Answer:
Step-by-step explanation:
This is a Compound interest problem with a decreasing rate. It is given by the formula:
A = P(1 +/- R)^T
Where A = amount after time T
P = principal or initial amount
R = rate of increase or decrease
T = time elapsed
There's +/- because + is used in the case when the amount is increasing at a particular rate and - is used whe the amiunt is decreasing.
In 2000 there were 5,400 birds and the number of birds is decreasing by 3% (0.03) every year.
The number of birds, y, that will be there x years after 2000 will be:
y = 5400( 1 - 0.03)ˣ
2025 is 25 years ahead of 2000, so x = 25
Therefore, the number of birds in 2025 will be:
y = 5400(1 - 0.03)^25
y = 5400(0.97)^25
y = 5400 * 0.467
y = 2522 birds
There will be 2522 birds in 2025.
The equation to represent the number of birds after x years is y = 5,400(1 - 0.03)^x. To find the number of birds in 2025, we use x = 25 in the equation to get y ≈ 3,295 birds.
Explanation:To write an equation that represents the number, y, of birds x years after 2000 with a yearly decrease of 3%, we use the formula for exponential decay, which is y = a(1 - r)^x. Here, a is the initial amount, r is the rate of decrease, and x is the number of years since 2000.
In this case, the initial number of birds in 2000 was 5,400, so a = 5,400, and the rate of decrease is 3%, meaning r = 0.03. The equation becomes y = 5,400(1 - 0.03)^x.
To find out the number of birds in 2025, we calculate x as the number of years from 2000 to 2025, which is 25 years. Thus, the calculation results in y = 5,400(1 - 0.03)^25. After solving, we round the result to the nearest whole number.
Performing the calculation, y ≈ 3,295 birds.
Red: y = 7x
Blue: y = 5x
Green: y - 4x
Purple: y= 34
As x gets very large, which function becomes largest and remains so?
y = 7x
y = 5x
y = 4x2
y = 3
Final answer:
As the independent variable x grows very large, the quadratic function y = 4x^2 will outpace the linear functions y = 7x, y = 5x, and y = 34, hence it will become the largest and remain so.
Explanation:
The student is asking about the behavior of different linear functions and a quadratic function as the independent variable x becomes very large. When examining the functions given, we notice that three of them, y = 7x, y = 5x and y - 4x are linear, while the fourth, given the context should likely be a quadratic function y = 4x2, although that wasn't presented correctly in the question. As x grows, the function with the highest degree will become the largest. In this case, the quadratic function y = 4x2, which grows at a rate proportional to the square of x, will outpace the linear functions, whose growth is only directly proportional to x. Thus, as x becomes very large, the quadratic function “y = 4x2” becomes the largest and remains so.
Determine a series of transformations that would map polygon ABCDE onto polygon
A'B'C'D'E'?
1-10-9-8-7 -6 -5 -4 -3 -2 -1,
1
2
3
4
5
6
7
8
9 10 11 12
B'
followed by a
1. T1: Translate ABCDE.
2. R1: Rotate the translated polygon.
3. S1: Scale the rotated polygon.
4. F1: Reflect the scaled polygon if needed.
To determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E', you can break down the process into individual steps. Here, I'll describe each transformation step:
1. Translation:
Translate polygon ABCDE to align its center of mass with the center of mass of polygon A'B'C'D'E'. This ensures that the polygons are roughly in the same position. Let's denote this transformation as "T1."
2. Rotation:
Rotate the translated polygon so that one of its sides aligns with a side of polygon A'B'C'D'E'. You can use the center of mass as the pivot point for rotation. Denote this transformation as "R1."
3. Scaling:
Scale the rotated polygon proportionally to match the size of polygon A'B'C'D'E'. This will make sure that the two polygons have the same size. Denote this transformation as "S1."
4. Reflection:
Reflect the scaled polygon if needed to match the orientation of polygon A'B'C'D'E'. This step may not always be necessary, depending on the orientation of the two polygons. Denote this transformation as "F1" (for reflection).
So, the series of transformations can be written as follows:
1. T1: Translate ABCDE.
2. R1: Rotate the translated polygon.
3. S1: Scale the rotated polygon.
4. F1: Reflect the scaled polygon if needed.
These transformations will map polygon ABCDE onto polygon A'B'C'D'E' while preserving their size and shape.
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PLEASE ANSWER ASAP!!
