Given:
The function is:
[tex]p(t)=500(0.25)^t[/tex]
Where p(t) represents the number of milligrams of the substance and t represents the time.
To find:
The correct explanation for the number 0.25 and 500 in the given function.
Solution:
The general exponential function is:
[tex]y=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/decay factor. If [tex]0<b<1[/tex], then decay factor and if [tex]b>1[/tex], then growth factor.
We have,
[tex]p(t)=500(0.25)^t[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=500[/tex], it means initial there are 500 milligrams of the substance.
[tex]b=0.25[/tex], this value is less than 1, it means the substance is decreasing by a factor of 0.25.
Therefore, 0.25 means the substance is decreasing by a factor of 0.25 and 500 means the initial value of substance is 500 milligram.
Select the equivalent expression.
the equivalent expression is C
Factor the following expression.
12x2 + 22x + 8
Answer:
The answer is 2(23x+4).
[tex]12 {p}^{5} r \div ( - 10pq)[/tex]
ASAP!!!! PLS HELP
Answer:
Step-by-step explanation:
[tex]\frac{12p^{5}r}{-10pq} = \frac{-6p^{5-1}r}{5q}\\\\=\frac{-6p^{4}r}{5q}[/tex]
[tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
Find a polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity3 , and 2 as a zero of multiplicity 1.
The polynomial function of degree 7 with the given zeros and multiplicities is: f(x) = x³(x + 2)³(x - 2)
To find a polynomial function with the specified zeros and multiplicities, we can construct it using the factors that correspond to each zero and multiplicity.
Since -2 has a multiplicity of 3, it means it appears three times as a zero. Similarly, 0 has a multiplicity of 3, and 2 has a multiplicity of 1.
A polynomial function with these zeros and multiplicities can be written as:
f(x) = (x + 2)³ × x³ × (x - 2)
To make it a polynomial of degree 7, we can multiply it by an additional linear factor:
f(x) = (x + 2)³ × x³ × (x - 2) × (x - r)
Where "r" is a constant representing the last factor. This factor ensures the degree of the polynomial is 7.
Now, we need to find the value of "r" to complete the polynomial. Since we already have three factors with multiplicity 3 and one factor with multiplicity 1, the polynomial has already reached its degree of 7.
Therefore, we don't need to include the "x - r" factor, and the final polynomial is:
f(x) = (x + 2)³ × x³ × (x - 2)
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The polynomial function of degree 7 with -2 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 2 as a zero of multiplicity 1 is f(x) = x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2.
To find a polynomial function of degree 7 with the given zeros and multiplicities, we can start by constructing the factors of the polynomial.
Since -2 is a zero of multiplicity 3, we have the factor (x + 2)^3. Similarly, since 0 is a zero of multiplicity 3, we have the factor x^3. Lastly, since 2 is a zero of multiplicity 1, we have the factor (x - 2).
Multiplying these factors together, we obtain:
(x + 2)^3 * x^3 * (x - 2)
Expanding this expression, we get:
(x^3 + 6x^2 + 12x + 8) * x^3 * (x - 2)
To simplify further, we multiply the terms:
(x^6 + 6x^5 + 12x^4 + 8x^3) * (x - 2)
Expanding again, we obtain:
x^7 - 2x^6 + 6x^6 - 12x^5 + 12x^4 - 24x^3 + 8x^3 - 16x^2
Combining like terms, we get:
x^7 + 4x^6 - 12x^5 + 20x^4 - 16x^2
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Discover the rate of change (slope) of these two points. (-4,5) and (5,-4).
Answer:
-1
Step-by-step explanation:
y2-y1/x2-x1
-4-5/5- -4
-9/9
-1
If all the members of a team are juniors or seniors, and if the ratio of juniors to seniors on the team is 3:5, what percent of team members are seniors?
Answer:
S = 62.5%
Step-by-step explanation:
Let the junior members be J.Let the senior members be S.Given the following data;
Ratio of J:S = 3:5 = 3 + 5 = 8
To find what percent of team members are seniors;
[tex] S = \frac {5}{8} * 100 [/tex]
[tex] S = \frac {500}{8} [/tex]
S = 62.5%
Additionally, to find what percent of team members are juniors;
J = 100 - S
J = 100 - 62.5
J = 37.5%
Ryan took a hike on sunday. he hiked uphill for 15 minutes. then he hiked another River for 12 minutes. he hiked downhill for 8 minutes along a river for 5 minutes. how many seconds did Ryan hike on Sunday? plz help
Answer:
2400 seconds
Step-by-step explanation:
Answer:
40 min = 2400 sec
Step-by-step explanation:
A jeweler had a fixed amount of gold to make bracelets and necklaces. The
amount of gold in each bracelet is 6 grams and the amount of gold in each
necklace is 16 grams. The jeweler used 178 grams of gold and made 7 more
necklaces than bracelets. Write a system of equations that could be used to
determine the number of bracelets made and the number of necklaces made.
