Final answer:
To find the equivalent equation for the monthly growth of the wildflowers, we need to convert the yearly growth rate to a monthly growth rate. The monthly growth rate is the 12th root of the yearly growth rate. The equivalent equation is Y=1000((1.08)^(1/12))^mx.
Explanation:
To find an equivalent equation that represents the monthly growth of the wildflowers, we need to convert the yearly growth rate into a monthly growth rate. Since there are 12 months in a year, the monthly growth rate is the 12th root of the yearly growth rate.
Given the equation Y = 1000(1.08)^x, where x represents the number of years, the equivalent equation for the monthly growth rate is Y = 1000((1.08)^(1/12))^mx.
Here, a = 12, b = 1/12, c = 1.08, and d = m.
The value we get are :
a = 1000
b = 1.00692
c = 0
d = 0
The given equation, Y=1000(1.08)^x, represents the yearly growth of wildflowers, where:
Y is the number of wildflowers in year x.
1000 is the initial number of wildflowers (at year x=0).
1.08 represents the yearly growth factor (8% increase).
x is the year number.
To find the equivalent equation for monthly growth, we need to consider that there are 12 months in a year. This means the yearly growth factor can be further divided into monthly growth factors.
Divide the exponent by the number of months:
In the yearly equation, the exponent x represents the year number. To represent months, we need to divide x by 12 (number of months in a year).
The new equation becomes: Y = 1000 * (1.08)^(x/12).
Apply the power of a power property:
(a^b)^c = a^(b*c). In this case, a = 1.08, b = 1/12, and c = x.
The equation becomes: Y = 1000 * ((1.08)^(1/12))^x.
Simplify the equation:
Calculate (1.08)^(1/12) using a calculator. This value is approximately 1.00692 (rounded to nearest thousandth).
Substitute this value back into the equation: Y = 1000 * (1.00692)^x.
Therefore, the equivalent equation representing the monthly growth of wildflowers is:
Y = 1000 * (1.00692)^x
Values of a, b, c, and d:
a = 1000 (initial number of wildflowers)
b = 1.00692 (monthly growth factor)
c = 0 (no x term in the exponent)
d = 0 (no constant term)
Question:
Some studies find that the yearly growth rate of a certain wildflower can be modeled by the equation Y=1000(1.08)^x. Use the properties of exponents to show an equivalent equation that represents the monthly growth of the wildflowers. Find the values of a, b, c, and d. Round to the nearest thousandth as needed.
11) Find the length of side x. picture is above!
I will give you 20 points and
brainliest
Answer:
25m :)
Step-by-step explanation:
What is the length of the diagonal of a 10 cm by 15 cm rectangle?
Answer:
18.02 cm
Step-by-step explanation:
A diagonal makes a rectangle into two right triangles. So if we use the Pythagorean theorem we can find the hypotenuse which is the diagonals.
Remember, because we know the length and width, we know the two sides.
10^2 + 15^2 = c^2
100+225 = c^2
325 = c^2
18.027 ≈ c
We can use the Pythagorean theorem to solve for the diagonal. The diagonal is the same as the hypotenuse of a triangle.
Pythagorean Theorem: a² + b² = c²
Now, solve for the diagonal.
(10)² + (15)² = c²
100 + 225 = c²
325 = c²
√325 = √c²
18.0277... = c
Round if necessary.
18.0277... = 18.03
Therefore, the diagonal of the rectangle is approximately 18.03cm.
Best of Luck!
Evaluate the geometric series. Please help me!!
Answer:
- 85
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
1[tex](-2)^{n-1}[/tex] ← is the n th term of a geometric series
with a = 1 and r = - 2
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
= [tex]\frac{1((-2)^{8}-1 }{-2-1}[/tex]
= [tex]\frac{256-1}{-3}[/tex]
= [tex]\frac{255}{-3}[/tex]
= - 85
can someone please explain this trigonometry question? uses sin/cos/tan
Answer:
The answer to your question is below
Step-by-step explanation:
Data
Right triangle
hypotenuse = 24
Opposite side = 15
Adjacent side = ?
