Given that,
Series 1: 3, 5.5, 8..... and series 2: 33/2, 57/2, 81/2.
To find,
The value of n.
Solution,
Let n is the no of terms in both the series.
For 3, 5.5, 8
First term, a = 3 and common difference d = 2.5
Sum of n terms of a series is given by :
[tex]S=\dfrac{n}{2}(2a+(n-1)d)[/tex]
So,
[tex]S=\dfrac{n}{2}(2\times 3+(n-1)2.5)\\\\S=\dfrac{n}{2}(6+2.5(n-1))\ ....(1)[/tex]
For 33/2, 57/2, 81/2
First term, a = 33/2 and common difference, d = 12
nth term of a series is given by :
[tex]a_n=a+(n-1)d[/tex]
For 2nd terms,
[tex]a_2=\dfrac{33}{2}+(2-1)\times 12\ ....(2)[/tex]
According to question, sum of the first n terms of the arithmetical progression 3, 5.5, 8. .... is equal to the 2nth term of the arithmetic progression 33/2, 57/2, 81/2
From equation (1) and (2) :
[tex]\dfrac{n}{2}(6+2.5(n-1))=\dfrac{33}{2}+ 12\\\\\dfrac{n}{2}(6+2.5(n-1))=\dfrac{57}{2}\\\\n(6+2.5(n-1))=57\\\\6n+2.5n^2-2.5n-57=0\\\\2.5n^2+2.5n-57=0\\\\\text{On solving the above quadratic equation, we get the value of x as follows :}\\\\x=4.126,-5.526[/tex]
Neglecting the negative value, we get the value of n = 4.126
or
n = 4
Hence, the value of n is 4.
A large vehicle has wheels with
a 2-foot radius. These wheels are turning at 650 rpm. Find the linear velocity in mph.
A wheel with radius 2 ft has circumference 2π(2 ft) = 4π ft, and this is the distance traveled by a fixed point on the edge of the wheel as it completes one revolution. So we have
1 rev = 4π ft
1 mi = 5280 ft
1 h = 60 min
Turning at a rate of 650 rpm (rev/min), the linear velocity would then be
650 rev/min = (650 rev/min) * (4π ft/rev) * (1/5280 mi/ft) * (60 min/h)
650 rev/min = 325π/11 mi/h
650 rpm ≈ 92.82 mph
Please help me. Thnx
Answer:
-2.42, -0.8, 0.33, 1.23
Step-by-step explanation:
Which mixed number is represented by the shaded
area? 2 2/5, 2 3/5, 2 2/3, 2 3/2?
Answer:
2 3/5
Step-by-step explanation:
Jermaine paid $10 for an item and the shop owner gave him $2 in change. Which expression represents how much
less he would have in his wallet?
10 - (-2)
|--10- (-2)
-2.(-10)
2+ (10)
Answer:
10-(-2)
Step-by-step explanation:
Alonzo works as a car detailer. He charges $175 per car. He is planning to move out of his parents' house and rent his first apartment. He will need to
pay $115 for application fees, $965 for security deposit, and first and last months' rent at $1,240 per month. He has $1,886 in savings. How many cars
must he detail to have enough money to rent the apartment
cars
Answer:
10 cars
Step-by-step explanation:
Variable c = car
Step 1: form an equation
175c + 1886 = 115 + 965 + (1240)2
Step 2: isolate variable c and solve
175c + 1886 = 3560
175c = 3560 - 1886
175c = 1674
c = 1674 ÷ 175
c = 9.56....
*He will not get paid until the full car is detailed. Therefore, decimals (seen as half a car) will not pay him anything.*
Step 3: round up to the nearest whole number
c = 10
Answer:
correct answer is 9
Step-by-step explanation:
Tyler wrote the function f(x)=25x–15 to find the amount of money he would make after washing x cars. Select all of the values below that are in the domain of Tyler's function.
