The breakdown of a sample of a chemical compound is represented by the function p(t) = 500 (0.25)^t, where p(t) represents the number of milligrams of the substance and t represents the time. In years. In the function p(t), explain what 0.25 and 500 represent.
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.
Work out 2/3 of 30.
2/3 of 30
30:3=10
10*2=20
2/3 of 30 = 20
Answer:
20
Step-by-step explanation:
of means multiply
2/3 * 30
60/3
20
Find the area of this triangle.
Round to the nearest tenth.
7 m
125°
14 m
?] m2
Enter
Answer:
40.1
Step-by-step explanation:
i just did it and got it right
What is the interquartile range of the data set shown below?
25, 28, 32, 35, 36, 40, 46
Answer:
IQR = 12
Step-by-step explanation:
interquartile range is the difference between quartile 3 and quartile 1
in this set of data Q3 = 40 and Q1 = 28
so IQR = 12
can someone help please !! giving brainlist to anyone who answers
3 is the correct one!
Write an equation that meets these criteria:
1. It has a solution of x=5.
2. It includes the numbers 3, 7, and 8, and at least
two different operations (addition, subtraction,
multiplication, and division.)
Answer:
3x = 7 + 8
Step-by-step explanation:
3x = 7 + 8
3x = 15
x = 3
Se desea construir un parque con forma de sector circular con un radio de 402 pies y un ángulo central de 45°. ¿Cuál será la superficie ocupada por dicho parque?
Answer:
63462 pies
Step-by-step explanation:
De la pregunta anterior, debemos encontrar el área del sector
La fórmula se da como:
θ / 360 × πr²
Dónde:
θ = 45 °
radio = 402 pies
Área del sector =
45/360 × π × 402²
= 63461.742399 pies
Aproximadamente el área de la ocupada por el parque = 63462 pies
which statement would be true if you evaluate the expression (980+205)÷5
a. the solution is 5 times as small as 980-205
b. the solution is 5 times as small as 980+205
c. the solution is 5 times as large as 980+205
d. the solution is 5 times as large as 980-205
How can you determine whether a linear binomial is a factor of a polynomial without using the remainder theorem?
A linear binomial is a factor of a polynomial if the polynomial value is 0 at the zeros of the linear binomial
How to determine the factor?Assume a polynomial function is
P(x) = (x - 3)(x + 1)(x -2)
And a linear binomial is:
x - 3 = 0
We start by calculating the value of x in x - 3 = 0
x = 3
Next, we substitute x = 3 in P(x) = (x - 3)(x + 1)(x -2)
P(3) = (3 - 3)(3 + 1)(3 -2)
Evaluate
P(3) = 0
Since P(3) = 0, then the linear binomial x - 3 is a factor of P(x) = (x - 3)(x + 1)(x -2)
Read more about remainder theorem at:
https://brainly.com/question/13328536
#SPJ1
In 7 years, Tom will be half as old as Patty. Using P to represent Patty’s age now, write an expression for Tom’s age in 7 years.
Answer:
(P + 7) / 2 or 1/2(P+7)
Happy learning!
--Applepi101
14.
Which of the quadratic functions has the narrowest graph?
A. 9x2
B. 2/5x2
C. -10x2
D. -0.9x2
Answer:
A. 9x2
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
0
)
Focus:
(
0
,
1
36
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
1
36
x
y
−
1
9
0
0
1
9
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
0
)
Focus:
(
0
,
5
8
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
5
8
x
y
−
2
8
5
−
1
2
5
0
0
1
2
5
2
8
5
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
0
)
Focus:
(
0
,
−
1
40
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
1
40
x
y
−
1
−
10
0
0
1
−
10
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
0
)
Focus:
(
0
,
−
0.2
¯
7
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
0.2
¯
7
x
y
−
2
−
3.6
−
1
−
0.9
0
0
1
−
0.9
2
−
3.6
Which expression entered into a graphing calculator will return the probability
that at most 10 heads come up when flipping a coin 25 times?
A. binomcdf(25, 10,0.5)
B. binomcdf(10, 0.5, 25)
C. binomcdf(25, 0.5, 10)
D. binomcdf(10,25, 0.5)
SUBMIT
If GH = HI And FI =10 what is GI
Answer:
20
Step-by-step explanation:
By HL and CPCTC, GF = FI, so GI = 2FI = 2(10) = 20.
I will give 25 points for it if solve this problem
Answer:
5/27
30/81 = 10/17
it's just ratios but if you need then vice versa, swap numerator and denominator
Answer:
the person on top is correct :)
Step-by-step explanation:
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 – 8x < 2x + 3?
Answer:
I’m gay
Step-by-step explanation:
Answer:
Add 8x to both sides of the inequality.
Step-by-step explanation:
I got it right
Thank you everyone for helping me this year to get good grades I am giving points.
What percent of 602 is 358?
Answer:
168.16%
Step-by-step explanation:
A drawer contains 2 red shirts and 4 blue shirts. A second drawer contains 3 pairs of grey pants and 2 pairs of blue pants. A third drawer contains 8 pairs of white socks and 7 pairs of blue socks.