Process
1.- Calculate the adjacent side using the Pythagorean theorem.
hypotenuse² = opposite side² + adjacent side²
-Solve for adjacent side
Adjacent side² = hypotenuse² - opposite side²
-Substitution
Adjacent side² = 24² - 15²
-Simplification
Adjacent side² = 576 - 225
Adjacent side = 351
-Result
Adjacent side = 18.73°
2.- Find the value of x°
a) Using sin x
sinx = Opposite side/Hypotenuse = 15/24 = 0.625
x = 38.68°
b) Using cos x
cos x = Adjacent side/Hypotenuse = 18.73/24 = 0.78
cos x = 38.68°
c) Using tan x
tanx = Opposite side / Hypotenuse = 15/18.73 = 0.80
tan x = 38.68°
Explain why P(AD) and P(DIA) from the table below are
not equal.
Answer:
P(A) ≠ P(D)
Step-by-step explanation:
P(A|D) = P(AD)/P(D)
P(D|A) = P(AD)/P(A)
The two denominators are not equal, so the quotients cannot be equal.
P(A|D) and P(D/A) are not equal because the total number of A and D are not equal.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
From the table, we have the following parameters:
n(A) = 8
n(D) = 10
n(A and D) = 2
P(A|D) and P(D|A) are both conditional probabilities, and they are calculated using:
P(A|D)=2/10
=1/5 = 0.2
P(D/A)= 2/8
=1/4
From the above computations, we have:
P(A|D)≠P(D/A)
Hence, P(A|D) and P(D/A) are not equal because the total number of A and D are not equal.
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Which of the following is the correct representation for a translation 8 units right and 4 units down?
Answer:
A. (x + 8, y - 4)
Step-by-step explanation:
When something is translated to the right, x goes up, and when something is translated down, y goes down.
Alternatively, eft means down for x and up means up for y.
can a smart person help me out? I really need help with these three questions
Answer:
1.= 2.4 Hours
2.= 8 miles per hour
3.= 150 miles per hour
Step-by-step explanation:
There are 2 green,5 yellow, 6 red,and 7 blue marbles in a bag. Erin picks one marble from the bag without looking. What is the probability she will pick a marble out of the bag that is blue?
a) 7% b) 20% c) 35% d) 54%
Answer:
c 35%
Step-by-step explanation:
2 green,5 yellow, 6 red,and 7 blue marbles
2+5+6+7 = 20 marbles
P(blue) = blue marbles / total marbles
= 7/20
= 35/100
=35%
DELLO
How many solutions exist for the given equation?
3(x - 2) = 22 - x
zero
O one
two
infinitely many
The number of solutions for the given equation is one.
Here, we have,
To determine the number of solutions for the equation 3(x - 2) = 22 - x, we can solve it and analyze the result.
Let's simplify and solve the equation step by step:
3(x - 2) = 22 - x
3x - 6 = 22 - x
4x = 28
x = 7
After simplifying, we find that x = 7.
Now, we can analyze the number of solutions:
Since we have found a specific value for x that satisfies the equation, namely x = 7, there is exactly one solution.
Therefore, the number of solutions for the given equation is one.
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A 12-sided die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. Find the probability of rolling a 9.
Answer:
1/12
Step-by-step explanation:
Since all are equally likely, each outcome has a probability of 1/12.
P(9) = 1/12
Answer:
1/12
Step-by-step explanation:
The probability of rolling a nine is given by the number of good outcomes over the total outcomes
P(9) = number of 9's / total
=1/12
Which expression is equivalent to 3(7x – 5)?
Answer:
21x-15
Step-by-step explanation:
Use the distributive property:
3×7x=21x
3×5=15
Don't forget the - sign!!!
So,
3(7x - 5) = 21x - 15
Final answer:
The expression 3(7x - 5) using the distributive property is equivalent to 21x - 15, which is obtained by multiplying 3 by each term inside the parenthesis.
Explanation:
The expression 3(7x
- 5) is equivalent to 21x - 15. This process is known as the distributive property, where you multiply the number outside the parenthesis by each term inside the parenthesis. Let's break it down step by step:
Multiply the first term inside the parenthesis by 3: 3 ×7x = 21x.
Multiply the second term inside the parenthesis by 3: 3 ×(-5) = -15.
