The series in sigma notation is: representing terms increasing by 4 starting from -5.
To represent the series in sigma notation, let's first examine the pattern of the terms.
The given series starts with -5 and each subsequent term increases by 4. We can express this pattern using the formula:
[tex]\[ a_n = -5 + (n - 1) \times 4 \][/tex]
Here, [tex]\( a_n \) represents the \( n \)th term of the series[/tex].
Now, let's break down the components of the formula:
-[tex]\( -5 \) is the initial term of the series.- \( (n - 1) \) accounts for the position of each term in the series. When \( n = 1 \), \( (n - 1) = 0 \), so the first term is \( -5 \). As \( n \) increases, \( (n - 1) \) increases by 1, causing the series to increase by 4 each time.- \( 4 \) is the common difference between consecutive terms in the series.[/tex]
Next, we represent the series using sigma notation:
[tex]\[ \sum_{n=1}^{5} (-5 + (n-1) \times 4) \][/tex]
This notation indicates that we sum up the expression [tex]\( -5 + (n-1) \times 4 \) for \( n \)[/tex] ranging from 1 to 5, which covers all the terms of the given series.
In summary, the series is represented in sigma notation as described above, capturing the pattern of increasing terms starting from -5.
Ms. Burke invested $53,650, part at 10.5% and the rest at 12%. If the income from the 10.5% investment is one third of that from the 12% investment, how much did she invest at each rate?
Answer:
$14,800 at 10.5%
$38,850 at 12%
Step-by-step explanation:
Investment at 10.5% (x):
(0.12[$53,650 - x])/0.105x = 3
$6,438 - 0.12x = 0.315x
0.435x = $6,438
x = $14,800
Investment at 12%:
= $53,650 - $14,800
= $38,850
Answer: Investments: @ 10.5%, $14,800; @ 12%, $38,850
Proof: (income from 1st is 1/3 that of the income from the 2nd):
= (0.105[$14,800])/(0.12[$38,850])
= $1,554/$4,662
= 1/3
Let's denote as 'x' the amount of money invested by Ms. Burke at the rate of 10.5%. Given that the total amount of investment is $53,650, it follows that the remaining money invested at 12% is given by $53,650 minus 'x'.
The income from the 10.5% investment is 0.105 multiplied by 'x' and the income from the 12% investment is 0.12 multiplied by the quantity $53,650 minus 'x'.
According to the problem statement, the income from the 10.5% investment is one-third of the income from the 12% investment. Therefore, we can write down the following equation:
0.105*x = (1/3)*0.12*($53,650 - x)
We solve this equation to determine 'x'. The solution for this equation yields 'x' equal to approximately $14,800. This means Ms. Burke invested approximately $14,800 at 10.5%.
Also, we know that the difference between the total amount invested and the amount invested at 10.5% will give us the amount invested at 12%. Hence, by subtracting $14,800 from $53,650, we obtain $38,850.
Therefore, Ms. Burke invested approximately $14,800 at the rate of 10.5% and $38,850 at the rate of 12%.
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HELP!what is the circumference of a circular swimming pool with a radius of 8 feet? round answer to nearest tenth
c = 2πr = 2π(8) = 16π = 50.3 ft rounded to the nearest tenth
a plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works. if he charges hayden $122 for the house visit how long did the plumber work
Answer:
The plumber worked for 43 minutes.
Step-by-step explanation:
A plumber charged $70 for the first 30 minutes of each house call plus $4 for each additional minute he works.
Now, the total amount to be paid to the plumber C(x) as a function of x number of minutes that he works can be modeled by the equation
C(x) = 70 for x ≤ 30 minutes and C(x) = 70 + (x - 30)4 for x > 30 minutes.
Now, the plumber charges Hayden $122 for the house visit. In that case, x must be greater than 30 minutes.
So, we can write
122 = 70 + (x - 30)4
⇒ 122 = 70 + 4x - 120
⇒ 4x = 172
⇒ x = 43 minutes.
Therefore, the plumber worked for 43 minutes. (Answer)
Round 132874015 to the nearest hundreds-thousands.
Answer:
Step-by-step explanation:
132,874,015 rounded to the nearest hundred thousand....
132,900,000 <===
There are 158 students registered for American History classes. There are twice as many students registered in second period as first period. There are 10 less than three times as many students in third period as in first period. How many students are in each period?
