Using proportions, it is found that the volume is 64 times larger than the volume of the original figure.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, each of the 3 dimensions will be four times greater, hence, the change in the volume will be given by:
V = 4³ = 4 x 4 x 4 = 64.
The volume is 64 times larger than the volume of the original figure.
More can be learned about proportions at https://brainly.com/question/24372153
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Find the 43rd term of the algebraic sequence if a21 = −32 and a50 = −119.
PLEASE REALLY NEED HELP WITH THISSSS
70 POINTS!!!!!!!!!!!!!!!!!!!!!
Answer:
- 98Step-by-step explanation:
Given
[tex]a_{21}=-32[/tex][tex]a_{50}=-119[/tex]Find [tex]a_{43}[/tex]
We know that
[tex]a_n=a_1+(n-1)d[/tex]Appy this to the two known terms and find the first term and the common difference
[tex]a_1+20d=-32[/tex] ⇒ [tex]a_1=-20d-32[/tex] [tex]a_1+49d=-119[/tex] ⇒ [tex]a_1=-49d-119[/tex]Find the coomon difference
-20d - 32 = - 49d - 11949d - 20d = 32 - 11929d = - 87d = - 87/29d = - 3Find the first term
a₁ = - 20(- 3) - 32 = 60 - 32 = 28Now find the 43th term
a₄₃ = 28 + 42(- 3) = 28 - 126 = - 98Answer:
-98
Step-by-step explanation:
General form of an arithmetic sequence:
[tex]a_n=a+(n-1)d[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termd is the common difference between termsGiven:
[tex]a_{21}=-32[/tex][tex]a_{50}=-119[/tex]To find the 43rd term we need to construct an equation for the nth term. To do this, find the first term and the common difference by substituting the given information into the general formula to create a system of equations that can be solved.
[tex]\begin{aligned} \underline{\textsf{Equation 1}}} \\ a_{21} & =-32 \\ \implies a+(20-1)d & = -32 \\a+20d & =-32 \end{aligned}[/tex]
[tex]\begin{aligned} \underline{\textsf{Equation 2}}} \\ a_{50} & =-119 \\ \implies a+(50-1)d & = -119 \\a+49d & =-119 \end{aligned}[/tex]
Subtract Equation 1 from Equation 2 to eliminate a:
[tex]\begin{array}{r l}a+49d & = -119\\- \quad a+20d & = -32\\\cline{1-2}29d & = -87\end{aligned}[/tex]
Solve for d:
[tex]\implies d=\dfrac{-87}{29}=-3[/tex]
Substitute the found value of d into one of the equations and solve for a:
[tex]\implies a + 20(-3)=-32[/tex]
[tex]\implies a=28[/tex]
Substitute the found values of a and d into the general formula to create an equation for the nth term:
[tex]\implies a_n=28+(n-1)(-3)[/tex]
[tex]\implies a_n=31-3n[/tex]
Finally, substitute n = 43 into the found formula to find the 43rd term of the sequence:
[tex]\implies a_{43}=31-3(43)=-98[/tex]
Learn more about arithmetic sequences here:
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what is the LCM for 9 and 12
Please Answer Both Questions!
If your correct I'll mark you brainliest if someone else answers
Only answers needed
Answer:
Card 9: 62.8 Card 10: 235.5 Card 11: 79.94 Card 12: 230.79
Step-by-step explanation:
Last week, the price of apples at a grocery store was $1.06 per pound. This week, apples at the store are on sale at a 10% discount. What is the total price of 4/1/2 pounds of apples this week at the grocery store?
Answer: $6.48
Step-by-step explanation:
1.60 * 0.1 = $0.16
1.60 - 0.16 = $1.44
1.44 * 4.5 = $6.48
what is the length of the third side(AC)
Answer:
Step-by-step explanation:
Use pythogeream theroem:
Explanation in image attached :)
help pls I give brainiest
rewrite the equation by completing the square, 4x^2-4x+1=0,
Answer:
(x-0.5)^2=0
Step-by-step explanation:
x^2-x+0.25=0
(x-0.5)^2=0
Find the range of the graph below
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The range for the given function is ~
[tex]\qquad \tt \dashrightarrow \: - 6 \leqslant y \leqslant 9[/tex]
Because, maximum value of y is 9 and minimum value is -6. so range lies between these two points (including them).
Please help
Workout a b and c
Answer:
a=21° b=70°
Step-by-step explanation:
a=21°(Vertically Opposite Angles)
b+110°=180° (linear pair)
b=180-110
b=70°
[please mark me brainliest]
Answer:
a = 21°
b = 70°
c = 89°
Step-by-step explanation:
angle of measure b and the angle of measure 110 are two supplementary angles
Then b + 110 = 180
Therefore b = 180 - 110 = 70°
angle of measure b and the angle of measure 21 are two opposite angles
Then a = 21
We Know that the sum of the interior angles of a triangle equal to 180
Then a + b + c = 180
Therefore c = 180 - a - b = 180 - 21 - 70 = 159 - 70 = 89°
what two numbers that can multiply into 60 and add into 19
Answer:
15 and 4
Step-by-step explanation:
we must first find the Factors:
1, 2, 3, 4, 5
60, 30, 20, 15, 12
Now we can add them to find what adds to 19
1+60 = 61
2+30 = 32
3+20 = 23
4+15 = 19
Find the width of a cereal box that has a volume of 5,568 cm3 and is 29 cm long and 48 cm high.
Check the picture below.
