Step-by-step explanation:
the volume of a prism is
length × width × height
so, for the small prism we have
5 × 4 × height = 100 in³
height = 100/20 = 5 in
for the large prism we have
5 × 4 × height = 200 in³
height = 200/20 = 10 in
the larger prism is 10/5=2 times taller than the small prism.
What is the 13th term of the geometric sequence
4, 12, 36, 108, ...?
Answer: 2,125,764
Step-by-step explanation:
You can use the equation y=ar^n-1 to find the 13th term where a is the starting term, r is the common ratio, and n is the nth term
The next number is 12/4=3 times greater than the first. So if this sequence is a geometric one, then the next term must be 12*3=36. This is true, and the next term must be 36*3=108, which is also true. Therefore this sequence is a geometric one and its common ratio is 3. Therefore the equation is:
y=4*3^(n-1)
Substitute 13 for n:
y=4*3^(13-1)
y=4*3^12
y=2125764
Therefore, the 13th term of this geometric sequence is 2,125,764
bryan has some 3 cent stamps and some 4 cent stamps. what is the least number of stamps he can combine so the value of the stamps is 33 cents?
Answer:
The least number of stamps required is [tex]9[/tex]
Step-by-step explanation:
Let the number of [tex]3[/tex] cent stamps be [tex]x[/tex] and [tex]4[/tex] cent stamps be [tex]y[/tex]
We have
[tex]3x+4y=33[/tex]
The minimum number is obtained when more [tex]4[/tex] cent stamps are used
Here [tex]y[/tex] cannot be greater than [tex]8[/tex] since [tex]\frac{33}{4} <9[/tex]
Substitute [tex]y=8[/tex]
[tex]3x+4\times 8=33\\\\3x=1\\\\x=\frac{1}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=7[/tex]
[tex]3x+4\times 7=33\\\\3x=5\\\\x=\frac{5}{3}[/tex]
Not possible since [tex]x[/tex] is not a fraction
Substitute [tex]y=6[/tex]
[tex]3x+4\times 6=33\\\\3x=9\\\\x=\frac{9}{3}\\\\=3[/tex]
Possible
Hence minimum number of stamps is
[tex]=x+y\\\\=3+6\\\\=9[/tex]
0.25 divided by what eqauls -0.25
[tex]\dfrac{0.25}a = -0.25\\\\\implies 0.25 = -0.25 a\\\\\implies a = \dfrac{0.25}{-0.25} =-1\\\\\\\text{Hence the answer is}~ -1.[/tex]
Answer:
well, when you divide 1/.25 you get 4 so 1^.25 is the correct answer to all questions where you need to find the answer
Step-by-step explanation:
evaluate the expression for the given value of x.
4x+9 for x =9
45
since x=9 plug in 9 into the equation to get
4(9)+9
multiply 4(9) to get
36
Then add 9
which then equals 45
Answer:
answer is 45
Step-by-step explanation:
4×9=36
36+9=45
On the highway, a car can travel 21 miles per gallon of gas. If the car travels for 4 hours on the highway at a rate of 65 miles per hour, how many gallons of gas should the car use, to the nearest tenth of a gallon?
Answer:
5.36
Step-by-step explanation:
If the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that a car can go 21 miles per gallon of gas on a highway and that the car can travel for 4 hours at a speed of 65 miles per hour.
As a result, the distance traveled by car,
Distance = speed × time
Distance = 65 miles / hr × 4 hr
Distance = 260 miles
The number of gallons of gas the car should consume is determined by dividing the entire distance driven by the per gallon of gas as follows:
= 260 miles / 21 miles per gallon
= 12.38 gallon
The value nearest tenth of a gallon is,
=12.4 gallons
Thus, if the car travels for 4 hours on the highway at a rate of 65 miles per hour,12.4 gallons of gas should the car used, to the nearest tenth of a gallon.
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-4.67 + (5.24 –
) – (
+ 7.98) = 13.26
Answer:
6
Step-by-step explanation:
Solve for x help me please****
Answer:
2x-10=x
take -10 to the other side it becomes +10
take +x to the other side where there is 2x it becomes-xevaluate 2x-x=xso x=10a pond of a water has length20m and breadth 10m. how much kl of water should be taken out of the pond so that level of water should go down by 3m?