There are 28 students in first period and 56 students in sceond period and 74 students in third period
Solution:
Let the number of students in first period be "x"
Let the number of students in second period be "y"
Let the number of students in third period be "z"
There are 158 students registered for American History classes.
Therefore,
x + y + z = 158 ---------- eqn 1
There are twice as many students registered in second period as first period
number of students in second period = twice of number of students in first period
y = 2x ------- eqn 2
There are 10 less than three times as many students in third period as in first period
number of students in third period = 3 times number of students in first period - 10
z = 3x - 10 ------ eqn 3
Substitute eqn 2 and eqn 3 in eqn 1
x + 2x + 3x - 10 = 158
6x = 168
x = 28Substitute x = 28 in eqn 2
y = 2(28)
y = 56Substitute x = 28 in eqn 3
z = 3(28) - 10
z = 84 - 10
z = 74Thus there are 28 students in first period and 56 students in sceond period and 74 students in third period
3(x-4)+5x=4x+4(x-3) is this conditional
The given equation is not the conditional equation.
Step-by-step explanation:
A conditional equation is true only certain values of the numbers present in it.
for example x + 3 = 9 is true only, if x = 6
3x - 5 = 10 is true only, if x = 5
The given equation is an Identity equation in which both sides of the equation is equal.
3(x - 4) + 5x = 4x + 4(x - 3)
3x - 12 + 5x = 4x + 4x - 12
8x = 8x.
Melanie equally shares 25 meters of paper to create 9 banners
Question: Which situation is represented by [tex]\frac{25}{9}[/tex]?
Option A: Melanie equally shares 25 meters of paper to create 9 banners
Option B: Quill gives way 9 baseball cards from a pack of 25 cards.
Option C: George invites 25 kids and 9 adults to his birthday party.
Option D: Becca create 9 rows with 25 buttons.
Answer:
Solution:
Option A: Melanie equally shares 25 meters of paper to create 9 banners.
The fraction is [tex]\frac{25}{9}[/tex].
Option B: Quill gives way 9 baseball cards from a pack of 25 cards.
The fraction is [tex]\frac{9}{25}[/tex]
Option C: George invites 25 kids and 9 adults to his birthday party.
Here, 25 + 9.
Option D: Becca create 9 rows with 25 buttons.
Here, 9 × 25.
Hence the answer is Option A: Melanie equally shares 25 meters of paper to create 9 banners.
3 friends are camping in the woods, Bert, Ernie and Trevor. they each have their own tent and the tents are set up in a triangle. Bert and Ernie are 10 m apart. The angle formed at Bert is 30 degrees. The angle formed at trevor is 105 degrees. how far apart are Ernie and Trevor?
Answer:
12 m apart
Step-by-step explanation:
Final answer:
To find the distance between Ernie and Trevor in the camping scenario, trigonometry principles utilizing the law of sines can be applied effectively, resulting in a distance of approximately 15.54m between them.
Explanation:
To find the distance between Ernie and Trevor, we can use trigonometry. Let's focus on the triangle formed by Bert, Ernie, and Trevor. Since Bert and Ernie are 10m apart with a 30-degree angle at Bert, we can use the law of sines to find Ernie and Trevor's distance. By the law of sines:
Sin(30°) / 10m = Sin(Trevor's angle) / ET distanceSolve for ET distance to find the distance between Ernie and Trevor.ET distance = 10m * (Sin(105°) / Sin(30°))ET distance ≈ 15.54m91 tiles to make 13 hot plates. how many tiles to make 1 hot plate?
Answer:
7 tiles
Step-by-step explanation:
91/13=7
Answer:
7
Step-by-step explanation:
if 91 tile = 13 hot plate
X tile = 1 hot plate
(let X represent the number of tiles for one plate)
cross miltiply: 91×1 =13×X
X = 91/13
X =7 tiles
6y - 9y - 4 = -2y - 2 Solve for y
Please give step-by-step answer and explaination.
if there are 60 chocolate bars and they are one dollar each and I have 19 left how much money will I have
Answer:
60(if you sell all)
Right now you have: 41 dollars
Step-by-step explanation:
Answer: you will have 41 dollars.
Step-by-step explanation:
because if you had 60 chocolate and now you had 19 left you sold 41 chocolate bars and you multiply that by how much there are which is 1 dollar and 41 time 1 is 41.
Which is the simplified form of n-6p3
The simplified form of n-6p³ is n-6p³.
