Answer:36
Step-by-step explanation:
For each year t, the number of trees in Forest A is represented by the function A(t) = 72(1.025). In a neighboring forest, the number of trees in Forest B is represented by the function B(t) = 63(1.029).
Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?
Round your answer to the nearest tree.
Forest A or B will have _________ more trees.
Answer:
Forest A will have 6 more trees.
Step-by-step explanation:
The number of trees in Forest A is represented by the function:
[tex]A(t)=72(1.025)^t[/tex]
And Forest B is represented by:
[tex]B(t)=63(1.029)^t[/tex]
And we want to determine which forest will have the greater number of trees after 20 years.
So, evaluate both functions for t = 20. For Forest A:
[tex]\displaystyle \begin{aligned} A(20)&=72(1.025)^{20} \\ &=117.9803...\\ &\approx 118 \text{ trees} \end{aligned}[/tex]
And for Forest B:
[tex]\displaystyle \begin{aligned} B(20) &= 63(1.029)^{20} \\ &=111.5958... \\ &\approx 112 \end{aligned}[/tex]
Therefore, after 20 years, Forest A will have 6 more trees.
For questions #1 and #2:
A) Write one sentence in your own words, describing the step you need to solve the problem.
B) Write the answer
EXAMPLE:
x/3 = 5
A. Multiply both sides by 3.
B. Answer is 15.
Question #1:
x - 3 = 10
Question #2:
2x = 8
I need help pleaseeeeee
Answer:
question 1
if you want x to stand alone
you will take the -3 off by crossing it to the other side
NB when a negative number crosses the equal sign it becomes positive
x =10+3= ×=13 is the final answer
Step-by-step explanation:
question 2
you will divide both sides by 2(because we want x to stand alone)
so final answer is ×=4
The rectangular floor of a storage shed has an area of 580 square feet. The length of the floor is 9 feet more than its width (see figure). Find the dimensions of the floor.
Length= ? Ft
Width= ? Ft
9514 1404 393
Answer:
length: 29 ftwidth: 20 ftStep-by-step explanation:
Assuming the dimensions are integer numbers of feet, you're looking for factors of 580 that have a difference of 9.
580 = 1×580 = 2×290 = 4×145 = 5×116 = 10×58 = 20×29
The last pair of factors differs by 9, so ...
the length is 29 feet; the width is 20 feet.
I need help solving this math problem
Three student representatives, a president, a secretary, and a treasurer, are to be chosen from a group of five students: Andrew, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men
Answer:
Hence there are 6 different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men.
Step-by-step explanation:
We know that,
Total males = 3,
Total Females = 2,
Now we want 2 males and a female.
Then the choices are,
[tex]= ^{3} C_{2} \times ( ^{2} C_{1} )\\\\= 3 \times 2\\\\=6[/tex]
Find the area of 11 by 2
What is the area of triangle ABC? Round to the nearest whole number
9514 1404 393
Answer:
C. 837
Step-by-step explanation:
The remaining angle is ...
C = 180° -A -B = 180°-62° -67° = 51°
The law of sines tells us that the length AC is ...
AC/sin(B) = AB/sin(C)
AC = AB·sin(B)/sin(C) = 40·sin(67°)/sin(51°)
Using the area formula given, we now have ...
area = 1/2(AB)(AC)sin(A)
= (1/2)(40)(40·sin(67°)sin(62°)/sin(51°) ≈ 836.7
The area of the triangle is about 837 square units.
IMPORTANT NEED ANSWER ASAP !!
The stem plot shows the number of mini-marshmallows eaten in one minute by a group of people competing in a contest.
Row1 with a 2 to the left of the bar with a 9 to the right. Row 2 with a 3 to the left of the bar with 8, 9 to the right. Row 3 with a4to the left of the bar with 2, 6, 7, 8, 8to the right. Row 4 with a5to the left of the bar with 3, 5, 5, 5 to the right. Row 5 with a 6to the left of the bar with 1, 3, 7to the right.
Key: 2|9 = 29 mini-marshmallows
Which of the following is a correct statement about the distribution?
There are no outliers.
The distribution is skewed left.
The center is around 44.
The distribution is bimodal.
Step-by-step explanation:
mark me as brainlist...........
Answer:
I got to say, the other guy got it good. Thanks dude.
