Step-by-step explanation:
I think there are some typos in a)
anyway, this is a geometric sequence.
that means that after a starting value each new term is created by multiplying the previous term by a certain factor.
a)
s1 = 450
factor f = 2.5
so,
s2 = 450×2.5 = 1125
and so on.
from that we see that
sn = 450×(2.5)^(n-1)
and as
450/2.5 = 180
or
450 = 180×2.5
we can "extract" another 2.5 factor from the basic 450.
so,
sn = 180×2.5×(2.5)^(n-1) = 180×(2.5)^n
b)
s5 = 180×(2.5)⁵ = 17,578.125 or rounded 17578
c)
the question is unclear. are the bacteria of previous generations still there, when a new one is generated ?
then the 2.5 factor creates the sum implicitly, and the total number of bacteria in the first 10 generations is simply the 10th term s10.
s10 = 180×(2.5)¹⁰ = 1716613.76953125 = 1,716,614
or is it meant to sum the numbers of each generation (the old bacteria "go away", when the next generation is generated) ?
the sum of the first n terms of such a geometric sequence is
sum = a1×(1 - f^n)/(1 - f)
so, for our first ten terms
sum = 450×(1 - 2.5^10)/(1 - 2.5) =
= 450×-9535.7431640625/-1.5 =
2860722.94921875 = rounded 2,860,723
pls help me i need help
Answer:
3x was subtracted from the left side, but 3x was subtracted from the right side. The Subtract Property of Equality states that you can subtract the same number from each side and the equation will remain true. But 3x and 3 are not the same number (unless x is 1).
x = -8/5
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
[tex](7x+3x)+(21)=5[/tex] [tex]10x + 21 = 5[/tex]Step 2: Subtract 12 from both sides.
[tex]10x + 21 - 21 = 5 - 21[/tex] [tex]10x = -16[/tex]Step 3: Divide both sides by 10.
[tex]\frac{10x}{10} = \frac{-16}{10}[/tex] [tex]x = -\frac{8}{5}[/tex]9514 1404 393
Answer:
3x31x = -1.6Step-by-step explanation:
You answer this sort of question by comparing each line to the line above to see what the differences are. In the second line, the term 3x is missing from the left side of the equal sign, and the value 5 has been changed to the value 2 on the right side. The wording of the statement you're to fill in tells you that it should read ...
3x was subtracted from the left side, but 3 was subtracted from the right side.
... 3x and 3 are not the same number (unless x is 1 .)
__
The correct solution is ...
7x +21 +3x = 5 . . . . . . given
10x +21 = 5 . . . . . . . . . collect terms
10x = -16 . . . . . . . . . . . subtract 21 from both sides
x = -1.6 . . . . . . . . . . . . divide both sides by 10
_____
Additional comment
It can often work well to "read ahead" when answering a question or series of questions. The later questions or comments often provide clues that help you understand how to answer the earlier questions.
Here, for example, it becomes clear that 3x and 3 were subtracted from the different sides of the equation. You can find that out simply by reading the rest of the statement you're to fill in. These are the answers to the questions asked in the first part of the statement.
Solve the inequality: 2-8x>34, show work
Step-by-step explanation:
we are to first collect like terms here I mean all numbers that look alike are to be out on the same side so we are now going to have.
[tex]2 - 8x > 34[/tex]
[tex] - 8x > 34 - 2[/tex]
[tex] - 8x > 32[/tex]
now we are to divide both sides with the coefficient of x and we are to get
[tex] - 8x \div - 8 < 32 \div - 8 = x < 4[/tex]
2|3x-9|+5<25 help please
The volume of the prism below is 180in3. What is the value of x?
gsgs helpppp.plssssss
Ashley, Kevin, and Deshaun served a total of 96 orders Monday at the school cafeteria. Kevin served 4 times as many orders as Deshaun. Deshaun served more orders than Ashley. How many orders did they each serve.
Answer:
D = 96
K = 96 x 4 = 384
A= 4
Step-by-step explanation:
Deshaun = 96
Kevin = 96 x 4 = 384
Ashely = 384 / 96 = 4
Simplify the following expression. ‐3 + 7(a – 3b – 1) – 4(10 – a + 2b)
Answer:
11a−29b−50
Step-by-step explanation:
Hope this helps brodie
The simplified expression for ‐3 + 7(a – 3b – 1) – 4(10 – a + 2b) is 11a - 29b - 50.