Explanation:To simplify the expression n-6p³, we need to combine like terms. Since n and 6p³ do not have any common factors, the simplified form of the expression is n-6p³.
y=4x-8 y=2x-2
plz help me find the answer
slove for substitution
The solution is [tex](3,4)[/tex]
Step-by-step explanation:
To solve the equation by substitution method, we need to substitute an equivalent value of a variable in one equation to an another equation.
The given two equations are [tex]y=4x-8[/tex] and [tex]y=2x-2[/tex] .
Thus, we know the equivalent value of y from one equation, let us subsitute the value of y from the equation [tex]y=2x-2[/tex] to the equation [tex]y=4x-8[/tex]
[tex]4x-8=2x-2[/tex]
Subtracting 2x from both sides of the equation, we get,
[tex]2x-8=-2[/tex]
Adding 8 to both sides of the equation, we get,
[tex]2x=6[/tex]
Dividing by 2 on both sides of the equation,
[tex]x=3[/tex]
Now, substituting [tex]x=3[/tex] in the equation [tex]y=2x-2[/tex], we get,
[tex]\begin{aligned}y &=2 x-2 \\&=2(3)-2 \\&=6-2 \\y &=4\end{aligned}[/tex]
Thus, the solution is [tex](3,4)[/tex]
Suppose a triangle has two sides of length 2 and 3 and that the angle
between these two sides is 60°. What is the length of the third side of the
triangle?
ОА. 7
В. 2
ооо
SUBMIT
Answer:
Answer is √7 ( not A, not B)
Step-by-step explanation:
BD/AB = sin 60°
BD/2 = √3/2
BD = √3
AD/AB = cos 60°
AD/2 = 1/2
AD = 1
CD = 3 -1 = 2
BC = √BD² + CD² = √(3 + 4) = √7
si p+ 2p+3p=12, ¿cual es el valor de 5p -1
For this case we have the following equation:
[tex]p + 2p + 3p = 12[/tex]
To solve we follow the steps below:
We add similar terms from the left side of the equation:
[tex]6p = 12[/tex]
We divide between 6 on both sides of the equation:
[tex]p = \frac {12} {6}\\p = 2[/tex]
Finally, we have to:
[tex]5p-1 = 5 (2) -1 = 10-1 = 9[/tex]
Answer:
[tex]p = 2\\5p-1 = 9[/tex]
Find the missing angle in the following right triangle with a second angle that measures 32degrees
Check the picture below.
3.5 belongs to which number sets
3.5 belongs to Rational number sets mainly and also belongs to Real Numbers.
Step-by-step explanation:
Number Sets are nothing but group of number classified into groups.
They are Natural, Whole, Integers, Rational, Irrational and Real numbers.
Natural number set = {1,2,3...},
Whole number set= {0,1,2,3...},
Integers = { ....-2, -1, 0, 1, 2, ....},
Rational numbers = { Integers, Decimals, Fractions},
Irrational numbers = { non fractional numbers eg: π,[tex]\sqrt{2}[/tex] etc.}
Real = { Natural, Whole, Integers, Rational, Irrational }.
Any number which is a fraction resulting in a decimal value is Rational Number sets.
3.5 is a decimal number so it can be Rational Number sets also Real Number sets.
PLEASE HELP < I NEED HELP, TRYING TO MAKE HONOR ROLL
Translate the sentence into an equation.
Twice the difference of a number and 7 equals 2 .
Use the variable x for the unknown number.
Answer:
2(x-7) = 2
Step-by-step explanation:
First, let's look at the first part -- "Twice the difference of a number and 7". The difference between a number (x) and 7 means x-7. It also says twice the difference, so we are going to multiply x-7 by 2. So that ends us with 2(x-7)
The last part -- "equals 2" means we will set what we currently have to 2. 2(x-7) = 2
Answer:
2(x-7)=2
Step-by-step explanation:
The difference of a number and 7 is x-7 (difference means subtract)
Now the question says twice so that is what we do 2(x-7) now equal that to two 2(x-7)=2
Can someone please help me with this problem :)
Answer:
x = 28.3
Step-by-step explanation:
Three people split an amount of money. 1 268 dollars and 1 gets 200 dollars. The third gets 40 percent. What is the amount?