What is the solution to the system of equations below?
y =2/5x - 3 and x = –10
1. (-10, -7)
2. (-10, -1)
3. (-7, -10)
4. (-1, -10)
Please help me out with this math question... if two people answer, I will brainlist. 5 stars and thanks for every answer and comment. I would really appreciate an answer. :-)
Answer:
20 (Assuming even distribution of letters)
Step-by-step explanation:
There are 26 letters in the alphabet.
Vowels consist of 5 of these letters.
The percentage of total letters that are vowels is:
[tex]\frac{5}{26} *100= 19.231[/tex] (3dp)
As we have total 105 letters, and we know the percentage of vowels to letters - we can work out how many of these letters we expect to be vowels by finding a percentage of the total number.
19% of 105 is:
[tex]105*0.19=19.95[/tex]
Which is approximately equal to 20
What is the rule for a geometric sequence whose first term is 6 and the common ratio is 2?
Answer:
6/2
Step-by-step explanation:
Answer:
An = 6*2^(n-1)
Step-by-step explanation:
It is okay to download information without asking a lab instructor as long as it is for your online class.
Please select the best answer from the choices provided
OT
OF
Answer:
false
Step-by-step explanation:
on eng 2020
The correct option is " Option 2" i.e., False.
It is given that somebody is trying to download an information without asking a lab instructor.
We have to tell that whether it is a right thing or not ?
What do you mean by moral values ?
Moral values are defined as the guidelines that assist a person in deciding between right and wrong.
It is not a right thing to use any private thing without the permission of the owner.
Hence it is also not okay to download information without asking a lab instructor even if you are using it for your online classes.
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Find the area of the figure.
Simplify (3-4i) (-6-6i)
Answer: -42+6i
Step-by-step explanation:
1. Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.
−18−18i+24i−24
2. Collect like terms.
(−18−24)+(−18i+24i)
3. Simplify.
−42+6i
Helena borrowed $189 from her parents to
buy an electric bass. She paid back $56
last week and $64 this week. How much
does Helena still owe her parents?
A $133
C $69
B $120
D $29
A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars
he checks, 4 have defects. If 10,500 cars will be checked this month, predict the total number of cars that will have
defects.
Answer:
i predict the 150 will have defects
Step-by-step explanation:
you do 280 divided by 4 which gives you 70
then 10,500 divided by 70 which gives you
There is a probability that 150 total autos will have defects if 10,500 vehicles are inspected this month.
What is Possibility?A chance that something might exist, happen, or be true: the state or fact of being possible.
Given, A worker at an automobile assembly plant checks new cars for defects. Of the first 280 cars he checks, 4 have defects.
Out of 280 cars defected = 4
out of 10500 cars defected = (4* 10500) / 280
out of 10500 cars defected = 150
therefore, If 10,500 cars will be checked this month there is a possibility of getting a total number of cars that will have defects of 150.
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A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the
reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin.
Answer:
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
Step-by-step explanation:
The missing figure( i.e diagram) from the question is attached below:
Now ; given that :
The focus of the sun's rays is at a point L = 5 inches away from the vertex of the reflector. Also the distance of the parabolic curve be a= L = 5
So the equation for a cross section of the oven's reflector with its focus on the
positive y axis and its vertex at the origin is expressed as:
x² = 4 L y
x² = 4 (5) y
x² = 20 y
y = [tex]\frac{x^2}{20}[/tex]
The focus of the solar oven's reflector is (0,a)
If you charge $2,000 on a credit card today, how much will the
balance be in seven years (assuming no additional fees) if the
credit card has 14.99% APR that is compounded monthly?
A = P(1 + )
Answer:
$5,674.30
Step-by-step explanation:
Use the Compound Amount formula:
A = P(1 + r/n)^(n*t), where r = APR as a decimal fraction = 0.1499
and n = 12 (compounded monthly).
Then A = $2,000(1 + 0.1499/12) )^(7*12)
= $2,000(1 + 0.0125)^84
= $2,000(1.0125)^84 = $2,000(2.837) = $5,674.30
There are 72 boys and 90 girls on the math team,
For the next math competition, Mr. Johnson would like to arrange all of the students who
rows with only girls or only boys in each row.
What is the greatest number of students that can be in each row
Answer:
The students can be arranged in rows of 18 that is 4 rows of boys and 5 rows of girls
Step-by-step explanation:
what ordered pair represents the y-intercept of the graph of the equation y=-4x-7
Answer:
(0,-7)
Step-by-step explanation:
y-intercepts are when x=0
Angle 3 and Angle 6 are examples of which type of angle pair?
