A population of bacteria can be modeled by the function f (t) = 400 (0.98)^t, where t is the time in hours. Which of the following best describes the rate of change in function? (dont use advanced math please)
Answers
1) We can write an exponential function as
\(y=a(b)^x\)Since then we can examine our function:
\(f(t)=400(0.98)^t\)2) Let's set a table to check this rate of change:
x | y
-1 | 408.16
0 | 400
1 | 392
2 | 384.16
3 | 376.47
Note how the va
Since we can rewrite that function as:
\(\begin{gathered} f(t)=400(1-0.02)^t \\ y=a(1-r)^t \end{gathered}\)We have a decay of 2% per hour since 0.98 is lesser than 1.
3) And the answer is decrease 2% per hour
Related Questions
What side-angle relationship is given in the following triangle?
A. ASA
B. AAA
C. SSS
D. SAS
Answers
They are giving u all sides.
Without more information or a diagram, it's not possible to definitively determine which side-angle relationship (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of sides and angles known in a triangle.
Explanation:Given the question, it's clear that we are discussing a concept in Geometry - the side-angle relationships in a triangle. However, without more information or an accompanying diagram, it isn't possible to definitively determine which of the side-angle relationships (ASA, AAA, SSS, SAS) the triangle fits. These acronyms represent different combinations of side and angle information known about a triangle. For example, ASA means that we know two Angles and the Side between them. SAS relates to knowledge of two Sides and the Angle between them, and so forth. More information or a visual representation would allow a more conclusive answer.
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Is the inverse of the following conditional true?
If t<5, then t>6.
Answers
The inverse of the conditional "If t<5, then t>6" is "If t≥5, then t≤6" is not always true but true for some values of t.
What is a function?An expression, rule, or law that defines a relationship between one variable and another variable.
Let's first consider the original statement: "If t<5, then t>6."
This statement is saying that if t is less than 5, then it must be greater than 6, which is impossible since no number can be less than 5 and greater than 6 at the same time.
So the original statement is always false, no matter what value of t we choose.
So, the inverse of "If t<5, then t>6" is "If t≥5, then t≤6".
This statement is saying that if t is greater than or equal to 5, then it must be less than or equal to 6.
This statement is true for any value of t that is greater than or equal to 5 and less than or equal to 6.
Hence, the inverse of the conditional "If t<5, then t>6" is "If t≥5, then t≤6" is not always true but true for some values of t.
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What is the solution coordinates to the graphed system of equations?
Answers
Answer:
We conclude that the solution coordinates to the graphed system of equations will be:
(x, y) = (1, -5)Step-by-step explanation:
From the given graph it is clear that there are two lines:
Red and BlueIt is clear that the red and blue lines meet or intersect at the point (1, -5). The point where the two lines meet is called the point of intersection.
In other words, the two lines meet at:
at x = 1, and y = -5
Thus, the point of intersection of two lines is:
(x, y) = (1, -5)We also know that the point of intersection of two lines is the solution of the system of equations.
Therefore, we conclude that the solution coordinates to the graphed system of equations will be:
(x, y) = (1, -5)Gold leaf can be bought in 8cm square sheets.
There are 25 sheets in one booklet.
Work out the total area that can be covered using one booklet of gold leaf.
Answers
Step-by-step explanation:
El pan de oro se puede comprar en hojas cuadradas de 8 cm.
Hay 25 hojas en un folleto.
Calcule el área total que se puede cubrir con un cuadernillo de pan de oro
Hector left his house at (-9,9) on a map of Coleville and walked to the zoo at (-9,2). From there he walked
east to his friend's house. He walked a total distance of 24 blocks.
If each unit on the map represents one block, what are the coordinates of Hector's friend's house?
Answers
Answer:
(-33,2)
Step-by-step explanation:
HELP! DUE SOON!! SO CONFUSED!!!
Answers
Answer: 4.3 meters
Step-by-step explanation:
Let the angle opposite the 3-meter side be \(\alpha\).
Using the Law of Sines,
\(\frac{\sin \alpha}{3}=\frac{\sin 25^{\circ}}{2}\\\\\sin \alpha=1.5 \sin 25^{\circ}\\\\\alpha=\arcsin(1.5 \sin 25^{\circ})\)
Using the sum of the angles in a triangle, the angle opposite the side \(\ell\) is \(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})\).