The total amount is $ 780
Solution:
Let the total amount be "x"
Given that,
First person gets $ 268
Second person gets $ 200
Third person gets 40 %
This means, third person gets 40 % of total amount
Third person = 40 % of x
[tex]Third\ person = 40 \% \times x\\\\Third\ person = \frac{40}{100} \times x\\\\Third\ person = 0.4x[/tex]
We know that, total amount is equal to sum of amount got by all three persons
Total amount = first person + second person + third perosn
[tex]x = 268 + 200+ 0.4x\\\\x - 0.4x = 268 + 200\\\\0.6x = 468\\\\x = \frac{468}{0.6}\\\\x = 780[/tex]
Thus the total amount is $ 780
Evaluate the expressions 3x-2 and 4x+4 for the following value of x.
Question:
Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2
Answer:
Part a: [tex]4x+4>3x-2[/tex]
Part b: [tex]4x+4=3x-2[/tex]
Part c: [tex]4x+4>3x-2[/tex]
Part d: [tex]4x+4>3x-2[/tex]
Explanation:
Part a: Substituting [tex]x=0[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Part b: Substituting [tex]x=-6[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}[/tex]
The value of [tex]3x-2[/tex] and [tex]4x+4[/tex] are equal.
Thus, [tex]4x+4=3x-2[/tex]
Part c: Substituting [tex]x=5[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Part d: Substituting [tex]x=-2[/tex], we get,
[tex]\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}[/tex]
The value of [tex]3x-2[/tex] is less than [tex]4x+4[/tex]
Thus, [tex]4x+4>3x-2[/tex]
Final answer:
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Explanation:
Part a: 4x+4>3x-2
Part b: 4x+4=3x-2
Part c: 4x+4>3x-2
Part d: 4x+4>3x-2
Part a: Substituting x=0, we get,
[tex]\begin{aligned}3 x-2 &=3(0)-2 \n&=-2\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(0)+4 \n&=4\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Part b: Substituting x=-6, we get,
[tex]\begin{aligned}3 x-2 &=3(-6)-2 \n&=-18-2 \n&=-20\end{aligned}\begin{aligned}4 x+4 &=4(-6)+4 \n&=-24+4 \n&=-20\end{aligned}[/tex]
The value of 3x-2 and 4x+4 are equal.
Thus, 4x+4=3x-2
Part c: Substituting x=5, we get,
[tex]\begin{aligned}3 x-2 &=3(5)-2 \n&=15-2 \n&=13\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(5)+4 \n&=20+4 \n&=24\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Part d: Substituting x=-2, we get,
[tex]\begin{aligned}3 x-2 &=3(-2)-2 \n&=-6-2 \n&=-8\end{aligned}[/tex]
[tex]\begin{aligned}4 x+4 &=4(-2)+4 \n&=-8+4 \n&=-4\end{aligned}[/tex]
The value of 3x-2 is less than 4x+4
Thus, 4x+4>3x-2
Which values for x and y make the statement (x-5)(y+6)=0 true?
Answer:
X=5 and y=-6
Step-by-step explanation:
Positive five cancels out -5 and—6 cancels out positive six, so you are left with 0 which equals 0.
what’s 12.3+0.61+100
Answer:
12.3 + 0.61 +100= 112.91
Step-by-step explanation:
All you have to do is make all the values have two place values and then add.
John is driving around town. When he reaches the gas station, he notes that he has traveled 20 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.
If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
Answer:
d = 5t + 20
Step-by-step explanation:
d represents the distance and t represents the time, in hours
Let he equation which model this situation ⇒ d = a t + b
Where a and b are constant.
Let the gas station is the starting point
So, at gas station t = 0 , d = 20
∴ 20 = 0 * a + b ⇒ b = 20
When he reaches home 2 hours later notes that he has traveled 30 miles.
and with substituting with b = 20
∴ 30 = 2 * a + 20
2a = 30 - 20 = 10 ⇒ a = 10/2 = 5
∴ d = 5t + 20
The equations that can be used to model this situation d = 5t + 20
What is the surface area of the regular pyramid below? I’ll would be helpful if you guys list down the steps !
Answer:
The answer to your question is A = 648 u²
Step-by-step explanation:
I attach the solution because it said that I was writing improper words.
5. On one day, four cooks and four waiters earned $360. On another day, working the same number of
hours and at the same rate of pay, five cooks and six waiters earned $480. How much does a cook and
how much does a waiter earn each day?
