Answer:
When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.
Step-by-step explanation:
Answer:
[tex]y =Ae^{-kx}[/tex]
would be the exponential decay function for initial population A and decaly rate is -k.
Step-by-step explanation:
Exponential decay occurs when rate of change of population or any other quantity is proportional to the present population or quantity present
i.e. if y is the population
then dy/dx = -ky where k is a positive constant of proportionality
[tex]\frac{dy}{y} =-kdx\\ln y = -kx+C\\y = e^{-kx+C} =Ae^{-kx}[/tex]
The polygons below are similar. Find the value of x. Polygons ABCD and EFGH are shown. AB equals 6. BC equals 8. CD equals 10. AD equals x. EF equals y. FG equals 6. GH equals z. HE equals 12. 4.5 7.5 12 16
Answer: The value of x = 16 units, y = 4.5 units and z = 7.5 units.
Step-by-step explanation:
Since we have given that
ABCD and EFGH are two similar polygons.
Dimensions of ABCD are as follows :
AB = 6 units
BC = 8 units
AD = x units
CD = 10 units
Dimensions of EFGH are as follows :
EF = y
FG = 6 units
EH = 12 units
GH = z
Since they are similar:
[tex]\dfrac{AB}{EF}=\dfrac{BC}{FG}=\dfrac{CD}{GH}=\dfrac{AD}{EH}\\\\\dfrac{6}{y}=\dfrac{8}{6}=\dfrac{10}z}=\dfrac{x}{12}[/tex]
First we take,
[tex]\dfrac{6}{y}=\dfrac{8}{6}\\\\y=\dfrac{36}{8}\\\\y=4.5\ units[/tex]
similarly,
[tex]\dfrac{8}{6}=\dfrac{10}{z}\\\\z=\dfrac{60}{8}\\\\z=7.5\ units[/tex]
similarly,
[tex]\dfrac{8}{6}=\dfrac{x}{12}\\\\x=\dfrac{96}{6}\\\\x=16\ units[/tex]
Hence, the value of x = 16 units, y = 4.5 units and z = 7.5 units.
Answer:
its not 7.5!!! i just took the test and its wrong!!
−6 − (−2)
-4
-8
4
12
Answer:
-4
Step-by-step explanation:
When you subtract a negative number, it is like adding a positive.
-6 - (-2)
-6 + 2
-4
Answer:
I think the answer is -4
Step-by-step explanation:
First change the -(-2) to 2: Next you would add -6-2 to get -4(why you add is because you changed the subtraction sign to addition when you simplified the equation).
In △ABC, CH=33 ft. What is the length of CX¯¯¯¯¯¯ ? Enter your answer in the box. ft A triangle A B C. Side B C is the base. F, G, and H are the midpoints of sides A F, B G, and C H respectively. Midpoints of each side connect to the opposite vertex. A F is the median of line segment B C. B G is the median of line segment A C. C H is the median of line segment A B. Medians intersect at a point labeled X. Single tick marks are on the line segments A H and H B. Double tick marks are on the line segments B F and F C. Triple tick marks are on the line segments A G and G C.
Answer:
The length of CX is 22 ft.
Step-by-step explanation:
Given information: In triangle ABC, F, G, and H are the midpoints of sides BC, CA, and AB respectively.
The medians FA, BG and CH intersect each other at point X.
According to the property of triangle, the intersection point of medians is called centroid and the centroid divides each median in 2:1.
Since X is centroid, therefore points X divides the median CH in 2:1, therefore we can say that CX:XH is 2:1.
It is given that the length of CX is 33.
[tex]CX=\frac{2}{3}CH[/tex]
[tex]CX=\frac{2}{3}\times 33[/tex]
[tex]CX=2\times 11[/tex]
[tex]CX=22[/tex]
Therefore the length of CX is 22 ft.
Answer:
22 ft
Step-by-step explanation:
33-1/3(33)=22
what is a number n is at least 10
Answer: n≥10
Step-by-step explanation:
The symbol ≥ means “greater than or equal to.” So, n≥10 means “n is greater than or equal to 10,” which basically means “n is at least 10”.
Answer:
n≥10
iready
holp it help
What does it mean when it says leave it in terms of pi-3.14....
Hello,
When you are leaving an answer in terms of pi, you are simply leaving the pi symbol in the answer. Here is the symbol: π
- I . A -
In mathematics, 'leave it in terms of pi' means expressing the answer using the symbol π instead of decimal approximation. Pi is an irrational number, so it goes on forever without repeating. To leave an answer in terms of pi, keep π in the expression and perform calculations with it.