Combine these results to get the equivalent expression: 21x - 15.
A gardener has a circular garden, which he divides into four quadrants. He has four different kinds of flowers, and he wants to assign a flower to each quadrant, so that adjacent quadrants are not planted with the same kind of flower. (Also, the gardener can use the same flower more than once.) How many different gardens are possible?
Answer:
84Explanation:
Call the quadrants I, II, III, and IV, counterclockwise, and the kinds of flowers A, B, C, and D.
Start by assigning a flower of kind A to quadrant I.
Then, quadrant II can have flower B, C, or D.
If it is B, then quadrant III can have either A, C, or D. If it isIf quadrant III has A, then quadrant IV can have either B, C, or D. That is 3 different gardens.
If quadrant III has C, then quadrant IV can have either B or D. That is 2 different gardens.
If quadrant III has D, then quadrant IV can either either B or C. That is 2 different gardens.
Those are all the possible different gardens if A is assigned to quadrant I and B is assigned to quadrant II: 3 + 2 + 2 = 7.
Working yet with A in quadrant I but assigning C to quadrant II, you can make the same reasoning as above to get other 7 gardens.
The same with A in quadrant I but D in quadrant II, other 7 different gardents.
In total, you find 7 × 3 = 21 different gardens when flowers of kind A are assingned to quadrant I.
Starting with a flower of kind B in quadrant I, there will be other 21 different gardens. The same for C and D. Then, in total, there are 4 × 21 = 84 different possible gardens.
Answer:
84
Step-by-step explanation:
Quadrants A and C either have the same kind of flower, or they have different flowers.
If quadrants A and C have the same kind of flower, there are 4 ways to choose this flower. There are then 3 ways to choose the flower for quadrant B, and 3 ways to choose the flower for quadrant D, so there are 4 x 3 x 3 = 36 possible ways in this case.
If quadrants A and C have different kinds of flowers, then there are 4 ways to choose the flower for quadrant A, then 3 ways to choose the flower for quadrant C. Then there are 2 ways to choose the flower for quadrant B, and 2 ways to choose the flower for quadrant D, so there are 4 x 3 x 2 x 2 = 48 possible ways in this case.
Therefore, there are a total of 36 + 48 = 84 ways to plant the flowers.
Use the distributive property to expand the following expression.
−3(2x+(−7)+5y)
Answer:
-6x +21 -15y
Step-by-step explanation:
−3(2x+(−7)+5y)
Distribute
-3*2x + -3*-7 + -3*5y
-6x +21 -15y
SCENARIO
You and your friend are playing a game with spinners. The two spinners are pictured below. To win each round, you have to land on a number that is bigger than the one your friend lands on. Which spinner would you rather have? Explain your answer.
I need an answer by April 24 ASAP! ;-;
Answer:
1
Step-by-step explanation:
because on how you show for 2 when you want to win have an accurate meaning of an number
Answer: Either spinner
Step-by-step explanation: I hope this makes sense, as I had the same question :)
I would choose either spinner because there is an equally likely probability to land on a greater number using either one. If you join the same numbers together on spinner 1 (all the 1's together, 2's together, and 3's together), the section they would make would be the same size as that same number section on spinner 2.
OR (more detailed one)-
The probability of landing on a number greater than your friend on either spinner is equally likely. 1 and 2 on the first spinner are both 3/8 of the spinner and 3 is 2/8 which is the same ratios as the second spinner. The difference is that on spinner #1, the numbers are split up and spread out from each other (ex. 1,2,3,2,3,1), and in spinner #2 all the 1's, 2's, and 3's are together to make bigger looking chunks. The area of each number is the same on both spinners.
Hope this helps!!!! :):):)
In a sample of 150 cars, 18 cars failed a safety inspection. The sampling method had a margin of error of 0.02
What is the interval estimate for the proportion that would fail in the form
(lower limit, upper limit)?
Answer:
(Lower limit, Upper limit) = (0.10, 0.14)
(Lower limit, Upper limit) = (10%, 14%)
Step-by-step explanation:
Total number of cars = 150
Cars that failed the safety inspection = 18
The proportion is given by
p = 18/150
p = 0.12
p = 12%
The confidence interval is given by
p ± margin of error
Where margin of error is 0.02
0.12 ± 0.02
Lower limit = 0.12 - 0.02
Lower limit = 0.10
Lower limit = 10%
Upper limit = 0.12 + 0.02
Upper limit = 0.14
Upper limit = 14%
(Lower limit, Upper limit) = (0.10, 0.14)
(Lower limit, Upper limit) = (10%, 14%)
Answer:
(0.10, 0.14)
Step-by-step explanation:
In a circle with a radius of 6 m, an arc is intercepted by a central angle of 7π/4 radians.
What is the arc length?
Answer:
The arc length is 52.
Which line segment is a diameter of circle F?
Answer:
AC
Step-by-step explanation:
We know that a diameter of a circle is any straight line segment that passes through the center of the circle such that whose endpoints lie on the circle. It is also be known as the longest chord of the circle.
In the given figure we can see that only AC and BE are the line segments that pass through the center of the circle such that whose endpoints lie on the circle.
Answer:
AC
Step-by-step explanation:
solve where x is a real number
Answer:
4,-4
Step-by-step explanation:
-4 times -4 equals 16
4 times 4 equals 16
Answer:
x=4
Step-by-step explanation:
square root of 16 and x^2 is 4
The product of $7d^2-3d+g$ and $3d^2+hd-8$ is $21d^4-44d^3-35d^2+14d-16$. What is $g+h$?
Step-by-step explanation:
To find the product with unknown values of variables, multiply the terms and equate the value to the given product.
[tex](7d^{2} - 3d + g)(3d^{2} + hd - 8)[/tex] = [tex]21d^{4} + 7hd^{3} - 56d^{2} - 9d^{3} - 3hd^{2} + 24d + 3gd^{2} + ghd - 8g[/tex]
[tex](7d^{2} - 3d + g)(3d^{2} + hd - 8)[/tex] = [tex]21d^{4} + (7h-9) d^{3} + (3g-56-3h)d^{2} + (24+gh)d -8g[/tex] ... (1)
Comparing eq(1) to the product given in question,
-8g = -1
g = 2
24 + gh = 14, sub g =2,
24 + 2h = 14
h = -5
Is the slope Positive, Negative, Zero or Undefined?
Find the slope
What does m=
Answer:
Positive
Step-by-step explanation: The slope is 4/3
Answer:
slope is positive m=4/3
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 9.1 m and a base with a circumference of 12.1 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
[tex]V=35.3\ m^3[/tex]
Step-by-step explanation:
-Given the cone's height is 9.1m and the Circumference is 12.1
#We use the circumference formula to calculate the radius:
[tex]C=2\pi r\\\\12.1=2\pi r\\\\r=\frac{12.1}{2\pi}=\frac{6.05}{\pi}\ cm[/tex]
-The volume of the cone using the radius above can then be calculated as follows:
[tex]V=\pi r^2\frac{h}{3}\\\\=\pi\times(\frac{6.05}{\pi})^2\times \frac{9.1}{3}\\\\\\=35.3\ m^3[/tex]
Hence, the cone's volume is [tex]35.3\ m^3[/tex]
The playground of a school has areas fixed for various activities. One-fifth of the playground is used for students to sit and read. Of the remaining playground, is used for playing soccer. The rest of the playground is used for playing basketball. Which equation represents the part of the playground used for soccer?
Answer:
2/3* 4/5 = 8/15
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached file below.
Given:
One-fifth (1/5) of the playground is used for students to sit and read2/3 is used for playing soccer The rest of the playground is used for playing basketballSo assume that the the playground is divided into 5 equal part
=> 1 part is used for students to sit and read or (1/5)
=> the remaining equal part is 4 or (4/5)
Because 2/3 of the remaining part is used for playing soccer
=> the equation represents the part of the playground used for soccer is:
2/3 of 4/5
= 2/3* 4/5
= 8/15
To find the part of the playground used for soccer, remember one-fifth is for reading, leaving four-fifths. Then, calculate three-quarters of the remaining area for soccer.