Answer:
Step-by-step explanation:
c = cooks, w = waiter
4c + 4w = 360....multiply by -5
5c + 6w = 480...multiply by 4
=================
-20c - 20w = - 1800 (result of multiplying by -5)
20c + 24w = 1920 (result of multiplying by 4)
=================
4w = 120
w = 120 / 4
w = 30 <=== waiters make $ 30
4c + 4w = 360
4c + 4(30) = 360
4c + 120 = 360
4c = 360 -120
4c = 240
c = 240/4
c = 60 <=== cooks make $ 60
A 16 inch laptop has a screen that is 8 inches tall how wide is the screen ?
To find the width of a 16-inch laptop screen that is 8 inches tall, we can use the 16:9 aspect ratio typical for screens and calculate that the width is approximately 14.22 inches.
Explanation:Finding the Width of the Laptop Screen
To find out how wide a 16-inch laptop screen is, given that it is 8 inches tall, we can use the Pythagorean theorem assuming the screen has a 16:9 aspect ratio which is typical for laptop screens. To use the Pythagorean theorem, we first need to establish the diagonal (16 inches) as the hypotenuse of a right-angled triangle, with the height and width as the other two sides.
As per the given scale factor for this problem (1/160), it does not seem relevant to finding the width using the Pythagorean theorem. Instead, we can use the aspect ratio to find the width. For a 16:9 aspect ratio:
Height = 9x
Width = 16x
Given the height (8 inches) and assuming it to be 9x:
9x = 8 inches
x = 8 / 9
Now to find the width which is 16x:
Width = 16 * (8 / 9)
Width = 14.222... inches (approximately)
The width of the screen is therefore approximately 14.22 inches.
Grandma says Baby Bertha (BB) should get $1,000 at birth plus $50 per year. But Grandpa disagrees; he thinks that BB should get $1,000 at birth plus an additional 4% of the accumulated amount each year. Grandma and Grandpa will continue to contribute additional funds to the account as long as BB doesn’t take a withdrawal. Which option should BB’s parents select? Why?
BB's parents should choose the option with a 4% annual increase on the accumulated amount because it leverages compound interest, likely resulting in significantly higher growth over time compared to the fixed contribution strategy.
Explanation:The question involves deciding between two financial strategies for Baby Bertha's (BB) savings account: a fixed annual contribution ($1,000 at birth plus $50 per year) versus a dynamic contribution that includes an initial amount plus an annual percentage increase ($1,000 at birth plus an additional 4% of the accumulated amount each year). To determine which option BB's parents should select, we must understand the impact of compound interest and how it can significantly increase the future value of a savings account over time.
With the fixed contribution strategy, the amount added each year is constant, leading to linear growth. In contrast, the 4% annual increase on the accumulated amount option leverages the power of compound interest, likely resulting in exponential growth of the account's value over time. This strategy takes advantage of the principle that earnings are reinvested to generate their own earnings in subsequent years, a core tenet of compound growth.
Given the long-term nature of the saving plan (assuming BB won't withdraw the funds prematurely), the option with a 4% annual increase on the accumulated amount is more advantageous. This decision leverages compound interest, which is known to significantly increase the value of investments over extended periods. Hence, BB's parents should select Grandpa's option for the potential of greater financial growth.
Triangle is three centimeters longer than twice the length of th shortest side.the thrid side is twice as long as the shortest side.the perimeter of the triangle is 88 centimeters
Answer:
17
Step-by-step explanation:
x + 2x + 3 + 2x = 88
5x = 85
x = 17
Final answer:
To find the sides of the triangle, set the shortest side as x cm, leading to the calculation that the shortest side is 17 cm, the second side is 37 cm, and the third side is 34 cm.
Explanation:
The question is based on finding the lengths of the sides of a triangle given the perimeter and relationships between the sides. Let the shortest side be x cm. Therefore, according to the information given, the second side is 3 cm longer than twice the shortest side, which makes it 2x + 3 cm, and the third side is twice as long as the shortest side, so it is 2x cm. The perimeter of the triangle, which is the sum of the lengths of its sides, is 88 cm. We can set up the equation to solve for x:
x + (2x + 3) + 2x = 88
5x + 3 = 88
5x = 85
x = 17 cm
Thus, the shortest side of the triangle is 17 cm, the second side is 2(17) + 3 = 37 cm, and the third side is 2(17) = 34 cm.
A 40ft tall building cast a shadow of 10ft. At the same time another building cast a shadow of 24 ft. How y’all is the second building?
Answer:
Every 4 feet in height would be 1 foot in length, so I want to say about 96ft
Step-by-step explanation: