a point 7/10 a way from A and B is (-1/5, 37/70).
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How many seals would be needed to replace the ? And keep both sides balanced
Answer:
6 zebras
Step-by-step explanation:
find the length of each segment with the given endpoints
(3, -2) and (-4, 7)
Exact Distance: [tex]\sqrt{130}[/tex] units
Approximate Distance: 11.4018 units
===================================================
Explanation:
Use the distance formula to have the following steps
[tex](x_1,y_1) = (3,-2) \text{ and } (x_2, y_2) = (-4,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-4))^2 + (-2-7)^2}\\\\d = \sqrt{(3+4)^2 + (-2-7)^2}\\\\d = \sqrt{(7)^2 + (-9)^2}\\\\d = \sqrt{49 + 81}\\\\d = \sqrt{130}\\\\d \approx 11.4018\\\\[/tex]
The exact distance is [tex]\sqrt{130}[/tex] units
This approximates to about 11.4018 units.
Rose, Bill, Jean, and Candice each received different seat numbers to watch the performance. The seat numbers were either 53, 64, 108, or 216. Candice
received the only seat number with a factor of 16. Bill received the seat number that is the greatest multiple of 8 from the group of seats. Rose received the
only seat number that is a prime number. Which seat number did Jean receive?
A .Jean received seat number 53.
B .Jean received seat number 64.
C .Jean received seat number 108.
D .Jean received seat number 216.
It should be noted that the seat number is C
Jean received seat number 108.
How to illustrate the information?It should be noted that from the information, The seat numbers were either 53, 64, 108, or 216. Candice received the only seat number with a factor of 16. This is 64.
Bill received the seat number that is the greatest multiple of 8 from the group of seats. This is 216.
Rose received the.only seat number that is a prime number. This is 53
Therefore, the remaining number is 108.
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|−9| − |−5| i hate next gen but help pls
Answer:
4
Step-by-step explanation:
[tex]\mathrm{-9 = 9, -5 = 5,\:because\:they\:are\:in\:absolute\:value}\\9 - 5 = 4[/tex]
Answer:
-4
Step-by-step explanation:
−9 − (−5)
Multiply
−1 by −5.
−9 + 5
Add
−9 and 5.
you get...
−4
Use the Angle Addition Postulate to find the measure of the unknown angle
Answer:
103
Step-by-step explanation:
61+42 = 103