Define the variables that you use to write the system.
Answer:
6b+16n=178
n=b+7
Step-by-step explanation:
Let b=the number of bracelets made
Let n=the number of necklaces made
System of Equations:
6b+16n=178
n=b+7
The following is a parallelogram solve for the variables
Which expression is equivalent to StartAbsoluteValue 8 EndAbsoluteValue + StartAbsoluteValue Negative 7 EndAbsoluteValue?
Answer:
15
Step-by-step explanation:
Given :
StartAbsoluteValue 8 EndAbsoluteValue + StartAbsoluteValue Negative 7 EndAbsoluteValue
THE ABSOLUTE value of any given number is the positive equivalent of that number ; hence ;
|8| = 8 ;
|-7| = 7
Hence,
|8| + |-7| = 8 + 7 = 15
Answer:
15
Step-by-step explanation:
Find the missing angle measurements of HFG ? , fill in the boxes
Answer:
Angle HFG = 24 degrees
Step-by-step explanation:
From the diagram, we have the following;
Angle EFH and angle HFG are complementary (they add up to be 90 degrees)
angle EFH + angle HFG = 90
Angle HFG = 90-66
Angle HFG = 24 degrees
True or False
The radius of the circle is congruent to the radius of an inscribed regular polygon inside the circle.
A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. The given statement is True.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The given statement is true and can be observed in the given image below.
Hence, the given statement is True.
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Use this picture to solve for X
Answer:
x=2
Step-by-step explanation:
i would set up a system of equation using the pythagorean theorem:
1^2+x^2=z^2
4^2+x^2=y^2
Add up these equations to get:
17+2x^2=y^2+z^2
But notice that
y^2+z^2=5^2
So you can substitute
17+2x^2=25
2x^2=8
x^2=4
x=2
:)
4x + 5 = 3x + 4??????????
4x + 5 = 3x +4
4x - 3x = 4-5
x = -1
value of x is equal to -1
Answer:
x = -1
Step-by-step explanation:
4x + 5 = 3x +4 (subtract 3x from both sides)
-3x -3x
=1x =0
rewrite: x + 5 = 4 (subtract 5 from both sides)
-5 -5
=0 =-1
Therefore x = -1 (Please mark brainliest hope i helped :)
Plz help ill give brainlyest
Answer:
your answer would be become 11 feet
if each square on the grid represents 400mi square how many miles will jacob's family travel?
Answer:
80miles
Step-by-step explanation:
Area of a square grid = L²
L is the side length of the grid
Given that Area of the square = 400mi square
400 = L²
L =√400
L = 20miles
To get the number of miles travelled, we will find its perimeter
P = 4L
P = 4(20)
P = 80miles
Hence Jacob's family travels 80miles
John got $30 for weeding the garden. He used money to buy a $15.25 video game and three snacks that cost $1.25 each. He bought his friend a snack too. If he went home with 1/6 of the money he started with, how much did his friends snack cost? A $5.00 B $6.00 C $8.50 D $11.00 E $13.50 F $14.75
Answer:
B
Step-by-step explanation:
His friends snack was 6 dollars.
15.25+1.25= 16
16+1.25= 17.25
17.25+1.25= 19
1/6 of 30 is 5 because 5x6=30.
30-19=11
He has to have 5 left over so the snack was 6 dollars.
Help me with this problem !!!!!!!!!!
Answer:
Hi, your answer is y=[tex]-\frac{1}{2} x[/tex]-3
Step-by-step explanation:
We will use the slope-intercept formula which is
[tex]\frac{y2-y1}{x2-x1}[/tex]
We will use two points in this case I'll use
(-2,-2) and (-8,1)
[tex]\frac{1-(-2)}{-8-(-2)}[/tex]=[tex]-\frac{3}{6}[/tex] which can be simplified as [tex]-\frac{1}{2}[/tex]
Your Y will be -3
which your final answer will be y=-1/2x-3
Hope this helps :)
Sally is three times as old as Sam. The sum of their ages is 84. How old is Sally?
Answer:
Sally is 63
Step-by-step explanation:
Represent Sally's age by x and Sam's by y.
Then x = 3y and x + y = 84.
Substituting 3y for x in the second equation, we get:
3y + y = 84, or 4y = 84, or y = 21. Since Sally is 3 times as old as Sam, we multiply 21 by 3: Sally's age is 3(21 years) = 63 years
p borrowed Rs. 16000 from a person at 12 % per Annum simple interest and lent the whole amount to Q at the same rate of annually compound interest, how much did he gain after 3 years ? Find it.
Answer:
P earned $ 718.85.
Step-by-step explanation:
Given that P borrowed $ 16000 from a person at 12% per annum simple interest and lent the whole amount to Q at the same rate of annually compound interest, to determine how much did he gain after 3 years the following calculation must be performed:
16,000 x 0.12 x 3 = X
1,920 x 3 = X
5,760 = X
16,000 x (1 + 0.12 / 1) ^ 3 = X
16,000 x 1.12 ^ 3 = X
16,000 x 1.404928 = X
22,478.85 = X
22,478.85 - 16,000 = 6,478.85
6,478.85 - 5,760 = X
718.85 = X
Therefore, P earned $ 718.85.