Answer:
They look like they are 90° angles
Step-by-step explanation:
(What are the options?)
Which is an example of a non-statistical question?
Question 1
Question 2
Question 3
Question 4
Questions
What did each person in our class have for lunch yesterday?
What did each child in preschool have for lunch yesterday?
What did Maria have for lunch today?
What did each person in our class have for lunch today?
question 1
question 2
question 3
question 4
Answer:
What did Maria have for lunch today?
Step-by-step explanation:
For each of the other questions we can collect data
For Maria it is one piece of information
Answer:
Question 3: What did Maria have for lunch today?
Step-by-step explanation:
Statistical questions are to analyse a population based on a sample. Maria is one individual, not a population
Hermina cut a 10" by 20" piece of cardboard down the diagonal. What is the length c of the cut, in inches?
The length of the diagonal of the rectangular cardboard Hermina cut
is 10√5''.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, Hermina cut a 10" by 20" piece of cardboard down the diagonal.
So, The diagonal can be thought of as the hypotenuse of a right-angle triangle with a base 20'' and a height of 10''.
Therefore,
Hypotenuse² = Base² + Height².
Hypotenuse² = 20² + 10².
Hypotenuse² = 400 + 100.
Hypotenuse² = 500.
Hypotenuse = √(500).
Hypotenuse = 10√5''.
So, The length of the diagonal is 10√5''.
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The length of the cut (c) is 5 times the square root of 20 inches, which is approximately 22.36 inches when rounded to two decimal places.
When Hermina cuts a 10" by 20" piece of cardboard down the diagonal, she essentially creates two right triangles. The diagonal of a rectangle splits it into two congruent right triangles. This diagonal acts as the hypotenuse of each right triangle.
In a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse (c) if we know the lengths of the other two sides (a and b).
The Pythagorean theorem states: c^2 = a^2 + b^2, where c is the length of the hypotenuse.
In this case, one side (a) is 10 inches long, and the other side (b) is 20 inches long. Plugging these values into the formula:
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
Now, to find c, we take the square root of both sides to isolate c:
c = √500
To simplify the square root:
c = √(25 * 20)
c = 5√20
In summary, Hermina's diagonal cut creates two right triangles, and the length of the cut (c) can be found using the Pythagorean theorem. The calculated length is approximately 22.36 inches.
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) Graph the image of U(-9, -2) after a reflection over t
A car travels 25 ⅕ miles in ⅔ of an hour. What is the average speed, in miles per hour?
Answer:
37 4/5 miles per hour
Step-by-step explanation:
Take the miles and divide by the time
25 1/5 ÷ 2/3
Change the mixed number to an improper fraction
(5*25 +1)/5 ÷ 2/3
126/5 ÷ 2/3
Copy dot flip
126/5 *3/2
378/10
Changing to mixed number
10 goes into 378 37 times with 8 left over
37 8/10 which simplifies to 37 4/5
37 4/5 miles per hour
If angle 1 is 70°, what is the measure of angle 3?
7
4
2
.
3
Answer:2
Step-by-step explanation:
What is the difference between the absolute value of –8 and the absolute value of 6? 2 8 14 16
Answer:
the answer should be 2
Step-by-step explanation:
the absolute value of something cannot be negative, the eight automatically becomes +8 and the difference between 8 and 6 is 2 (8-6=2)
Sara spent $5 from her savings
to buy a book. Then she spent
half of her remaining savings
when she paid $9 for a shirt.
How much money did Sarah have
in savings before she bought
the book and the shirt?
Answer:
sorry for this just wait im about to slove it
Step-by-step explanation:
found it.it was 23
Answer: 23$
Step-by-step explanation:
If half of Sara's remaining savings was 9$, her remaining savings after buying the book would be 18$. 18$+5$=23$. Good luck and have a nice day!
Complete this proof.
Given: EC AC, DB AC, ∠A = ∠F
Prove: ΔMDF ∼ ΔNCA
Answer:
Proved
Step-by-step explanation:
Given: EC || AC, DB || AC, ∠A = ∠F
Prove: ΔMDF ∼ ΔNCA
Solution
See diagram attached to the solution to better understand the following workings.
Redrawing ΔMDF or rotating to be facing the same direction.
EC is parallel to AC
DB parallel to AC
Using similar triangle theorem:
If ΔMDF ∼ ΔNCA
Ratio of Corresponding sides would be equal
(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)
DF/ CA = MD/NC = FM/AN
∠A = ∠F
∠M = ∠N
∠D = ∠C
Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.