A) 2
B. 2.3
D. 7.1
E.) 10
Country A produces eight times the amount of diamonds in carats produced in country B. If the total produced in both countries is 9,000,000 carats, find the amount produced in EACH country
Answer:
A=8,000,000
B=1,000,000
Step-by-step explanation:
A=8B
A+B=9,000,000
8B(because A=8B)+B=9,000,000
9B=9,000,000
B=1,000,000
A=8*B=8*1,000,000=8,000,000
solve the equation 4-2(x-7)=3(x+5)
Answer:
.6 or 3/5
Step-by-step explanation:
x = 3/5
Step-by-step explanation:Hi there !
4 - 2(x - 7) = 3(x + 5)
removing parentheses
(-)(-) = +
4 - 2x + 14 = 3x + 15
isolate the variable terms
4 + 14 - 15 = 3x + 2x
solve
3 = 5x
x = 3/5
Good luck !
Four times the difference of five and a number is eight
Answer:
The number is 7
Step-by-step explanation:
4 times 2 is 8, and 7-5 is two.
Diego's parents gave him a fish tank containing 20 goldfish. Each month, Diego purchases 3 goldfish to add to his fish tank.
Which inequality can be used to find m, the number of months after receiving his fish tank, when Diego will have more than 35 goldfish in his fish tank?
A. 3m+20 35
D. 20m+3>35
Answer: DDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
what is 32% in fraction form
Answer:
32/100
Step-by-step explanation:
32% is out of 100% so you put that in fraction form? 100% become the deminator
what does this even mean
if you were to graph the inequality would the circle be open or closed?
x > 45
Answer:
The "circle" you are referring to is only for inequality graphing.
A closed circle means that the "circle" is less than or greater than AND EQUAL TO wherever that point is on the graph.
A open circle means that the "circle" is less than or greater than wherever it is on the graph.
For your example,
X > 45 would be an open circle, because the alligator doesn't have an underline indicating it is also equal to 45.
The alligator indicates the direction and whether it also includes "equal to".
An example of a closed circle is this.
[tex]x \geq 45[/tex]; the line below the alligator indicates that it is also equal to 45.
whats the square root of 7
Give reasons of Mass
Answer:
Hope this helps
Step-by-step explanation:
When new substances are produced in a reaction we say a chemical change has occurred. These changes are very difficult, sometimes impossible, to reverse.
Atoms are not created or destroyed in a chemical reaction, they are just rearranged from the reactants to form the products. This is the reason why symbol equations must be balanced.
If a chemical reaction is completed in a closed system (when nothing extra can get in and nothing can escape), then the mass will remain constant. But, if the chemical reaction happens in an open system (where air can get in and out), then mass may appear to change.
In this simulation we will explore the mass changes in chemical reactions and endeavour to explain why they have occurred.
Answer:
Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram.
Melissa's books weigh 14.5 lb, Jonathan's weigh 12.516 and Candy's
books weigh 7.25 lb. What is the combined weight of all of the books?
14.5 + 12.516= 27.016. so then you would add 27.016 + 7.25= 34.266.
Tina is saving to buy a notebook computer. She has two options. The first option is to put $300 away initially and save $10 every month The second option is to put $200 away initially and save $30 every month . After how many months would Tina save the same amount using either option ? How much would she save with either option ? After Box month , Tina will save with either option.
Answer:
5 months, $350
Step-by-step explanation:
Under option 1, where Tina starts with $300 and adds $10 per month, her savings after m months will be ...
300 +10m
Under option 2, where Tina starts with $200 and adds $30 per month, her savings after m months will be ...
200 +30m
__
We want to find the value of m such that the two options produce the same result:
300 +10m = 200 +30m
100 = 20m . . . . . . . . . . . add -10m-200 to both sides of the equation
5 = m . . . . . . . . . . . divide by 20
Her savings balance after 5 months will be ...