To represent the part of the playground used for soccer, we need to consider that one-fifth of the playground is used for students to sit and read. Therefore, the remaining four-fifths of the playground is available for other activities. Since three-quarters of the remaining playground is used for playing soccer, the equation representing the part of the playground used for soccer is:
4/5 * 3/4 = 12/20 = 3/5
The number of triangles created is always two fewer than the number of sides (n) in the polygon.
How can you write this as an expression?
The number of triangles is (n-2)
what is the surface area of the box if it is scaled up by a factor of 10? surface area is 164, height is 4 in, width is 3 in, length is 10 in.
Answer:
16400 in ^2
Step-by-step explanation:
For area, we multiply by the scale factor squared
area 2 = sf^2 * area 1
Since the scale factor is 10,
area 2 = 10^2* 164
= 100*164
= 16400
Answer:
16,400 in²
Step-by-step explanation:
Ratio of Areas = (Ratio of sides)²
A/164 = 10²
A/164 = 100
A = 16400
An object is launched at 29.4 meters per
second (m/s) from a 34.3-meter tall
platform. The equation for the object's
height s at time x seconds after launch is
f(x) = -4.9x2 + 29.4x+ 34.3, where y is in
meters. What is the initial height of the
object?
29.4 meters
78.4 meters
34.3 meters
3 meters
Answer:
34.3 meters
Step-by-step explanation:
The generic equation for a movement with constant acceleration is:
S = So + Vo*t + (a*t^2)/2
Where S is the final position, So is the inicial position, Vo is the inicial speed, a is the acceleration and t is the time.
If we compare with our equation (where x is the time and f(x) is the final distance), we have that:
So = 34.3
Vo = 29.4
a = -9.8
So we have that the inicial position (So) of the object is 34.3 meters
Given f(x)=-5x+1 find f(6)
Answer:
f(6)=-29
Step-by-step explanation:
f(6)=-5(6)+1
f(6)=-30+1
f(6)=-29
The value of f(6) is -29.
Given,
f(x)= -5x+1
We need to find f(6).
How do we solve a function at a point?A function is denoted by f(x) and the point can be a value of x.
The x values are called domain and f(x) is called the output.
Example:
f(x) = x + 2
At x = 1
f(1) = 1 + 2 = 3.
Find f(x) = -5x + 1 at x = 6.
f(x) = -5x + 1
f(6) = - 5 x 6 + 1
= -30 + 1
= -29
This means the function f(x) is -29 at x = 6.
Thus the value of f(6) is -29.
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what is $5,158 round to the nearest percent
Solve the equation for x.
x/3 = (2x + 3)/7
Answer:
Our answer is [tex]x=9[/tex]
Step-by-step explanation:
First we will rearrange so we have to divide by 7.
[tex]\frac{x}{3}= \frac{2x+3}{7}[/tex]
Now we will cross multiply.
So...
[tex]x*7 \\3*2x+3[/tex]
Our new equation will look like:
[tex]7x=6x+9[/tex]
Now we have to isolate x.
So we have to subtract 6x from both sides.
[tex]7x-6=1x[/tex]
and
[tex]6x-6x=0[/tex]
Our new equation is:
[tex]1x=9[/tex]
Now divide.
Our answer is [tex]x=9[/tex]
Hope this helped!
1,THE POPULATION OF THREE TOWNS ARE 65,600, 13,400 AND 29,700 APPROXIMATE THE TOTAL POPULATION OF THE THREE TOWNS TO THE NEAREST THOUSANDS
2,REHEMA SPENT 1/8 OF HER SALARY ON TRANSPORT AND 1/4 ON FOOD IF SHE REMAINED WITH SH 80000 WHAT WAS HER SALARY....PLEASE ANSWER MY QUESTION FIRST I WILL MARK U BRAINLIEST
Answer:
1) 65600+13400+29700=108700
to the nearest thousand it will be 108000
2) 1/8+1/4=3/8
3/8-1=5/8
5/8× U=80000
U=80000÷5/8
U=128000
note that U is unknown
What is the formula (equation) for momentum?
Answer:
p=mv
Step-by-step explanation:
Answer:
The answer is p = m×v.
Step-by-step explanation:
The formula of momentum is p = m×v where m is the mass of object and v is the velocity of an object.