ΔMDF ∼ ΔNCA
Statement:
1. line EC is perpendicular to line AC, line is perpendicular to DB line AC, ∠A = ∠F
2. ∠F = ∠A
3. ∠1 =∠2
4. ΔMDF ∼ ΔNCA
Reason:
1. Given
2. Given
3. Alternate interior angles are equal
4. AA
(5a2 + 4ab – 3b2) – (–5ab + 4b2 + 3a2) = a2 + ab + ( b2)
Answer:
2a^2+ 9ab+ (-7b^2)
Step by Step Explanation
Hope this helps!! Have a great day!! : )
The simplified expression of [tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2)[/tex] is [tex]2a^2+ 9ab - 7b^2[/tex].
The expression is given as:
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2)[/tex]
Remove brackets
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 5a^2 + 4ab - 3b^2 +5ab - 4b^2 - 3a^2[/tex]
Collect like terms
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 5a^2 - 3a^2+ 4ab +5ab - 3b^2 - 4b^2[/tex]
Evaluate like terms
[tex](5a^2 + 4ab - 3b^2) - (-5ab + 4b^2 + 3a^2) = 2a^2+ 9ab - 7b^2[/tex]
The equation cannot be further simplified.
Hence, the simplified expression is [tex]2a^2+ 9ab - 7b^2[/tex]
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What is the output of the function f(p) = 3p – 2 when the input is 2? A. 0 B. 2 C. 4 D. 6 E. 8
Step-by-step explanation:
Step 1: Find f(2)
[tex]f(p) = 3p - 2[/tex]
[tex]f(2) = 3(2) - 2[/tex]
[tex]f(2) = 6 - 2[/tex]
[tex]f(2) = 4[/tex]
Answer: Option C, 4
Answer:
C. 4
Step-by-step explanation:
f(p) = 3p - 2
Is a function with:
Input: p
Output: 3p - 2
p = 2
f(2) = 3(2) - 2 = 6 - 2 = 4
26 Can anyone help!!!
Ok, first let's find how much a nickle is worth, a nickle is worth $0.05.
0.05 x 27 = $1.35
0.05 x 32 = $1.60
0.05 x 39 = $1.95
0.05 x 47 ≠ $2.45 (It's equal to $2.35)
I hope this helps!
I don’t know how to find the LCM for this.
Answer:
B
Step-by-step explanation:
7mn³|7m²n³ ---14mn^5
| m---2n²
LCM=7mn³×m×2n²
=14m²n^5
or LCM of 7,14 =14
Highest power of m=2
Highest power of n=5
LCM=14m²n^5
During his 2009 MVP season for the St. Louis Cardinals, Albert Pujols hit 93
singles, 45 doubles, 1 triple, and 47 home runs in a total of 568 at bats. The
following table arranges these data in terms of the number of bases for a hit,
counting O bases for the times when he did not get a hit and 4 bases for
home runs.
Number of
Bases
0
1
3
4
2
451
Number of
Times
382
47
To the nearest thousandth, what was E(X), the expected number of bases for
Albert Pujols in a typical at bat in 2009?
O
A. 0.327
OB. 0.487
O
C. 0.658
OD. 0.597
Answer:
E(Bases ) = 0.6584499955929 choice C.
Step-by-step explanation:
We want Expected number of bases during 2009
E(bases) = SUM (number of outcomes) *probabiility of outcome
93 + 45 + 1 + 47 = 176 hits
but there are a total of 568 bats
568 - 176 = 392 misses?
E(Bases) = 0* P( miss) + 1 * P( hitting singles) + 2*P(hitting doubles) + 3*P(hitting triples) + 4*P(home run)
E(Bases) = 0 + 93/568 + 2* (45/568) + 3*(1/568) + 4*(47/568)
0.16373239 + 0.158450 + 0.0052816901 + 0.33098591549
E(Bases ) = 0.6584499955929
Answer:
C 0.658
Step-by-step explanation:
What is the answer or this Equation. ‑1/2+(3/4•4/9) =
Answer:
4/25 would be the answer as;
-1/2 + 1/3 = -0.16666666666
Step-by-step explanation:
‑1/2+(3/4•4/9) =
-1/2 + (1/3) = -4/25
-0.16
However true answer is 16666666666/100000000000. = 0.1666666666
The rule is when fractions reoccur, we show closest and -4/25 is closer than -1/6
It wants to know what the area of the trapezoid is. Someone please help.
Answer:
is it 54?
Explanation:
there are about 54 squares which could also be called units