[tex]\textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=29\\ h=48\\ V=5568 \end{cases}\implies \begin{array}{llll} 5568=(29)w(48)\implies \cfrac{5568}{(29)(48)}=w \\\\\\ 4=w \end{array}[/tex]
need help asap please
Answer:
5 : 7
Step-by-step explanation:
First figure surface a * a * 6 = 6 a^2
now scale the dimesion by x
ax * ax * 6 = 6 a^2 x^2
= 150 x^2 = 294
x^2 = 294/150
x = 7 : 5 is th ratio of the larger to the smaller
find the volume of the cylinder. round your answer to the nearest tenth. 7 inches and 6 inches.
[tex]\pi r^{2}[/tex]Answer:
You must know the radius but...
Step-by-step explanation:
The formula to find volume of a cylinder is: B*h
B= area of base
h=height
To find the area of the base you need to know the radius since the formula to find area of a circle is: [tex]\pi r^{2}[/tex]
Once you find the area of the base you just multiply it by the height
You want to estimate the height of LSC-CF students. You choose a random sample of 100 students and find that the mean height of these students is 66 inches, with a S of 3 inches. Calculate a .95 confidence interval for LSC-CF students.
Answer:
1.35 to nearest whloe ounce
!!! 20 POINTS !!!
Linda rented 8 movies and 4 video games for a total of $37. The next month she rented 3 movies and 2 video games for a total of $17.
Find the rental cost for each movie and video game.
3.0 × 10^{8} ms− 1 i need the answer to this question please
Hey there!
3.0 * 10^8
= 3.0 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
= 3.0 * 100 * 100 * 100 * 100
= 3.0 * 10,000 * 10,000
= 3.0 * 100,000,000
= 300,000,000
Therefore, your answer is:
300,000,000
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
Solve: log4(7t + 2) = 2
t =
Answer:
t = 2
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{4}[/tex] (7t + 2) = 2 , then
7t + 2 = 4² = 16 ( subtract 2 from both sides )
7t = 14 ( divide both sides by 7 )
t = 2
Answer:
t = - 4/13
Step-by-step explanation:
If you are 15 years old now, which equation could be used to solve for your age, y, 12
years from now?
Add 12 to the current age:
Y = 15 + 12
Answer:
y=15x12
Step-by-step explanation:
Estimate 31+65 over 9.7
Answer:
9.9
Step-by-step explanation:
31
+ 65
96
96/9.7=
9.89 =
9.9
Hey there!
31 + 65 / 9.7
= 96 / 9.7
= 9.896907
31 ≈ 30
65 ≈ 70
9.7 ≈ 10
9.896907 ≈
30 + 70 / 10
= 100 / 10
= 10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What is 7/3 times 5/3 times 11/3 simplified?????
Answer:
14.26
Step-by-step explanation:
7/3 x 5/3 x 11/3 = 7(5)11/(3³)
35 x 11 = 385/27
385 / 27 = 14.26
What is the surface area of the milk carton
to the nearest square inch? Check your
answer for reasonableness.
Answer:
280 in ^2
Step-by-step explanation:
Hi ok heres how I did this:
SA of rectangular prism: S = 2(lw + lh + wh)
SA of triangle top thing(whats it called???): Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh
So basically for the square part, the surface area is
2(4*4+4*12+4*12), or 224
For the triangle part, the surface area is
4+4+4, or 12*4+2*4, or 48+8, or 56
224+56=280
The thing is I don't know why it says round though. Theres a chance its incorrect if they want something with a decimal. Let me know.
Can someone help me with this?
2u+14
hope it helps...!!!
A bag contains ten titles labeled B, C, D, E, F, G, H, I, J, and K. One time will be randomly picked. What is the probability of picking a vowel? Write your answer as a fraction in the simplest form.
Find the lateral area of the cone
Answer:
I think
Step-by-step explanation:
25x9
is 225
which should be it
Calculate the mean of the data set below. 28,40,53,39,45
Answer: 41.
Step-by-step explanation: To find the mean of a data set, you first need to add all the numbers together. It should look like this:
28 + 40 + 53 + 39 + 45 = 205.
The next step is to divide 205 by how many numbers you have in the data set. In this case, you have 5 numbers in the data set. Your work should look like this:
205 / 5 = 41.
Therefore, the mean of the data set is 41.
Hope this helps! :)
7. Janine rented an apartment for $900 a month. After a year, she bought a house with a monthly mortgage of $1,250. At the end of the year, she is able to deduct $4,900 in real estate taxes and $8,400 in interest. Janine's
taxable income is $42,000. Using the tax schedule below, how much was she able to save on her taxes due to her home ownership?
$2,940.00
Yw and pls mark me brainiest
if f(x)=-2x+6(4-3), what is f(8)
Answer:
f(8)= -16 + 6
Step-by-step explanation:
f(x) = -2x + 6(4-3)
f is a function. In this case, a function of variable x. So wherever x is written, swap it by the variable of a number which is 8.
5. Two buses leave Bangor at the same time and travel in opposite directions. One bus
averages 57 mi/h and the other bus averages 43 mi/h. After how many hours will the buses be
450 mi apart?
Fleur has 32 collectable playing cards. 3/8 of the playing cards are red. 2/8 of the playing cards are blue. The rest were green. How many of the playing cards were green? Explain how you found your answer.
what is pi and why do we need it
Answer:
Pi is a mathematical term we need under the circumstances of solving complex math problems.
Answer:
pi explains everything
Step-by-step explanation:
pi goes on forever, so u could look in pi and find your birthday and even your name (in letter/number code : a=1 z=26 etc...) its pretty cool