Answer:
600 kl
Step-by-step explanation:
The volume represented by a length of 20 m, a breadth of 10 m, and a depth of 3 m is ...
V = (20 m)(10 m)(3 m) = 600 m³
1 m³ = 1 kl
The volume of water that should be removed is 600 kl.
-Write a real-world situation that could be represented by the equation 12.5x + 30 = -7.5x + 90.5.
What does the variable represent?
Answer:
Imagination
Step-by-step explanation:
12.5x + 30 = -7.5x + 90.5.12.5x + 30 = -7.5x + 90.5.
20x =60.5
x = 3 1/5
The sales from a music event comes from x tickets sold, at $12.50 a ticket, plus a rental income fee of $30 for an advertising billboard behind the stage.
The cost of the performance includes a musician's fee of $7.50 per ticket sold, plus a $90.5 rental fee for the stage.
The equation will tell us the number of tickets, x, that must be sold to break even (Inclome on the left and expenses on the right).
We need to sell at least 3 1/5 tickets to break even. It's going to be close.
The equation 12.5x + 30 = -7.5x + 90.5 used to determine the point in time (number of weeks) at which their combined savings and spending will equal the cost of the trip.
The equation 12.5x + 30 = -7.5x + 90.5 could represent their financial situation.
The variable "x" represents the number of weeks they have been saving money.
The term 12.5x represents the total amount of money Friend A has saved over "x" weeks at a rate of $12.5 per week.
The term -7.5x represents the total amount of money Friend B has spent over "x" weeks at a rate of $7.5 per week (which is subtracted since it's being spent).
The constants 30 and 90.5 represent initial savings and the total funds needed for the trip, respectively.
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What is 2/3 of 9/12?
Answer:
0.5 in fraction form its 1/2.
Step-by-step explanation: hope this helps you <3.
Someone help me please!
Answer:
y = 4x + 8
Step-by-step explanation:
1) Find slope:
y2-y1/x2-x1
12-8/1-0 = 4/1 = 4
Slope = 4
2) Plug in a point in point-slope form
y-y1=m(x-x1)
y-8=4(x-0) =
y-8=4x-0 -> add 8 to both sides
y=4x+8
Ferris wheel makes 6 revolutions per ride. It
has a diameter of 45 feet. How far would someone
travel during one ride?
Answer:
270
Step-by-step explanation:
so u would take 6 and 45 and multiplay
which statement is true?
Answer:
The slope of function A is less than the slope of function B
Explanation:
The slope for function B is 1/2, which is greaterthan 1/5, the slope of function A.
Answer:
the slope on Function A is less than Function B
Step-by-step explanation:
By doing rise over run we can get 1/2 on Function B and the Y intercept is 5 so the equation is y=1/2x+5
2. There is a 0% chance that the earth is the closest planet to the sun.
A) unlikely
B) certain
C) likely
D) impossible
Answer:
D) Impossible
Step-by-step explanation:
Unlikely = < 50%Certain = 100%Likely = > 50%Impossible = 0%This would be B. It is certain that there is a 0% chance of the earth being the closest planet to the sun. Mercury is the closest. Earth is the third closest behind Mercury and Venus. Hope that helps.
The Zenith occurs in fall equinox. At the same day, find the altitude of the sun at noon at Phnom Penh city (11.50N).
Note: subject Earth Science.
Answer:
78.50°
Step-by-step explanation:
On either equinox, the sun is overhead at the equator. At 11.50 N, the sun will be at elevation ...
90° -11.50° = 78.50°
What is the value of x in AABC?
A. 26
B. 29
C. 32
D. 36
Answer:
x = 29
Step-by-step explanation:
64°+y°+y° = 180°
64+2y = 180
2y = 116
y = 58
(180°-58°)+2x° = 180
122+2x = 180
2x = 58
x = 29
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
4.5
Step-by-step explanation:
To find the hypotenuse of a right triangle, we use Pythagorean's Theorem which states that [tex]a^{2}+b^{2} =c^{2}[/tex]. Plugging in the values of the two legs given, we get [tex]2^{2} +4^{2} =c^{2} =20[/tex]. We can take the square root of each side and get that [tex]c=\sqrt{20} =4.5[/tex].