300 +10(5) = 300 +50 = 350
After 5 months, Tina will save $350 with either option.
the slope of the line below is 0.8. write the equation of the line in the point slope form using the coordinates of the labeled point (-2-3)
Answer:
y + 3 = 0.8(x + 2)
Step-by-step explanation:
Slope of line m = 0.8
[tex] (-2,\:-3)=(x_1,\:\y_1) [/tex]
Equation of line in slope point form is given as:
[tex]y - y_1 = m(x - x_1) \\ \\ y - ( - 3) = 0.8 \{x - ( - 2) \} \\ \\ y + 3 = 0.8(x + 2) \\ this \: is \: the \: equation \: of \: line \: in \: point \: \\ slope \: form \\ [/tex]
what is 2+3+4-5%= What is the anwser?
Answer:179 /20
(Decimal: 8.95)
Step-by-step explanation:
2+3+4− 5 /100
=5+4− 5 /100
=9− 5 /100
=9− 1 /20
= 179 /20
question 2 please help!!!!
1) El largo de un rectángulo mide el triple que su ancho. Si el ancho mide 12 cm, el perímetro del rectángulo es: Selecciona la opción correspondiente: a) 86 cm b) 90 cm c) 96 cm d) 102 cm 2) ¿Cuál es el perímetro de un heptágono regular de 2,45 m de lado? Selecciona la opción correspondiente: a) 14,7 m b) 12,25 m c) 17,15 m d) 20 m 3) Si una cancha de fútbol mide 98 m de largo y su ancho equivale a la mitad de esta medida, su perímetro es: Selecciona la opción correspondiente: a) 304 m b) 284 m c) 294 m d) 354 m 4) Frente a la casa de Carolina hay un parque que tiene 45 m de largo y 38 000 mm de ancho. Si ella da dos vueltas alrededor de este, ¿qué distancia en metros recorre? Selecciona la opción correspondiente: a) 160 metros b) 330 metros c) 166 metros d) 332 metros
Answer:
1) c) 96 cm
2) c) 17,15 m
3) c) 294 m
4) d) 332 metros
Step-by-step explanation:
1)
La fórmula para el perímetro de un rectángulo = 2L + 2W
= 2 (largo + ancho)
L = longitud
W = ancho
Se nos dice en la pregunta que:
La longitud de un rectángulo es tres veces su ancho. Si el ancho es de 12 cm
Por lo tanto,
L = 3 W
L = 3 × 12
Largo = 36cm
Por lo tanto, el perímetro =
2 (largo + ancho) cm
= 2 (36 + 12) cm
= 2 (48) cm
= 96 cm
2)
La fórmula para el perímetro de un heptágono regular = 7a
Donde a = longitud de un lado
De la pregunta,
a = 2,45 m laterales
Por lo tanto, el perímetro de un Heptágono regular = 7 (2,45 m)
= 17,15 m
3)
La fórmula para el perímetro de un rectángulo = 2L + 2W
= 2 (largo + ancho)
L = longitud
W = ancho
Se nos dice en la pregunta que:
Si un campo de fútbol tiene 98 m de largo y su ancho es igual a la mitad de esta medida,
Por lo tanto,
L = 98 m
W = 1/2 de longitud
Ancho = 1/2 (98)
= 49
Por lo tanto, el perímetro =
2 (largo + ancho) m
= 2 (98 + 49) m
= 2 (147) m
= 294 m
4)
El parque es de forma rectangular.
Longitud = 45 m
Ancho = 38.000 mm
Convertir mm en m
1 milímetro = 0,001 metro
38.000 milímetro =
38.000 × 0,001 metros
= 38 metros (38 m)
La distancia alrededor del parque = perímetro del parque
Perímetro = 2 (L + W)
= 2 (45 + 38)
= 2 (83)
= 166 m
Distancia alrededor del parque una vez = 166 m
Pero nos dijeron que dio la vuelta al parque 2 veces, por lo tanto, la distancia que recorrió = 166 m × 2
= 332m
Find the mean of the integers -45 -20 -35 -25 -40
Answer:
-33
The mean of the data set -45, -20, -35, -25, and -40 is -33.
