Answer:
Step-by-step explanation:
If the first floor of the Willis Tower is 21 feet high. and each additional floor is 12 feet high, then the floor heights as we move from one floor to another we keep increasing by 12feets and forms an arithmetic progression as shown;
21, (21+12), (21+12+12), ...
21, 33, 45...
a) To write an equation for the nth floor of the tower, we will have to find the nth term of the sequence using the formula for finding the nth term of an arithmetic sequence.
The nth term of an arithmetic sequence is expressed as [tex]T_n = a + (n-1)d[/tex]
a is the first term = 21
d is the common difference = 33-21 = 45-33 = 12
n is the number of terms
Substituting the given parameters into the formula;
[tex]T_n = 21+(n-1)*12\\T_n = 21+12n-12\\T_n = 21-12+12n\\T_n = 9+12n[/tex]
Hence the equation for the nth floor of the tower is expressed as [tex]T_n = 9+12n[/tex]
b) To get the height of the 65th floor, we will substitute n = 65 into the formula arrived at in (a)
[tex]T_n = 9+12n\\T_{65} = 9 + 12(65)\\T_{65} = 9+780\\T_{65} = 789 ft[/tex]
Hence the height of the 65th floor is 789feets.
Fill in the missing number. (please explain your answer)
Answer & Step-by-step explanation:
Make a fraction using the numerator:
[tex]\frac{48}{15} =\frac{x}{y}[/tex]
Simplify the fraction. Both the numerator and the denominator are multiples of 3, so divide top and bottom by 3 to the lowest possible integer:
[tex]\frac{16}{5}[/tex]
Insert into the equation:
[tex]\frac{48}{15}=\frac{16}{5}[/tex]
:Done
You can use different numbers too
(4x2 + 7x - 4) + (x2 – 7x + 14)
What is the answer?
Answer:
[tex]5x^2 + 10[/tex]
Step-by-step explanation:
[tex]4x^2 + x^2 = 5x^2\\7x + (-7x = 0\\-4 + 14 = 10[/tex]
Multiply. Express your answer in simplest form.
1
5
х
8
6
Answer:
1300
Step-by-step explanation:
Actual answer: 1290
Asim used 324 ft? of carpet for his living room floor. The living room floor
is in the shape of a square. What is the length of Asim's living room?
A9 ft
B18 ft
C36 ft
D 81 ft
Answer:
Hey there!
Area of a square: Length(Length)
324=Length^2
Length=18 ft.
Let me know if this helps :)
Answer:
D. 81ft
Step-by-step explanation:
Area covered by the carpet = 324ft
Room being a square , has 4 equal sides = [tex]\frac{324}{4}[/tex] ft = 81 ft
The length of Asim's living room is 81 ft
What is the value of the expression 10 · 2 + 9 + 3 . 42 ?
Answer:
32.42Step-by-step explanation:
[tex]10\times\:2+9+3.42\\\\\mathrm{Multiply\:the\:numbers:}\:10\times\:2=20\\=20+9+3.42\\\\\mathrm{Add\:the\:numbers:}\:20+9+3.42\\=32.42[/tex]
Answer:
32.42
Step-by-step explanation:
10 . 2 + 9 + 3 . 42
10×2 = 20
20 + 9 + 3.42
20 + 9 + 126 = 32.42
2000 people are selected randomly from a certain population and it is found that 389 people in the sample are over 6 feet tall. What is the point estimate of the proportion of people in the population who are over 6 feet tall
Answer: 0.195
Step-by-step explanation:
given data:
population = 2000 people.
people Who are over 6 feet tall = 389.
Solution:
the point estimate of people over 6feet tall
= no of people over 6 feet tall / total population size
= 389/2000
= 0.195
the point estimate of people over 6 feet tall is 0.195
Which of the following is a set of noncollinear points?
© P, R, T
OP,Q,R
® Q, R, S
DS, T, U
Answer:
P ,Q ,R
Step-by-step explanation:
Three or more points that doesn't lie on a straight lie are Non collinear points
A movie theater charges $8.25 per ticket. Which expression models the cost of buying t tickets? A) 8.25t B) 8.25+t C)8.25-t D)8.25/t
Answer: a. 8.25t
Step-by-step explanation:
From the question, we are informed that a movie theater charges $8.25 per ticket. The expression that models the cost of buying t tickets is gotten when we multiply $8.25 by t. This will be:
= 8.25 × t
= 8.25t
Therefore, expression that models the cost of buying t tickets is 8.25t. The correct answer is option A.
