Let a be the first term in the sequence, and d the common difference between consecutive terms. If aₙ denotes the n-th term in the sequence, then
a₁ = a
a₂ = a₁ + d = a + d
a₃ = a₂ + d = a + 2d
a₄ = a₃ + d = a + 3d
and so on, up to the n-th term
aₙ = a + (n - 1) d
The sum of the first 10 terms is 100, and so
[tex]\displaystyle \sum_{n=1}^{10} a_n = 100 \\ \sum_{n=1}^{10} (a + (n-1)d) = 100 \\ (a-d) \sum_{n=1}^{10} 1 + d \sum_{n=1}^{10} n = 100 \\ 10a+45d = 100[/tex]
where we use the well-known sum formulas,
[tex]\displaystyle \sum_{n=1}^N 1 = 1 + 1 + 1 + \cdots + 1 = N[/tex]
[tex]\displaystyle \sum_{n=1}^N n = 1 + 2 + 3 + \cdots + N = \frac{N(N+1)}2[/tex]
The sum of the next 10 terms is 300, so
[tex]\displaystyle \sum_{n=11}^{20} a_n = 300 \\ (a-d) \sum_{n=11}^{20} 1 + d \sum_{n=11}^{20} n = 300 \\ (a-d) \left(\sum_{n=1}^{20} 1 - \sum_{n=1}^{10} 1\right) 1 + d \left(\sum_{n=1}^{20} n - \sum_{n=1}^{10} n\right) = 300 \\ 10a+145d = 300[/tex]
Solve for a and d. Eliminating a gives
(10a + 145d) - (10a + 45d) = 300 - 100
100d = 200
d = 2
and solving for a gives
10a + 145×2 = 300
10a = 10
a = 1
So, the given sequence is simply the sequence of positive odd integers,
{1, 3, 5, 7, 9, …}
given recursively by the relation
[tex]\begin{cases}a_1 = 1 \\ a_n = a_{n-1} + 2 & \text{for }n>1\end{cases}[/tex]
and explicitly by
[tex]a_n = 1 + 2(n-1) = 2n - 1[/tex]
for n ≥ 1.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
a=1/2b, 2a=b
Step-by-step explanation:
Since angle a is 1/2 the size of angle b, a=1/2b and b=2a. In order to get a numeral answer, you need the number of one of the angles.
What is the area of the smaller rectangle?
Answer:
64 mm^2
Step-by-step explanation:
The area of the rectangles is calculated by multiplying width and length:
for the bigger rectangle:
12*48 = 576 mm^2
for the smaller rectangle:
4*16 = 64 mm^2
Identify any transformations that are used in each image below.
Reflections - how many lines of symmetry and what specific type: vertical (y-axis), horizontal (x-axis), diagonal (y=x or y=-x)
Rotations - of which order or how many degrees/angle of rotation
a. Reflectional symmetry only. The mirror line is vertical along the center of the sunglasses. The left half mirrors over this line to get the right half, and vice versa. There isn't any rotational symmetry because we can't rotate the glasses (some angle between 0 and 360 exclusive of both endpoints) to have the image be the same as the preimage.
---------------------
b. Rotational symmetry only. The puzzle can be rotated 90 degrees and the before and after image will be the exact same. There isn't any reflectional symmetry here.
----------------------
c. Reflectional symmetry and rotational symmetry. Effectively a combination of parts a) and b). We have a horizontal line of symmetry to go with a vertical one. The angle of rotation is 180 degrees.
----------------------
d. Reflectional symmetry and rotational symmetry. Similar to part c). This time the angle of rotation is 360/3 = 120 degrees. There are 3 lines of symmetry and they all pass through a vertex of the triangle, and the symmetry lines are perpendicular to the opposite side.
----------------------
e. Reflectional symmetry and rotational symmetry. We can rotate 180 degrees and not change the image. There are two lines of symmetry which pass through the center, one line is horizontal and the other vertical.