To simplify the expression -3 + 7(a - 3b - 1) - 4(10 - a + 2b), we can apply the distributive property and combine like terms:
-3 + 7(a - 3b - 1) - 4(10 - a + 2b)
= -3 + 7a - 21b - 7 - 40 + 4a - 8b
= (7a + 4a) + (-21b - 8b) + (-3 - 7 - 40)
= 11a - 29b - 50
Therefore, the simplified expression is 11a - 29b - 50.
To know more about simplified expression, refer here:
https://brainly.com/question/22860327
#SPJ2
10. In the figure to the right, AB is parallel to CD. Which statement proves that 23 = 277
A. If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
B. If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
.If two parallel lines are cut by a transversal, the corresponding angles are congruent.
D. If two parallel lines are cut by a transversal, the vertical angles are congruent.
Answer:
The answer is what I assume to be C. If two parallel lines are cut by a transversal, the corresponding angles are congruent
Step-by-step explanation:
Where is the image for this?
Hope this helped. ;)
Determine the equation of the line perpendicular to y = 1 - 1/4x and passing through the point (-3,5)
please I need help!!!!
Answer:
y = 4x + 17
Step-by-step explanation:
y = 1 - 1/4x = - 1/4 x + 1 .... slope -1/4
perpendicular line slope = - (1 / (-1/4) = 4
pass (-3,5): (y-5) / (x - -3) = 4
y-5 = 4x + 12
y = 4x + 17
what is the answer to the bottom question?
Answer:
its answer is the same as the top, s³+12
8 × 4× 8 = 256
12 × 12 × 12 = 1,728
256 + 1,728 = 1,984
total volume is: 1,984
5634 ÷ 18 and show work
Answer:
313
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Jack had m that problems to complete during his vacation. He solved the same number of problems every day and finished them all in 5 days. How many problems did Jack solve per day?
Answer: 1 problem per day
Step-by-step explanation:
m/5 problems completed in 5 days.
substite m with 5 because 5 days
5/5
5/5=1
Therefore Jack solved 1 question per day.
The number of problems Jack solve per day is 4 problems.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Number of days= 5days
Now,
To find how many problems Jack solved per day, we need to divide the total number of problems by the number of days. This is because he solved the same number of problems every day. So, we can write an equation as:
m / 5 = p
where m is the total number of problems and p is the number of problems per day.
To solve for p, we need to multiply both sides of the equation by 5 and get:
p = m
This means that Jack solved m problems per day.
For example, if m = 20, then Jack solved 20 / 5
= 4 problems per day.
Therefore, by algebra the answer will be 4.
More about the Algebra link is given below.
brainly.com/question/953809
#SPJ2
If I have 39 campers divided into groups of 6 with 1 counselor assigned to each group, what is the least number of camp counselors that will be needed
Answer:
7 counselors
Step-by-step explanation: 39 cannot be broken into 6 evenly, so you would either have 3 extra students without a counselor, or half of a counselor walking around, so 7.
Look at the sample work shown and determine the error, if any.
The multiplication property of equality was not performed correctly.
The addition property of equality was not used correctly.
There are no mistakes.
Answer:
There are no mistakes
Step-by-step explanation:
I did the assignment
Write your own problem, and solve it. Be ready to share the question tomorrow.
Answer: 1,409.737566825
1.785 * 789.768945 = 1,409.737566825
Step-by-step explanation:
Which expression is equal to 8.89? *
Answer:
1/4
Step-by-step explanation:
Find the perimeter of a triangle with sides of 12 inches, 14 inches, and 16 inches.
Answer: 42 inches
Step-by-step explanation:
a+b+c=perimeter
12+14+16=42 inches
Perimeter of the triangle = (12 + 14 + 16) inches
= 42 inches
Hello ! Can anyone help me with this ! Please and thank you
Answer:
Thank you for being so kind! X=15
Step-by-step explanation:
each expression combined is equal to 180.
so you must put 5x+9+7x-9 and solve to get 15!