Hope it helps.
The mean of given integers is -35.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
The given integers are -45, -20, -35, -25, -40.
We know that, mean = Sum of all the observations/Number of observations
= [(-45+(-20)+(-35)+(-25)+(-40)]/5
= (-45-20-35-25-40)/5
= -165/5
= -35
Therefore, the mean is -35.
To learn more about an arithmetic mean visit:
https://brainly.com/question/15196910.
#SPJ2
what is the measure of
Answer:
30 degrees
Step-by-step explanation:
∠BAC= ∠DAE (vert. opp. ∠s)
(x +10)°= (2x -10)°
x +10= 2x -10
Bring constants to 1 side, x terms to the other:
2x -x= 10 +10
x= 20 (simplify)
∠BAC= (x +10)°
∠BAC= (20 +10)° (substitute x=20)
∠BAC= 30°
Answer:
<bac=30°
Step-by-step explanation:
<bac=<ead (being vertically oppoaite angles)
(x+10)=(2x-10)
10+10= 2x-x
20°=x
now
<bac=(x+10)°
<bac=(20+10)°
so,<bac=30°
Square root of 2 to the power of four add 3 to the power of 2
Answer:
13
Step-by-step explanation:
i solved it for you
your welcome :)
In a recent year, the annual salary of the Governor of New York was $179,000. During the same year, the annual salary of the governor of Tennessee was $94,000 less. Write and solve an equation to find the annual salary of the Governor of Tennessee (y) in that year
Answer:
179,000-94,000=y y=85,000
WILL GIVE BRAINLIEST!
Yohan Blake ran the 2012 Olympic 200-meter race in 19.44 seconds. Compare his speed in that race to his speed in the 100-meter race, which he finished in 9.75 seconds. Round to the nearest hundredth.
A: 10.29 meters per second and 10.26 meters per second
A: 10.49 meters per second and 10.36 meters per second
A: 10.59 meters per second and 10.46 meters per second
A: 10.69 meters per second and 10.56 meters per second
Answer:10.29 meters per second and 10.26 meters per secon
Step-by-step explanation:
i know
Answer:
a the first one
Step-by-step explanation:
right on edge2020
Find the Median from the number set 6, 11, 7, 4, 12, 15, 1
Answer:
The answer is 7
Step-by-step explanation:
IS THERE ANOTHER WEBSITE JUST LIKE BRAINLY
Answer:
seriously, what's it called?
Sherman has 4 cats and 1 dog. He wants to buy a toy for each of his pets. Sherman has $46 to spend on
pet toys. How much can he spend on each pet? Enter the answer as a fraction in simplest form and then
as an amount in dollars and cents.
Sherman can spend (blank)
written as a fraction.
In dollars and cents, he can spend $ (blank)
on each pet.
Answer:
spend 8 bucks on cats then left over for the dog
Step-by-step explanation:
Printing a newsletter costs $1.50 per copy plus $450 in printer's fees. The copies are sold for $3 each.How many copies of the newsletter must be sold to break even?
Answer:
300 Copies
Step-by-step explanation:
Break even Units = Fixed Costs / (Price - Variable Cost)
Fixed Costs = $450
Variable Cost = 1.5
Price = 3
Break Even Units = 450 / (3 - 1.5)
Break Even Units = 450 / 1.5
Break Even Units = 300
300 Copies must be sold to break even.
I hope this helps!
-The BusinessMan
all the real square roots of 144.
Answer:
So the set of all real square roots of -144 is the empty set. The imaginary square roots are i12 and -i12.
Step-by-step explanation:
hopefully that helps you
The real square roots of 144 as requested are; 12 and -12.
According to the question;
We are required to determine all real square roots of 144.The square root represented as follows is;
√144±12Therefore, The real square roots of 144 as requested are; 12 and -12.
Read more;
https://brainly.com/question/11388449