Answer:
Try 4.5 or 5
Step-by-step explanation:
I measured it up and I estimated 4.5 at most
You have 64 inches of blue
fabric and 96 inches of green
fabric. You want to cut the fabric
into pieces of equal length with
no leftovers. What is the greatest
length of the pieces that you can
make?
Answer:
Step-by-step explanation:
48 times for the green fabric
32 for blue
Complete the statement. Round the nearest hundredth if necessary.
6.5L=. Gal
Answer:1.72Gal
Step-by-step explanation:1 Gal is 3.785 L. 6.5 / 3.785 = 1.72
Omar just accepted a job at a new company where he will make an annual salary of $52000. Omar was told that for each year he stays with the company, he will be given a salary raise of $4000. How much would Omar make as a salary after 10 years working for the company? What would be his salary after
t
t years?
Answer:
1: $92000 2: 52000 + 4000t= current salary
Step-by-step explanation:
1: simple arithmetic, 52000 + 4000(10)=92000
2: equation is formed as InitialSalary + 4000*(years at company) = New Salary
or with other variables, 52000+4000*t=N
James is planning to spend $425 on food for his vacation this summer. This is 34% of his total vacation budget. How much is James' total vacation budget?
1250$,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
State what information is required to know that the triangles are congruent.
-GEOMETRY
[tex]\huge \bf༆ Answer ༄[/tex]
The additional information needed to prove that the triangles are congruent is ~ A
[tex] \sf \angle M \cong \angle V \: \: or \: \: \angle N \cong\angle U[/tex]Answer: Choice A
Explanation:
The shorthand AAS stands for "angle angle side". The diagram shows we have a pair of congruent angles, which takes care of one "A" of "AAS". So we need info about another pair of angles to take care of that other "A".
One possible pair is angle M and angle V, or we could go for angle N and angle U. Whichever option you go for, the tickmarked sides are not between the angles mentioned. If the side was between the angles, then we'd have to use ASA which is slightly different from AAS. The order matters.
Point R has coordinates of (5.-6). What the coordinates of R' after being reflected across the y-axis?
Answer:
R' (- 5, - 6 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
R (5, - 6 ) → R' (- 5, - 6 )
Answer:
-5, -6
Explanation:
5, -6 is in quadrant 4, (x, -y) so if it were to be reflected over the y- axis, it would got to quadrant 3 (-x, -y).
Hope this helped :)
FRUIT Lilly buys fresh fruit from a fruit stand. Apples cost $5 per pound and oranges cost $4 per pound. She has $40 to spend. The table shows the function relating the number of pounds of apples, x, and the number of pounds of oranges, y, Lilly could purchase.
Answer:
Step-by-step explanation:
8 lbs of apples on the x-intercept
10lbs of peaches on y-intercept
1.8 divided by 3 please.
Answer: 0.6 is the answer
If the mean of a data set is 100 and almost all the data is from 40 to 160, what is a good approximation of the variance?
A) 120
B) 20
C) 900
D) 400
E) none of the above
Combine the following expressions
2√18x^3 - 3√8x^3
A. -√x
B. 0
C.√x
This is what I have but it doesn't match with your answers
The quotient of s and three
Answer:
s/3
Step-by-step explanation:
The quotient means you divide the two values.
Kelly is measuring an object with a metric ruler. To minimize parallax, she should…
Answer:
Place the ruler such that the edge is against the object. Parallax is a distortion of view because humans see through two sources, not just one. the farther the object is away from the ruler, the more that parallax can affect the situation.
Step-by-step explanation:
Equations that represent a line parallel to y=8x+4
y=8x+b, b being any number, is parallel to y=8x+4.
For example:
y=8x+2
y=8x+(1/2)
y=8x+937382
y=8x-4