Explanation:In mathematics, when it says 'leave it in terms of pi', it means that the answer should be expressed using the symbol π instead of rounding it to a decimal approximation like 3.14. Pi is an irrational number, meaning its decimal representation goes on forever without repeating. To leave an answer in terms of pi, you can keep π in the expression and perform any calculations with it. For example, if calculating the area of a circle, the formula would be A = πr², where r is the radius.
Find the approximate length of segment GH on the graph.
A) 4 units
B) 5.8 units
C) 7.8 units
D) 8 units
Answer:
The correct option is B.
Step-by-step explanation:
The distance between two points is
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
From the given figure it is clear that the coordinates of G are (1,2) and the coordinates of H are (6,5).
[tex]D=\sqrt{(6-1)^2+(5-2)^2}[/tex]
[tex]D=\sqrt{(5)^2+(3)^2}[/tex]
[tex]D=\sqrt{25+9}[/tex]
[tex]D=\sqrt{34}[/tex]
[tex]D=5.83[/tex]
[tex]D\approx 5.8[/tex]
The length of GH is 5.8 units. Therefore the correct option is B.
4 to the power of negative n equals 32 then what is n
n=-3
4^ -(-3)= 32
if you get the same bases == 4^-n= 4^3(=32)
so n =-3
it takes Zoe 12.5 minutes to swim 20 laps around the pool. what is Zoes’s unit rate
Answer:
The answer is 1.6
Answer:
1.6 minutes/lap
Step-by-step explanation:
Do 20 divided by 12.5 to get 1.6.
If rectangle ABCD is dilated by a scale factor of 1.5 with a center of dilation at vertex A, how does the area of A'B'C'D' compare with the area of ABCD?
Answer:
A’/A = 2.25
Step-by-step explanation:
Let the length and width of ABCD be l and w respectively.
A = lw
=====
For rectangle A’B’C’D’
l’ = 1.5l and w’ = 1.5w
A’ = l’w’
A’ = 1.5l × 1.5 w
A’ = 2.25 lw
=====
A’/A = 2.25lw/(lw) Cancel lw
A’/A = 2.25
The area of the dilated rectangle is 2.25 times that of the original.
Answer:
The answer is "D"
Step-by-step explanation:
Mable’s cookie recipe calls for 3/4 of a cup of flour. Her mother’s recipe calls for 2/3 as much as Mable’s. How many cups of flour does her mother’s recipe require?
HELPP!!! PLEASE IM TIMED
Answer:
1/2
Step-by-step explanation:
Graph the inequality c ≤ 3. How is the graph of c < 3 different from c ≤ 3?
To graph the inequality c ≤ 3, you draw a solid line at 3 on the number line and shade to the left. For c < 3, you draw a dotted line at 3 on the number line and shade to the left, without including 3.
Explanation:To graph the inequality c ≤ 3, you will draw a line at the value of 3 on the number line and shade the region to the left of the line. This includes the value 3 as well. This is because the inequality includes the symbol ≤, which means 'less than or equal to'.
On the other hand, to graph the inequality c < 3, you will draw a dotted line at the value of 3 on the number line and shade the region to the left of the line. However, this time the value 3 is not included in the solution because the inequality uses the symbol <, which means 'less than'.
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Which of the following items may be a good consideration in selecting a bank?
I. The bank sends a representative to the local mall to promote new applications.
II. Number of ATMs or bank branches near where you live, shop, work, or travel.
III. Knowledge of personal usage habits and needs
Answer:
II and III.
Step-by-step explanation:
Having branches near you is very important! Also knowing what you personally need from a bank is important
Answer:
3
Step-by-step explanation:
what is the equation in point -slope form of a line that passes trough the points (3,-5) and (-8,4)
Answer:
The equation in point - slope form of a line that passes through the points (3,-5) and (-8,4) is: y-(-5) = -(9/11) (x-3) or y+5 = -(9/11) (x-3)
Step-by-step explanation:
P1=(3,-5)=(x1,y1)→x1=3, y1=-5
P2=(-8,4)=(x2,y2)→x2=-8, y2=4
Equation in Point-Slope Form: y-y1=m(x-x1)
Slope: m=(y2-y1)/(x2-x1)
Replacing the known values:
m=[4-(-5)] / (-8-3)
m=(4+5) / (-11)
m=(9) / (-11)
m=-(9/11)
Equation in the point - slope form:
y-(-5) = -(9/11) (x-3)
y+5 = -(9/11) (x-3)
Please help, I'm working on an assignment.