only my freinds do not awnser
Pleaseee help me I’m stuck
Answer: 105
Step-by-step explanation:
its up by 30 and 35 of and onn
how to use Lcd in this problem? [a-2. -_1_ =_3_]find Lcd [ a+3 1 a-2]. (a+3)(a+2). multiply all neumerator to (LCD) a-2 - 1= 3 ___ _ a/+3. a+/2 (a-6 )(a+6) - 1 (a+2)(a+3)(a+2/)/*) negative a +positive2: distribuet: (a(a+3)++2. = (a+3)
It's not entirely clear to me what you're trying to solve, but it looks like the initial equation is
[tex]\dfrac{a-2}{a+3} -1 = \dfrac3{a+2}[/tex]
First convert each term into a fraction with the same (i.e. the least common) denominator. The first term needs to be multiplied by a + 2; the second term by (a + 3) (a + 2); and the third term by a + 3 :
[tex]\dfrac{a-2}{a+3}\cdot\dfrac{a+2}{a+2} -1\cdot\dfrac{(a+3)(a+2)}{(a+3)(a+2)} = \dfrac3{a+2}\cdot\dfrac{a+3}{a+3} \\\\ \dfrac{(a-2)(a+2)}{(a+3)(a+2)} - \dfrac{(a+3)(a+2)}{(a+3)(a+2)} = \dfrac{3(a+3)}{(a+3)(a+2)}[/tex]
Now that everything has the same denominator, we can combine the fractions into one. Move every term to one side and join the numerators:
[tex]\dfrac{(a-2)(a+2)-(a+3)(a+2)-3(a+3)}{(a+3)(a+2)} = 0[/tex]
Simplify the numerator:
[tex]\dfrac{(a^2-4)-(a^2+5a+6)-(3a+9)}{(a+3)(a+2)} = 0 \\\\ \dfrac{-8a-19}{(a+3)(a+2)} = 0[/tex]
If neither a = -3 nor a = -2, we can ignore the denominator:
[tex]-8a-19 = 0[/tex]
Solve for a :
[tex]-8a = 19 \\\\ \boxed{a = -\dfrac{19}8}[/tex]
How many ways can 5 different books be stacked on a shelf?
1) 24
2) 120
3) 2
4) 6
Answer:
120
Step-by-step explanation:
There are 5 different ways to put the first book
Now there are 4 books left
There are 4 different ways to put the second book
Now there are 3 books left
There are 3 different ways to put the third book
Now there are 2 books left
There are 2 different ways to put the fourth book
Now there are 1 book left
5*4*3*2*1
120
Simplify square root 4x squared
Answer:
[tex]\sqrt{4x^2}=2|x|[/tex]
Step-by-step explanation:
We are given the radical [tex]\sqrt{4x^2}[/tex] and we have to simplify it down as much as possible.
We first will have to find out what numbers are inside the square root, we can see that there is a 4 and an [tex]x^2[/tex], of which both can be taken out of the square root by simplification.
The square root of 4 is 2, and the square root of [tex]x^2[/tex] is [tex]x[/tex].
Due to how radicals work, we have to multiply 2 and [tex]x[/tex], but before that, we have to preserve how the radical was beforehand. We know that a radical cannot have a negative radicand, and due to that we must add absolute value to keep the equation's original status the same.
To sum it all up, our answer is [tex]2|x|[/tex], due to us simplifying it down, and applying absolute value to preserve the answer before it was simplified.
Cheers!
River Fun Boats rents paddle boats. The euqation C = 0.10t + 4 gives the charge in dollars, C, for renting a paddle boat for t minutes. What is the charge for renting the paddle boat for 20 minutes?
Answer:
6
Step-by-step explanation:
C=.10t+4
C=.10(20)+4
C=2+4
C=6
Write this number in scientific notation. 33,200
Answer:
104 = 10,000 x 3.32 = 33,200
Step-by-step explanation:
hope this helps
Hello There!
When we are writing numbers in scientific notation, we must make sure that the coefficient is between 1 and 10:
3.32x10^4
Hope this helps!
All the best! :)
[tex]GraceRosalia[/tex]
Enter your answer as a Mixed number pls.
The answer is [tex]2\frac{3}{4}[/tex] more gallons
Find the difference,
832 - 675
Answer:
157
Step-by-step explanation:
157 would be you're asnwer
please tell me If u got u right or if its incorrect
What is the x intercept of f(x) = x + 12
Answer:
-12,0
Step-by-step explanation:
i took the quiz
Answer:
The x intercept is -12
Step-by-step explanation:
Because we need to find the x intercept (x,0)
We can substitute y or F(x) into 0
0=x+12
Subtract 12 on both sides
x=-12
so (-12,0) or -12
Hope this helps!
HELP!! find x.
answer choices:
x=20
x=92
x=90
x=12
pls explain ur answer if u can
Answer:
x = 20
Step-by-step explanation:
I just plugged in the x possibilities until they both matched, and because they are on opposite sides, as in if they were in the same grid they would be right across from each other, they represent the same angle.
You could also set them equal to each other.
As in:
3x + 32 = 5x - 8
This would simplify (after isolating x) to:
40 = 2x
Divide by 2
20 = x
_________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
Step by step :3x + 32° + 5x - 8° = 180°
8x + 24° = 180°
8x = 180° - 24°
8x = 156°
x = 156 ÷ 8
x = 19,5°
x [tex]\approx[/tex] 20°✔ (A.)
3. Determine whether each relationship is a function. Explain