Using the Law of Sines,
\(\frac{\ell}{\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}=\frac{2}{\sin 25^{\circ}}\\\\\ell =\frac{2\sin(155^{\circ}-\arcsin(1.5 \sin 25^{\circ})}{\sin 25^{\circ}}\\\\\ell \approx 4.3\)
Answer: The correct answer is 4.3
Step-by-step explanation:
This is an Obtuse Scalene Triangle
Side a = 2
Side b = 3
Side c = 4.26571
Angle ∠A = 25°
Angle ∠B = 39.34°
Angle ∠C = 115.66°
Area = 2.70415
Perimeter p = 9.26571
Semiperimeter s = 4.63285
Calculate c, ∠B, and ∠C based on given a, b, and ∠A.
∠B = arcsin(b·sin(A)/a)
= 0.68662 rad = 39.34°
∠C = 180° - A - B = 2.01864 rad = 115.66°
c = a·sin(C)/sin(A) = 4.26571 = 4.3
What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?
y = x + 3
y = x + 7
y = 3x – 13
y = 3x + 5
Answers
Answer:
x+3
Step-by-step explanation:
that's the line which passes through
Escribe una desigualdad que represente c, la cantidad de velas que necesita vender para pagar Knotts. Explique o muestre su razonamiento
Answers
The inequality c ≥ 20 represents the minimum number of candles that need to be sold to pay for a visit to Knotts costing $100 when each candle is sold for $5.
How to Write an Inequality Statement?To write the inequality that represents c, we need to consider the cost of the visit to Knotts and the price of each candle that is being sold. Let's assume that the cost of the visit to Knotts is $100 and each candle is being sold for $5.
We know that the total amount of money she earns from selling c candles is given by 5c, and this amount must be greater than or equal to the cost of the visit, which is $100. Therefore, we can write:
5c ≥ 100
Dividing both sides of the inequality by 5, we get:
c ≥ 20
Therefore, the inequality that represents c is c ≥ 20. This means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.
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jerry weighs 105 pounds if a male brown bear weighs 11 times as much what is the brown bear's weight
Answers
Topic Test
Find the coordinates of PQ with endpoints P(2, -4) and Q(4, 2) under the translation left 3 units and up 4 units.
a. P'(-2, -4) and Q'(-4, -2)
b. P'(-1, 0) and Q'(1, 6)
c. P'(5, -1) and Q'(-2, -2)
d. P'(0, -7) and Q'(1, -1)
Please select the best answer from the choices provided
Answers
Answer:
B. P'(-1, 0) and Q'(1, 6)
Step-by-step explanation:
Please select the best answer from the choices provided
Answer:
The answer is A. P'(-2, -4) and Q'(-4, -2)
Step-by-step explanation:
OMG, I just did the Topic Test for Math on Edge earlier today! Good luck on it!
Use the number line below, where , , and . a. What is the value of y? b. Find RS and ST. R S T a. What is the value of y? y 4 (Type an integer or a decimal.) b. Find RS and ST. RS 4.2 (Type an integer or a decimal.)
Answers
Answer:
y = 4
RS = 35
ST = 26
Step-by-step explanation:
Given:
RS = 8y + 3
ST = 5y + 6
RT = 61
Required:
a. Value of y
b. Numerical lenght of RS and ST
SOLUTION:
a. Points R, S and T are collinear, therefore, based on segment addition postulate, the following equation can be created to find the value of y:
\( RS + ST = RT \)
\( (8y + 3) + (5y + 6) = 61 \) (substitution)
Solve for y
\( 8y + 3 + 5y + 6 = 61 \)
Combine like terms
\( 8y + 5y + 3 + 6 = 61 \)
\( 13y + 9 = 61 \)
Subtract 9 from both sides
\( 13y + 9 - 9 = 61 - 9 \)
\( 13y = 52 \)
Divide both sides by 13
\( \frac{13y}{13} = \frac{52}{13} \)
\( y = 4 \)
b. RS = 8y + 3
Plug in the value of y
RS = 8(4) + 3 = 32 + 3
RS = 35
ST = 5y + 6
Plug in the value of y
ST = 5(4) + 6 = 20 + 6
ST = 26
Answer:
Guy above me is Wrong its 14
Step-by-step explanation:
Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5
Answers
Answer:
f(-5) = 30
f(0) = 5
f(3) = 14
Step-by-step explanation:
=> f(x) = x²+5
for , f(-5) = (-5)² +5
=> 25 +5
=> 30
for , f(0) = (0)² +5
=> 5
for , f(3) = (3)² + 5
=> 9 + 5
=> 14
Determine the number of triangular films that can be formed by using the measurements a = 17 cm,b = 23 cm, and m∠A = 40°. Solve each triangle. Round to the nearest tenth.