Latoya brought a new rack for her CD collection. She has 977 CDs. Each row of the rack holds 12 CDs. How many rows can she fill? Write the answer as a mixed number.
PLEASE HELP ASAP 50 POINTS! What correctly identifies the property shown?
(−4.3)+5.4=5.4+(−4.3)
A. Associative property
B. Commutative property
C. Opposite of a sum property
Answer:
Commutative property
Step-by-step explanation:
Hope that helps!
in triangle LNM, what is the value of x?
If all sides have the same length, then this is an equilateral triangle. Therefore, the measures of the angles are the same and amount to 60°.
Therefore we have the equations:
7x - 3 = 60 add 3 to both sides
7x = 63 divide both sides by 7
x = 9
----------------
11y + 5 = 60 subtract 5 from both sides
11y = 55 divide both sides by 11
y = 5
Check:
m∠N = (7x - 3)° → m∠N = (7(9) - 3)° = (63 - 3)° = 60°
m∠M = (11y + 5)° → m∠M = (11(5) + 5)° = (55 + 5)° = 60°
CORRECT :)
Answer: x = 9 and y = 5Use division instead of the images to divide 18 by 4. What is the quotient of the division? What is the remainder?
When 18 is divided by 4, the quotient is 4 and the remainder is 2.
Explanation:The division of 18 by 4, can be performed using long division or mental math. First, understand that 'dividend' is the number being divided (18), 'divisor' is what you divide by (4), 'quotient' is the result of the division and 'remainder' is what is left over.
Step 1: Divide 18 by 4. 4 fits into 18 four times (4 x 4 = 16).
Step 2: Subtract the 16 from 18 to find the remainder. 18 - 16 equals 2.
So, the quotient of 18 divided by 4 is 4 and the remainder is 2.
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What is the correlation coefficient with the following data points: (15,36), (13,22), (12,6), (11,20)?
A.0.75
B.-0.75
C.0.65
D.-0.65
Answer:
The correct answer Is B ! i did a study on this before
Step-by-step explanation:
Answer with Step-by-step explanation:
The formula for correlation coefficient is:
[tex]\dfrac{\sum xy-\dfrac{(\sum x\sum y)}{n}}{\sqrt{(\sum x^2-\dfrac{(\sum x)^2}{n})(\sum y^2-\dfrac{(\sum y)^2}{n})}}[/tex]
x y x² y² xy
15 36 225 1296 540
13 22 169 484 286
12 6 144 36 72
11 20 121 400 220
∑ 51 84 659 2216 1118
Correlation coefficient=
[tex]\dfrac{1118-\dfrac{51\times 84}{4} }{\sqrt{(659-\dfrac{51\times 51}{4})(2216-\dfrac{84\times 84}{4} ) } } \\\\=\dfrac{47}{\sqrt{8.75\times 452} } \\\\=\dfrac{47}{\sqrt{3955} }\\ \\=0.75[/tex]
Hence, correct option is:
A. 0.75
in class,12 students like to play vollyboll. if 30% of the students in the class like to play volleyball,how many students are in the class?
Answer:
Hope this helps! If you have any questions feel free to ask.
Step-by-step explanation:
To find the total number of students in the class, you can use the given information of the percentage and the number of students who like to play volleyball.
Explanation:To find the total number of students in the class, we can use the information given. It is stated that 30% of the students in the class like to play volleyball, and there are 12 students who like to play volleyball. Let's assume the total number of students in the class is x.
So, we can set up the equation 0.30x = 12 to represent the percentage of students who like to play volleyball. Solving this equation, we get x = 12 / 0.30 = 40. Therefore, there are 40 students in the class.
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inline skates are on sale for 35% off the regular price
a. What fraction off is this discount?
b. The original price of one pair of inline skates is $124.99. What is
the sale price?
c. A tax of 5% is computed on the sale price. What is the total cost of the inline skates?
We have answered a three-part mathematical question. First, we converted 35% to a fraction, resulting in 7/20. We then calculated the sale price of inline skates by deducting this percentage from the original price to reach $81.24. Finally, we computed a 5% tax on the sales price to find a final total cost of $85.3.
Explanation:This question moves through several concepts in percentage and tax calculation. The first part of the question asks you to express 35% as a fraction, which, when reduced, can be represented as 7/20.
For the second part of the question, in order to calculate the sale price, we need to compute 35% ($43.75) of the original price ($124.99) and deduct this amount from the original price, resulting in a sale price of $81.24.