You choose one item from each drawer without looking. What is the probability of each outcome?
a) A blue shirt, blue pants, and blue socks
b) A red shirt, blue pants, and white socks
c) Nothing blue
Answer:
b . may be
may it helped u ....
a straight line has equation y=5-3x
what is the gradient of the line?
Answer:
-3
Step-by-step explanation:
1. rearrange so it's in the formula y=mx+C
2. y=-3x+5
y=mx+C
M=gradient
-3=m
gradient= -3
what is the slope of a line containing points (2,-1) (3,5)
Answer:
slope(m)=6
Step-by-step explanation:
(2 , -1)=(x1 , y1)
(3 , 5)=(x2 , y2)
use formula : y2 - y1/x2 - x1
=5-(-1)/3-2
=5+1/1
=6/1
=6
therefore slope of a line is 6.
Write the expanded form of the given expression.
(x^4)(x^4)
Answer:
[tex]x^{8}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex]x^{4}[/tex] × [tex]x^{4}[/tex] = [tex]x^{(4+4)}[/tex] = [tex]x^{8}[/tex]
a rectangle pool is 6 meters wide and 9 meters long. What is the area of the pool
30 square units is how much units ?
Answer: 30 units
:))
Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4.
Answer:
[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]
Step-by-step explanation:
We want to write the equation of a line that passes through the point (3, -1) and is perpendicular to the line:
[tex]y=6x-4[/tex]
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
The slope of the given equation is 6.
So, the slope of our perpendicular line is the negative reciprocal of 6, which is -1/6.
Next, we are given that it passes through the point (3, -1). Since we are given a point and know the slope, we can use the point-slope form. Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
We will substitute -1/6 for m and (3, -1) for (x₁, y₁). Hence:
[tex]\displaystyle y-(-1)=-\frac{1}{6}(x-(3))[/tex]
Simplify:
[tex]\displaystyle y+1=-\frac{1}{6}(x-3)[/tex]
Our answer is valid as it as, but we can simplify this into slope-intercept form. Distribute:
[tex]\displaystyle y+1=-\frac{1}{6}x+\frac{1}{2}[/tex]
And subtract one from both sides. Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]
A circle in the standard (x,y) coordinate plane has
center C(−1,2) and passes through A(2,6). Line
segment AB
___ is a diameter of this circle. What are the
coordinates of point B ?
Given:
Center of a circle is at point C(-1,2).
AB is the diameter of the circle.
Coordinates of the point A are A(2,6).
To find:
The coordinates of point B.
Solution:
Let the coordinates of point B are (a,b).
If AB is the diameter of the circle, then A and B are end points of diameter of the circle and the center C is the midpoint of AB.
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Point C = Midpoint of AB
[tex](-1,2)=\left(\dfrac{2+a}{2},\dfrac{6+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{2+a}{2}=-1[/tex]
[tex]2+a=-1\times 2[/tex]
[tex]a=-2-2[/tex]
[tex]a=-4[/tex]
Similarly,
[tex]\dfrac{6+b}{2}=2[/tex]
[tex]6+b=2\times 2[/tex]
[tex]b=4-6[/tex]
[tex]b=-2[/tex]
Therefore, the coordinates of point B are (-4,-2).
help ill give brainliest
Answer:
Bottom Left
Step-by-step explanation:
We can check by seeing the numbers with the tens place that has the digit 1.
We have numbers 10, 10, 15, 15, 15
That means one's digit values of 0, 0, 5, 5, 5
The bottom left is the only option.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer: bottom left
Step-by-step explanation:
A king rules a small mountain kingdom which is in the form of a square of length 4 kilometers. The square is described by the coordinate system0≤≤4,0≤≤4. The king has four adult children, each of which has a luxury palace located at the points (1,1),(3,1),(1,3),(3,3). Each child owns all the land that is nearer their palace than any other palace.
Sketch a Voronoi diagram to represent this information.
Answer:
i can not get the answer
Jake has 12 sheep all but 9 die how many does he left ?
12
9
3
Answer:
Jake has 9 sheep left
Step-by-step explanation:
As the question says, Jake has 12 sheep and all but 9 die. This means that he has 9 sheep left.
Answer:
3
Step-by-step explanation:
Jake has 12 sheeps but 9 died
Jake loss 9 sheeps
Solution:
12-9
=3
How much money should be deposited in an account today that earns 4% compounded monthly so that it will accumulate to $10,000 in 5 years?
Answer:
$8206.37
Step-by-step explanation:
According to the Question,
Given, Some money should be deposited in an account today that earns 4% interest Annually. but it is compounded monthly so (4/12)% Will be the new interest Rate .
Now, What Money Should be Invested For 5 years(60 months) to get $10000 in Return .
The Formula for Compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex] .
We have, r=4% , n=12 , t=5 & A=$10000 Put These all value in above equation.
[tex]10000=P(1+\frac{0.04}{12})^{60}[/tex]
[tex]P= \frac{10000}{1.0033^{60} }[/tex] ⇔ $8206.37 Should be invested .
Please help me‼️
Question: select all the equations that can be represented by a straight line when graphed on the coordinate plane
Answer:
B, D, EStep-by-step explanation:
Straight line equation is in the form of:
ax + by = cLets verify the options:
A- no, simplified, it is 1 + xy = 9xB- yesC- no, because of y²D- yesE- yesF - no, simplified it is a quadratic equation