PLS HELP!!!!
Answers
The solution of the triangle have been shown below.
How do you solve the triangle?To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.
Given that;
a/Sin A = b/SinB
Sin B = bSin A/a
B = Sin-1(bSin A/a)
B = Sin-1 (23Sin 40/17)
B = 60.4 degrees
Then we have that
C = 180 - (40 + 60.4)
= 79.4 degrees
Then;
a/sinA = c/Sin C
c= aSin C/Sin A
c = 17 * Sin 79.4/Sin 40
c = 16.71/0.643
c = 25.9
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NO LINKS!!
Consider the function f(x) = log₂(x - 2) - 5
Answers
Answer:
a) See attachment.
b) Domain: (2, ∞)
Range: (-∞, ∞)
c) As x → 2⁺, f(x) → -∞
As x → ∞, f(x) → ∞
d) f(3) = -5
e) x = 4
Step-by-step explanation:
Given logarithmic function:
\(f(x)=\log_2(x-2)-5\)
Part aAs the argument of a log function can only take positive arguments, the domain is restricted to x > 2 and there is a vertical asymptote at x = 2.
To find the x-intercept, set the function to zero and solve for x:
\(\implies \log_2(x-2)-5=0\)
\(\implies \log_2(x-2)=5\)
\(\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b\)
\(\implies x-2=2^5\)
\(\implies x-2=32\)
\(\implies x=34\)
Therefore, the x-intercept is (34, 0).
Substitute x = 10 into the function to find a second point on the curve:
\(\implies f(10)=\log_2(10-2)-5\)
\(\implies f(10)=\log_2(8)-5\)
\(\implies f(10)=\log_2(2)^3-5\)
\(\implies f(10)=3\log_2(2)-5\)
\(\implies f(10)=3(1)-5\)
\(\implies f(10)=3-5\)
\(\implies f(10)=-2\)
Therefore, a second point on the curve is (10, -2).
Part bAs the argument of a log function can only take positive arguments, the domain is restricted to x > 2:
Interval notation: (2, ∞)The range is unrestricted:
Interval notation: (-∞, ∞)Part cAs x approaches x = 2 from the positive side, the function approaches negative infinity:
As x → 2⁺, f(x) → -∞As x approaches positive infinity, the function approaches positive infinity.
As x → ∞, f(x) → ∞Part dFrom inspection of the graph:
f(3) = -5Check by evaluating f(3) algebraically:
\(\implies f(3)=\log_2(3-2)-5\)
\(\implies f(3)=\log_2(1)-5\)
\(\implies f(3)=0-5\)
\(\implies f(3)=-5\)
Part e
From inspection of the graph:
f(x) = -4 ⇒ x = 4Check by evaluating f(x) = -4 algebraically:
\(\implies \log_2(x-2)-5=-4\)
\(\implies \log_2(x-2)=1\)
\(\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b\)
\(\implies x-2=2^1\)
\(\implies x-2=2\)
\(\implies x=4\)
I'm trying to figure out if I have this problem done correctly.
Answers
the initial expression is:
\(\sqrt[]{30}\cdot\sqrt[]{5}\)so we can simplify it:
\(\sqrt[]{30\cdot5}=\sqrt[]{150}\)and 150 is not a factor of 4,9 or 16 so:
Blank 1: na
blank 2: 150
Jessica used 2/3 of her money to buy books and 1/6 of her money to buy notebooks. She then had $30 left. How much money did Jessica have before shopping?
Answers
Answer:
Step-by-step explanation:
The total amount of money she spent on books and notebooks is:
2/3x + 1/6x = 5/6*x
Jessica had $30 left, so we can set up an equation:
x - 5/6*x = 30
Simplifying the equation:
1/6*x = 30
x = 180
The graph of which equation passes through the
point
Answers
Answer:
The answer is A.
A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:
5x+4y=8
we replace the variables with 4 and -3 (x with 4 and y with -3):
5(4)+4(-3)=8
20-12=8
8=8 so it passes.