How many 1/8 pounds meatballs can Rory make
Plzzz helpppp fast
Answer:
6
Step-by-step explanation:
since he has 2 pounds of ground beef and we are dividing these pounds into 8th's he would have a total of 16/8 meaning 8/8 for each pound of ground beef.
and since he used 5/8 for each of the two huge meat balls that means he used a total of 10/8 in total leaving 6/8.
[tex]16/8 = 8/8 + 8/8\\[/tex]
[tex]5/8 + 5/8 = 10/8\\16/8-10/8=6/8[/tex]
so since he is making 1/8 pound meatballs and he has 6/8 pounds of ground beef left he can make 6 of the 1/8 pound meatballs
simply the equation-2(-3 + 2z)
Simply the equation -2(-3 + 2z)
6 − 4z
Sarah has 273 feet of wire to make bead necklaces. If each necklace requires 1 2/3 feet of wire, how many necklaces can she make?
Oh boy, here we go again
First we must convert 1 2/3 to an improper fraction. By doing this, we get 5/3 (3/3 + 2/3)
So now we have 273 / 5/3
To divide this easier we can do something that when I learned it was called (keep, change, flip) which basically means keep the first fraction, change the sign from division to multiplication, and flip the second fraction
This now turns into: 273/1 * 3/5
Combine 273 and 3/5
273⋅3/5
Multiply 273
by 3
819/5
is your answer
Simplify to create an equivalent expression.
8- 4(-x+ 5)
Answer:
8 - 4(-x + 5) = 4x - 12Step-by-step explanation:
8 - 4(-x + 5) =
= 8 - 4•(-x) + (-4)•5 =
= 8 + 4x - 20 =
= 4x - 12
a trucking company shipped a total 151,375 boxes of fruit across the company. How many thousands of boxes of fruit were shipped?
Answer:
The trucking company shipped a total of 151 thousands of boxes of fruits
Step-by-step explanation:
Total boxes of fruits shipped= 151,375
How many thousands of boxes of fruit were shipped?
To find the thousands of boxes of fruits shipped, divide the total number of boxes of fruits shipped by 1000
That is
151,375 / 1000
= 151.375
Therefore, the trucking company shipped a total of 151 thousands of boxes of fruits
151,375
Place value of each figure from right to left
5= one
7= tens
3= hundred
1= thousand
5= ten thousand
1= hundred thousand
Shirley picked out a lite for $3.50 if she gave the family ten-dollar bill what is the fewest number of bills and coins that she could receive as change
Answer:
2 bills and 1 coin
Step-by-step explanation:
Given
[tex]Lite = \$3.50[/tex]
Required
Fewest number of bills and coins she can get receive as change
FIrst, we need to calculate her change
Change = Amount Paid - Lite
[tex]Change = \$10 - \$3.5[/tex]
[tex]Change = \$6.5[/tex]
Next is to split the change to bills and coins
[tex]\$6.5 = \$5\ bill + \$1\ bill + 50 cents[/tex]
The $5 and $1 makes 2 bills while the 50 cents makes 1 coin.
Hence, the minimum she could receive is 2 dollar bills and 1 coin as change
Explain why the sum of a rational number and an irrational number is always irrational.
Answer:
Irrational numbers are contradictory, even when combined with a rational number.
Step-by-step explanation:
Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.
Credit card companies use negative balances to represent when the credit card company owes the customer money and positive balances to represent when the customer owes the credit card company DIDIE. Sneha has a balance of 0 dollars with her credit card company, What does a balance of dollars represent?
Answer: Neither Sneha nor the credit card company owes money.
Solve the factorial
5!/3!
Answer:
20
Step-by-step explanation:
(5x4x3x2x1)÷(3x2x1)=
120÷6=
20
Evaluate: negative -20 divided by -10 pleas help
Answer:
2
Step-by-step explanation:
-20 divied by -10 is two
2 negavties make a positive
Answer:
2
Step-by-step explanation:
When both numbers are negative it canals out so the answer is positive.
The ABC triangle is isosceles
(AB=AC)
BC=EC
you needs to be prove that ABD overlaps to AEC
ΔABD overlaps to ΔAEC
Step-by-step explanation:ABC triangle is isosceles => ∡B ≡ ∡C
AB = AC
∡B ≡ ∡C } => ΔABD ≡ ΔAEC => ΔABD overlaps to ΔAEC
BD = EC
what is 14b +6b - 12 simplified?
Answer:
20b -12
Step-by-step explanation:
14b +6b - 12
Combine like terms
20b -12
PLEASE ANSWER I AM BEGGING!!!!!!Type a simplified fraction as an answer.
answer 5/6 decimal form is 0.83
Answer:
5/6
Step-by-step explanation:
100 ÷ 4 = 25
144 ÷ 4 = 36
Under root of 25 = 5
Under root of 36 = 6
Final Answer = 5/6
Hope this helps!