5.Stephanie and Ryan go together to a local video store. Stephanie rents two movies and three
games for a total cost of $24.30. Ryan rents three movies and one game for a total cost of
$18.25. How much does it cost to rent one movie? How much does it cost to rent one game? Show your work
Ranking correct answer brainliest :)
Answer:
b) tan 26° = 18/x
Step-by-step explanation:
tan is opposite/adjacent
Answer:
Answer B
Step-by-step explanation:
You have the angle, the opposite and are looking for the adjacent
The only solutions is using tan
tan = opposite / adjacent
Use the replacement set {3, 4, 9} to find the solution of the equation below.
3n−18=9
Answer:
[tex]n=9[/tex]
Step-by-step explanation:
[tex]3n-18=9[/tex]
[tex]3n+18=[/tex] +18
[tex]3n=27[/tex]
[tex]3(9)=27[/tex]
[tex]n=9[/tex]
A bike trail is 5 25 miles long. Rosie rides her bicycle on the bike trail 6 days a week. How many miles does Rosie ride per week? Choices are A. 30 2/5 miles B. 30 4/5 miles C. 32 2/5 miles D. 32 4/5 miles Thanks <3
Tomas needs lumber to make corner braces for a piece of furniture he is building. He cuts 4 feet from a board that is 8 feet long. With the wood
he has left, Tomas makes 18 corner braces of equal size. How many inches of wood does each brace use?
Answer:
Each brace uses 2.[tex]\overline 6[/tex] inches of wood
Step-by-step explanation:
The given parameters are;
The length of the board from which he cuts the wood = 8 feet
The length of the wood he cuts from the board = 4 feet
The number of corners on the braces of equal sizes he makes with the wood he has left = 18 corner brace
We have;
The length of the wood he has left = (The length of the board) - (The length of the wood he cuts from the board)
∴ The length of the wood he has left = 8 feet - 4 feet = 4 feet
The length of each brace the man can cuts from the wood he has left = (The length of the wood he has left)/(The number of corner braces he cuts)
∴ The length of each brace = (4 feet)/(18 braces) = (48/18) inches/(braces) = (8/3) inches/brace = 2.[tex]\overline 6[/tex] inches of wood per brace
A dog's leash is 4 m long and is attached to the corner of a 2 m × 2 m square doghouse at C, as shown. The dog is attached to the other end of the leash, at D. What is the area outside of the doghouse in which the dog can play? (A) 14π m^2 (B) 16π m^2 (C) 20π m^2 (D) 15π m^2 (E) 24π m^2
The area outside of the doghouse in which the dog can play is 16π m².
Thus, option (B) is correct.
Given:
The leash is 4 m long.
The doghouse is a 2 m × 2 m square.
First, the area of a square is given by side length squared
So, the area of the doghouse is:
Area of the doghouse = side length² = 2²
= 4 m².
Next, the area of the circle with a radius of 4 m.
The area of a circle is given by the formula A = πr²,
So, Area of the circle = π(4²) = 16π m².
Therefore, the area is 16π m².
Thus, option (B) is correct.
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There are 10 players on the swim team. How many ways can the coach
select 3 people to swim in the relay?
The coach can select 3 people to swim in the relay in 120 ways.
What is combination?'In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.'
According to the given problem,
Number of players = 10
Number of people to be selected = 3
We know,
[tex]^{n}C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex] where, n = Total number of players
r = Number of players to be selected
Number of ways to select 3 people out of 10 = [tex]^{10} C_{3}[/tex]
= [tex]\frac{10!}{3!*7!}[/tex]
= 120 ways
Hence, we can conclude, the coach can select 3 people out of 10 in 120 ways.
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answer this one for me thanks ppppp
Answer:
16.6 units
Step-by-step explanation:
Hi there!
We can use the Pythagorean theorem to help us solve this problem: [tex]a^2+b^2=c^2[/tex] where c is the longest side of a right triangle (the hypotenuse) and a and b are the other two sides
It's safe to assume that x is the longest side in this triangle, making it the c value. Plug 14 and 9 into the equation as a and b and solve for x:
[tex]14^2+9^2=x^2\\196+81=x^2\\277=x^2\\x=16.6[/tex]
Therefore, the value of x is 16.6 units when rounded to the nearest tenth.
I hope this helps!
What is the maximum value of this function?
b One of these numbers is the area of the outside curved surface of the cylinder, in cm', using
= 3. Which one?
A 15 B 30 C 1000 D 1500 E 3000
Answer:
B
[tex]area = 2\pi \: rh \\ = 2 \times 3 \times 5 \times 1 \\ = 30 \: {cm}^{2} [/tex]