-----------------------
f. Rotational symmetry only. We don't have reflectional symmetry due to the smaller petals not matching up when reflections happen. But we can rotate the figure 120 degrees the same way we can with figure d.
Can y’all help me pls
Answer:
The change in expected height for every one additional centimeter of femur length.
Step-by-step explanation:
The slope represents how the value along the y axis is affected by the value along the x axis. So if x = femur length and y = expected height,
the slope is how the expected height is affected by the femur length.
which is bigger 2m or 275cm
Answer:
275.
Step-by-step explanation:
If you convert 2m into CM you get 200.
If you convert 275 cm into M you get 2.75. So 275cm is bigger.
Raise 10 to the 3rd power then multiply the result by a
Answer:
1000a
Step-by-step explanation:
[tex] 10^3 \times a = 10 \times 10 \times 10 \times a = 1000 \times a = 1000a [/tex]
76. 30 students at a sports event are
wearing purple. This is 40% of the
students at the event. How many
students are at the event?
Answer:
75 students
Step-by-step explanation:
So firstly lets make convert these words to alegbra :
30 people are 40%of the total students at the event meaning that the following equation can be made :
30 = 40% of x (x is the unknown amount of students there)
30 = 40% * x
30 = 0.4x (we can convert the precentage into a decimal by dividing by 100)
Now that we have the equation that 30 = 0.4x we can evalute it and find x :
30=0.4x
30/0.4=0.4x/0.4 (divide by 0.4 on both sides)
75=x
So thats how we get that 75 students were in the event in total.
A display case of hat pins are marked 5 for $3. If Patty has $21, how many hat pins can Patty get? (assume no other taxes and fees)
What is 125.1 ÷ 6 and if you do how do you do it?
ans = 20.85
hope it helps...!!!
what is the radius of D
6 cm
12 cm
3 cm
24 cm
Answer:
3 Is the Radius
Step-by-step explanation:
Diameter is always 2R (R for radius), as they have given us the diameter of 6 we can conclude the answer by forming a simple equations
D=2R
6=2R
3=R
Your answer is incorrect
In the past year, Charmaine watched 28 movies that she thought were very good. She watched 80 movies over the whole year of the movies she watched,
what percentage did she think were very good?
0
?
Vector Vector C D. has an initial point of (–7, 2, 8) and a terminal point of (0, 7, 3). Vector Vector E F. has an initial point of (4, 1, –2) and a terminal point of (6, –2, –3). What is the component form of vector Vector C D minus vector E F.?
LeftAngleBracket negative 5, negative 8, 4 RightAngleBracket.
LeftAngleBracket 5, 8, negative 4 RightAngleBracket.
LeftAngleBracket 9, 2, negative 6 RightAngleBracket.
LeftAngleBracket negative 9, negative 2, 6 RightAngleBracket.
A vector is a quantity in physics that has both magnitude and direction. The component form of Vector CD minus vector EF is <5, 8, -4>.
What is a vector?A vector is a quantity in physics that has both magnitude and direction. It is often represented by an arrow whose length is proportionate to the magnitude of the quantity and whose direction is the same as that of the quantity.
The value of the Vector CD can be written as,
[tex]|\vec{CD}| = (0+7)\hat i+(7-2)\hat j+(3-8)\hat k = 7\hat i+5\hat j-5\hat k[/tex]
The value of the Vector EF can be written as,
[tex]|\vec{EF}| = (6-4)\hat i+(-2-(-1))\hat j+(-3-(-2))\hat k = 2\hat i-3\hat j-5\hat k[/tex]
Now, the component form of Vector CD minus vector EF can be written as,
[tex]\vec{CD} - \vec{EF} = < (7-2) , (5-(-3)) , (-5-(-1)) > = < 5,8,-4 >[/tex]
Hence, the component form of Vector CD minus vector EF is <5, 8, -4>.