NOW , for the slope:
slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).
THAT'S it thats the answer.
A human hair was measured to be 8.0•10-4 inch thick. A cat hair is measured to be 4.0•10^-1. How much greater is the thickness of the cat hair than the human hair? Writ this in standard form.
Whoever gets this right I will mark brainiest and 60 points!!
Answers
Answer:
500 times
Step-by-step explanation:
Divide the thickness of a cat hair by the thickness of a human hair.
4.0 × 10^-1 / 8.0 × 10^-4 =
= 0.5 × 10^3
= 500
500 times
if the system of equations y=b/6x-3 and y=2/3x-3 has infinitely many solutions, what is the value of b?
Answers
Answer:
b = 4
Step-by-step explanation:
4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions
Between which two consecutive integers will the square root of 170 fall?
Answers
We have two consecutive numbers n and (n+1).
We have to find n, so that the square root of 170 falls between n and (n+1).
We know that the square of 13 is 169, so the square root of 170 is between 13 and 14.
Express 4 as a fraction.
Answers
which would be 4/1
Recounting Rectangles
How many rectangles are
there in the figure below?
Answers
Answer:
gimme a second, I'll comment
Which graph shows the information in the table?
Calories in Salad Dressing
Number of Ounces of Salad
Dressing
2
3
4
5
Total Calories
300
450
600
750
Answers
Answer: Number 2
Step-by-step explanation: yes
15. Kate has 63 pens. She gives all the pens to her 9 friends. Each friend gets
the same number of pens.
Kate said that when she divided the number of pens that each friend got by 9,
the answer was equal to 63. Her friend Margo said that when the number of
pens each friend got was multiplied by 9, the answer was equal to 63.
Which girl is correct? Explain your answer. I will mark as brainlist and vote if you answer
Answers
The girl which is correct between kate and her friend Margo is Margo.
The correct answer option is option B
How to multiply?Number of pens Kate has = 63Number of Kate's friends = 9If each friend gets the same number of pens;
Number of pens each friend get = Number of pens Kate has / Number of Kate's friends
= 63 / 9
= 7
Check:
Number of pens each friend get × Number of Kate's friends = Number of pens Kate has
7 × 9 = 63
Therefore, Kate's friend, Margo is correct.
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Solve the two-step equation.
3
4
(x) − 1.72 = −6.82
1. The first step is to
✔ add 1.72
on both sides.
2. The second step is to
on both sides.
The solution is x =
.
Answers
Answer:
\(\boxed{\sf{x=-0.15}}\)Step-by-step explanation:
Isolate the term of x from one side of the equation.
34(x)-1.72=-6.82Rewrite the problem down.
⇒ 34x-1.72=-6.82
First, add by 1.72 from both sides.
⇒ 34x-1.72+1.72=-6.82+1.72
Solve.
⇒ -6.82+1.72=-5.1
Rewrite the problem down.
⇒ 34x=-5.1
Divide by 34 from both sides.
⇒34x/34=-5.1/34
Solve.
Divide the numbers from left to right.
⇒ -5.1/34=-0.15
⇒ x=-0.15
Therefore, the solution is x=-0.15, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Here is the correct answer is this
Step-by-step explanation:
Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Answers
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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Which equation is equivalent to the given equation?
x²- 10x = 14
-
(x - 10)² =-86
(x - 5)² = 39
(x - 5)²= = -11
(x-10)²= 114
Answers
Translate to an algebraic expression.10 more than dThe translation is
Answers
10 more than d is the same as d plus 10, so the algebraic expression is:
d + 10
Answer: d + 10
traveling 615 km with a vehicle that uses 5.9 L/100 km
Answers
Answer:
x = 36.2851
Step-by-step explanation:
5.9l -> 100km
x -> 615km
615km*5.9l = x/100km
x=36.285l
Answer:
61500
Step-by-step explanation:
i think this help
If x = 2, solve for y. y = 6.3x y=[?]
Answers
Answer: y = 12.6
Step-by-step explanation:
Since x = 2 and y = 6.3 * x, y = 6.3 * 2.
6.3 * 2 is equal to 12.6, so y is 12.6.
Answer:
y = 12.6
Step-by-step explanation:
y = 6.3x x = 2
Solve for y.
y = 6.3(2)
y = 12.6
So, the answer is 12.6