Sorry for the mistake before I did not see the under root!
Use the figure to find the Slant Height. 4 5 √(11)
Answer:
[tex]height = 4[/tex]
Step-by-step explanation:
By the Pythagorean Theorem, we know:
[tex]a^2 + b^2 = c^2[/tex]
Where [tex]c[/tex] is the slope.
Here we see the following:
[tex]a = 3\\b = ???\\c = 5[/tex]
Plug in the numbers:
[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\b = \sqrt{16}\\ b = 4[/tex]
For line graphs and bar graphs, the values measured by the vertical axis
depend on the values measured by the ______ axis.
Answer:
Horizontal
Step-by-step explanation:
Answer:
horizontal axis
Step-by-step explanation:
its a chart measured by x and y.
x meaning side to side and y meaning up or down.
and in any equation x makes y or usually y is defined by x.
Example: y = mx + b
so y = vertical and x = horizontal
Simplify (5x - 10) - (3x + 8)
Answer:
2x-18 is the answer.
Step-by-step explanation:
=(5x-10)-(3x+8)
Opening the brackets to simplify
=5x-10-3x-8
Combining the like terms
=5x-3x-10-8
=2x-18
Hope it will help you ^_^
Answer:
2(x-9)
Step-by-step explanation:
open the brackets by multillying - sign with the entries of the second bracket
5x-10-3x-8
adding like term variables
2x-18
taking common
2(x-9)
Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't touch the money in her account, she can find the amount she'll have the next year by multiplying her current amount by 1.03. How much will she have in 30 years
Answer:
$388.36Step-by-step explanation:
let us assume that the amount in her accounts compounds annually
Given data
principal p= $160
interest rate r= 3%= 0.03
time t= 30 years
At the end of 30 years the money she will will have can be expressed as
A= P(1+r)^t
A= 160(1+0.03)^30
A= 160(1.03)^30
A= 160*2.42726
A= $388.36
in 30 years she will have $388.36
La función y = 20000 + 1500x relaciona el valor total a pagar por un servicio de fletes y la distancia recorrida, en kilómetros, dentro de la ciudad. En este contexto, interpreta a qué corresponde: a. ¿Cuánto debe pagar por una distancia de 20 km? b. ¿Cuánto fue la distancia recorrida si pago un flete de $ 140.000?
Answer:
Los resultados están debajo.
Step-by-step explanation:
Dada la siguiente información:
y = 20.000 + 1.500x
Siendo:
y= costo total
x= kilometros recorridos
Entonces, si recorrio 20km:
y= 20.000 + 1.500*20
y= $50.000
Ahora, si pago $140.000, cuantos km recorrio:
140.000= 20.000 + 1.500*x
120.000/1.500= x
x= 80km
Area of a circle
R = 5cm
Area=
REMEMBER TO ANSWER TO 2 DECIMAL PLACES.
Answer:
78.52 cm sq.
Step-by-step explanation:
Area = pi x r^2
A = pi x (5)^2
A = pi x 25
A = 3.141 x 25
A = 78.52 cm sq.
Please please help and show steps
Answer: h=3v/pir^2 +1
Step-by-step explanation:
sorry i can't use the pi symbol so i'll be referring to pi as pi
^2 is squared
1/3pir^2(h-1) =v
simplify 1/3pir^2
pi/3r^2(h-1)=v
multiply both sides by 3 and simplify
3*pi/3r^2(h-1)=3v <-- simplify = pir^2(h-1)=3v
divide both sides by pir^2
pir^2(h-1)/ pir^2 = 3v/ pir^2
simplify
h-1 = 3v/pir^2
add 1 to both sides
h-1 +1 = 3v/pir^2+1
answer/ simplify:
h=3v/pir^2 +1
What is mAngleMHJ? A. 35° B. 50° C. 72.5° D. 92.5°
Answer:
The answer is B. 50°
Step-by-step explanation:
Got 100% on the test :)
The value of ∠MHJ is 50°. Therefore, option B is the correct answer.
We need to find the value of ∠MHJ.
What are vertically opposite angles?Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other.
Here, ∠MHJ and ∠KHL are two vertically opposite angles.
So, (x+15)°=(2x-20)°
⇒x=35°
Now, ∠MHJ=(2x-20)°=50°
Therefore, option B is the correct answer.
To learn more about the vertically opposite angles visit:
https://brainly.com/question/68367.
#SPJ6
If m = 8, how many solutions are there to the expression 7m?