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The bigger the payment that you make on your credit card bill, the
А less interest you wil have to pay in total
B more interest you will have to pay in total C higher your APR
D lower your annual fee
Answer:
A I think
Step-by-step explanation:
i-Ready
»Evaluate (8+t)³ - 6 when t = 2.
The value of the expression is
Practice: Numeric and Algebra
Answer:
994
Step-by-step explanation:
8+t(3) - 6 = 1000-6= 994
Strategic planning answers the question "__________"
Step-by-step explanation:
Where do you want to go from here?
What do you want to accomplish?
What obstacles will you have to overcome?
What problems will you have to solve?
What additional knowledge, skills, or resources will you require to achieve your strategic objectives?
The required Strategic planning answers the question "Where do we want to go and how do we get there?"
What is Strategic planning?Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them.
Here,
"Where do we want to go and how do we get there?"
Strategic planning is the process of defining an organization's vision, mission, values, goals, and objectives, and developing a roadmap to achieve them. It involves assessing an organization's current situation, identifying strengths, weaknesses, opportunities, and threats, and developing strategies to leverage strengths, address weaknesses, seize opportunities, and mitigate threats.
The end result is a plan that sets the direction for the organization and guides decision-making and resources allocation to achieve its goals and objectives.
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Necesito saber cómo lograr el 5 y 6.
Answer:
5) 12 pieces for $36
6) 12 pieces for $36
They require the same amount of wood pieces.
Step-by-step explanation:
5)
Sandbox A: ? = 2
one side is 6, the other is 4 + ? = 6, so 6-4= ? and 6 - 4 = 2
now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total
we know that each wood piece = 2 ft so:
24 / 2 = 12 pieces of wood
each piece costs $3, so we multiply...
12 * 3 = $36 for all the wood.
____________
Sandbox B: ? = 4
one side is 6, the other is 2 + ? = 6, so 6 - 2= ? and 6 - 2 = 4
now we add up the perimeter: 2 + 2 + 4 + 4 + 6 + 6 = 24ft total
we know that each wood piece = 2 ft so:
24 / 2 = 12 pieces of wood
each piece costs $3, so we multiply...
12 * 3 = $36 for all the wood.
A long-distance runner finished a race in 2.75 hours. How is the runner's time expressed
as a mixed number?
Solve the equation x^2+6x= -11/4
Answer:
Step-by-step explanation:
First, move the -11/4 to the other side, so the expression can equal 0.
[tex]x^2+6x+11/4=0[/tex]
To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.
[tex]4x^2+24x+11=0[/tex]
There are many ways to solve a quadratic equation (factoring, quadratic formula, completing the square).
Solving this equation by factoring is the easiest. Factoring with a leading coefficient greater than one can be difficult and there are many ways to accomplish it. The way I'm going to do it is to first find the factors of [tex]4x^2[/tex] and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.
[tex]4x^2[/tex]: 24x 11:
2x 22x 11
2x 2x 1
24x (works)
I'll then take the factors diagonal. (2x+1)(2x+11)=0
So [tex]x=-\frac{1}{2}, -\frac{11}{2}[/tex]
To find the time it will take for a train
to travel from Springfield to Franklin,
d
where d
use the expression s,
represents distance and s represents
speed.
Find the time if the train travels
at a speed of 79
miles per
hour.
I can buy a $1000 bond for $950. I get $50 / year and it matures in 20 years. What interest rate am I earning?
The interest rate you are earning on a bond that has a face value of $1000, a price of $950 and a coupon of $50 is 5.42%
What is the interest rate?The interest rate is the rate of return on the bond given its face value, coupon payments and price.
Interest rate can be determined using a financial calculator:
Cash flow in year 0 = -950 Cash flow in year 1 to 20 = 50 Cash flow in year 20 = 1000Interest rate = 5.42%
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I WILL GIVE BRAINLIEST ANSWER TO THE PERSON WHO GETS THIS QUESTION CORRECT
Answer: y = -2x + 1
Step-by-step explanation:
The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.