Lastly, we need to calculate and add a 5% sales tax to the sale price. 5% of $81.24 is $4.06. Adding this to the sale price, we get a total cost of $85.3.
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The difference between 8 less than q?
The Difference between expressions '8 less than q' and 'ans' is q - ans - 8.
The phrase '8 less than q' can be expressed as q - 8.
To find the difference between q - 8 and the answer 'ans', you subtract the two expressions: (q - 8) - ans.
This simplifies to q - 8 - ans, or q - ans - 8.
For example, if q = 15 and ans = 5, the difference would be 15 - 5 - 8, which equals 2.
So the difference between '8 less than q' and 'ans' is q - ans - 8.
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The probable question may be:
What is the difference between 8 less than q?
Indicate in standard form the equation of the line passing through the given point and having the given slope
R(4,0),m=5
What is the answer to linear equation: 5 = 6 - 7c
Answer:
c = 1/7
Step-by-step explanation:
Here we have to solve the linear equation.
We need to find the value of c.
5 = 6 - 7c
Isolate the variable and constants
Add 7c on both sides, we get
7c + 5 = 6 - 7c + 7c
7c + 5 = 6
Subtract 5 from both sides, we get
7c + 5 - 5 = 6 - 5
7c = 1
Dividing both sides by 7, we get
c = 1/7
Thank you.
Find missing length and reduce to fraction
26/24=x/16
26*2/3=52/3
In the decimal number 0.675, the 7 holds what place value? A. Thousandths B. Ten thousandths C. Hundredths D. Tenths
Answer:
C. Hundredths
Step-by-step explanation:
. tenths hundredths thousandths ten thousandths
. 6 7 5 0
triangle IJK is congruent to triangle PQR. If the measure of angle I=3x+4 and the measure of angle P=72-x, then determine the value of x
Answer:
X = 17°
Step-by-step explanation:
Given that triangle Δ IJK ≅ triangle Δ PQR.
Using CPCTC (corresponding parts of congruent triangles are congruent), we can say angle ∠I = angle ∠P.
given angle ∠I = 3x + 4, and angle ∠P = 72 - x.
Now solving angle ∠I = angle ∠P.
3x + 4 = 72 - x
3x = 72 - x - 4
3x = 68 - x
3x + x = 68
4x = 68
x = 68/4 = 17 degrees.
Hence, the value of x is 17°.
is 3x + 2x = 3 a function
The given equation is a function. After simplifying, it takes the form y = 3/5x, a simple linear equation. Understanding the behavior of even and odd functions is useful in comprehending this.
Explanation:The given expression, 3x + 2x = 3, needs to be first simplified before determining whether it is a function or not. The simplified expression is 5x = 3, which can be rearranged to the function form y = 3/5x. This is a simple linear equation, indicating a function. In general, an even function times an even function produces an even function, but an odd function times an even function gives an odd function. You can see this in the equations mentioned: x² e-x², x sin x, and xe-x².
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A third-grade gym class has 54 students. The gym teacher divides them into 9 groups. She then divides each group into 2 teams. How many students are on each team?
Answer:3
Step-by-step explanation: the reason why it's 3 is because 54 divided by 9 is 6 and 6 divided by 2 is 3
Solve each system by elimination
9) 5x+y=9
10x-7y=-18
Answer:
x=1, y=4
Step-by-step explanation:
5x+y=9
10x-7y=-18
To solve by elimination, we pick a variable to eliminate, or get rid of. I will multiply the first equation by -2 so we can get rid of x
-2( 5x+y)=9 *-2
-10x -2y = -18
Now we add this equation to the second equation
-10x -2y = -18
10x-7y=-18
-------------------------
-9y = -36
Divide each side by -9
-9y/-9 = -36/-9
y =4
We still need to solve for x
5x+y=9
Put in y=4
5x+4 = 9
Subtract 4 from each side
5x +4-4 = 9-4
5x = 5
Divide each side by 5
5x/5 = 5/5
x=1
Answer:
1,4
Step-by-step explanation:
add the equations in order to solve 1st variable, put the value in the other equations in order to solve- math way
The infinite geometric sum formula can be used to write 0.126126126...as a fraction. What is the numerator of this reduced fraction?
A. 7
B.14
C.42
D.126
Answer:
B.14Step-by-step explanation:
0.126126126... = x
1000x = 126.126126...1000x - x = 126999x = 126x = 126/999= 42/333= 14/ 111Numerator is 14
Correct answer is B.14