Hope this helps! Have a great day! :)
What additional piece of information must be known in order to calculate the volume of the cylinder below?
in.
the diameter of a base
the height of the cylinder
the area of a base
Othe radius of a base
Answer:
the height of the cylinder
Step-by-step explanation:
Find all solutions to the equation
in the interval [0, 2π). Enter the
solutions in increasing order.
cos 2x = cos x
X = [?],
Remember: cos 20 = cos²0 - sin²0
IMPORTANT: every " a, b, c and + , -" are meant to be exponents
The expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is an algebraic expression, and the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
How to simplify the expression?The expression is given as:
[tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Apply the power rule of indices
[tex](x^{a-b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex]
Expand the exponents of the expression
[tex]x^{a^2-b^2} \cdot x^{b^2 - c^2} \cdot x^{c^2 - a^2[/tex]
Apply the product rule of indices
[tex]x^{a^2-b^2+b^2 - c^2+c^2 - a^2[/tex]
Collect like terms
[tex]x^{a^2- a^2-b^2+b^2 - c^2+c^2[/tex]
Evaluate the differences
[tex]x^{0-0 - 0[/tex]
This gives
[tex]x^{0[/tex]
Evaluate the exponent
1
Hence, the result of simplifying the expression [tex](\frac{x^a}{x^b})^{a + b} \cdot (x^{b + c})^{b - c} \cdot (x^{c + a})^{c - a}[/tex] is 1
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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
x + 30 = 2x (since angleA = angle D, due to congruency between the two triangles.)
30 = 2x - x
30 = x
hope it helps...!!!
This figure represents a platform on a stage. The stage crew needs to paint it black. One gallon of paint will cover 40 square yards.
How many full gallons of paint does the crew need to buy in order to paint the entire platform?
Enter your answer in the box.
gallons
Answer:
14
Step-by-step explanation:
I took the test.
Answer:
14
Step-by-step explanation: I took the test
Edgar and June ate 75% of a pizza. If the pizza had 12 slices, how many slices did they eat
Answer:
9
Step-by-step explanation:
100% = 12
12/4= 3
25%=3
3+3+3=25%+25%=25%= 75%
A cylinder has a height of 5 centimeters. Its volume is 62.8 cubic centimeters. What is the
radius of the cylinder?
mund your answer to the nearest hundredth
Answer: 2
Step-by-step explanation: It would have been 1.99949 but rounded to the nearest hundreth is 2 :)
3(p-6)
Which of the expressions is equivalent to the given expression?
Part A
a) (3 * p)-6
b) (3* p)-(3 *6)
c) (3 +p) - (3 *6)
d) (3 * p)* (3-6)
Part B
Which expression is also equivalent to the given expression?
a) p-18
b)3p+6
c)3p-6
d)3p-18
plllsss answer! I don't understand this question.
Answer:
C and D
Step-by-step explanation:
Population density is the ratio of population to area. Its units are persons per square mile. Here, you're being asked to compare the population densities of several countries to the average population density in several US states.
__
averageThe idea of "average population density of the 10 states listed" is somewhat ambiguous. It could mean either of (a) the ratio of the total of the states' population to the total of their land area, or (b) the average of the population densities of the states. (In the attached, we computed both, but the answer remains the same using either number.)
When there are numerous identical calculations to be performed, it is convenient to let a spreadsheet do them. The attached spreadsheet shows the population densities for the 10 states and 5 countries listed.
Depending on how you define it, the average population density of the 10 states is about 10.5 or about 15.7 people per square mile. (15.7 is the average of the density numbers, found using the spreadsheet AVERAGE function.)
__
countriesThe 5 countries have population densities ranging from about 7.7 to 236 people per square mile. Two of the countries have density below 10.5, so are the answers to the question asked.
Canada (C) and Iceland (D) have population density below the US state average.