Step-by-step explanation:
A sculpture is made of soild tin in the shape of a cone, sculpture is 70 inches tall, its base has a radius of 9 inches, the tin cost $1.75 per cubic inch how much did it cost for the tin for the sculpture
Answer:
$10390.817
Step-by-step explanation:
Given that :
Sculpture is made in Shape of a cone with :
Height, h = 70 inches
Radius, r = 9 inches
Volume of a cone = 1/3πr²h
Volume = 1/3 * π * 9² * 70
Volume of sculpture = 5937.6101 in³
Cost per in³ = $1.75
Cost of tin for the sculpture :
Cost per in³ * volume of sculpture
$1.75 * 5937.6101 = $10390.817
urgent help needed !!!!!!
Answer:
use gauthmath
Step-by-step explanation:
you will thank me later
What is the domain of the function graphed below?
Answer:
x<7
Step-by-step explanation:
Do you know the answer to this question
Answer:
125$ worth because you would not spend it all if you picked 625 and the others would give way too many away
If P(x) = 2x2 – 3x + 7 and Q(x) = 8 - x), find each function value.
15. P(-3)
16. Q(2)
17. P(4)
18. Q(-3)
Answer:
15. 52
16. 6
17. 59
18. 11
Step-by-step explanation:
The profit, in dollars, of selling n items is given by P(n) = 0.86n - 2800. Identify the slope and the y-intercept.
Answer: 0.86 and -2800 (choice A)
Explanation:
Think of the given equation as y = 0.86x - 2800
Then compare it to y = mx + b
We see that m = 0.86 is the slope and b = -2800 is the y intercept.
Answer:
Slope: 0.86 , Y-intercept:-2800
Step-by-step explanation:
Linear equations go by the form of y=mx + c
where m is the gradient(slope of the graph) and c is the y-intercept
Write the fraction 24/40 in its simplest form.
Find dy/dx given that y = sin(cos(x))
Hi there!
[tex]\large\boxed{-sin(x)cos(cos(x))}[/tex]
Use the chain rule:
f(g(x)) = f'(g(x)) · g'(x)
Thus:
dy/dx sin(x) = cos(x)
dy/dx cos(x) = -sin(x)
Use the chain rule format:
f(x) = sin(x)
g(x) = cos(x)
cos(cos(x)) · (-sin(x))
-sin(x)cos(cos(x))
What is the height of a triangle of base 10m and an area of 60m²
A = 0.5*b*h
60 = 0.5*10*h
60 = 5h
5h = 60
h = 60/5
h = 12
Answer: The height is 12 meters.
Answer:
6 m
Step-by-step explanation:
Since the area is 60 m squared and the base is 10 m, the height is 12.
Formula: base x height / 2 = area
= 10 x height / 2= 60 m squared
60 / 10 = 6 x 2 = 12.
Hope this helps!
Please help with this function problem
Answer:
-2
-1
-2
Step-by-step explanation:
really ? this is a problem ? why ?
f(0) means the functional value for x = 0.
is x = 2 ? no.
so, automatically the other case applies, and f(0) = -2
f(2) means x=2
is x = 2 ? yes.
so that case applies, and f(2) = -1
f(5) means x=5
is x = 2 ? no.
so again, the case for x <> 2 applies, f(5) = -2
A new car costs $23000. The value decreases by 15% each year.(a) Write the exponential model to represent the cars value after t years. (b) To the nearest dollar, how much will the car be worth after 4 years?
Answer:
(a) 23000(1-15%)^t
(b) about 12006.14375
Step-by-step explanation:
(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t
And with the values, we get the exponential model 23000(1-15%)^t
(b) From question (a) we already have the model and the time period given here is 4 years. So putting it in the formula we get,
23000(1-15%)^4
=23000(1-15/100)^4
=23000(0.85)^4
=23000x0.52200625
=12006.14375 (Ans)
If computers sell for $1160 per unit and hard drives sell for $ 102 per unit, the revenue from x computers and y hard drives can be represented by what expression? If computers sell for $ per unit and hard drives sell for $102 per unit, the revenue from x computers and y hard drives can be represented by
Find y on this special right triangle
Answer:
Cos(x) = adjacent side/hypotenuse[tex]cos(45)=\frac{\frac{7\sqrt{2} }{2} }{x} \\\\cos(45)x=\frac{7\sqrt{2} }{2}\\\\\frac{\sqrt{2} }{2}x=\frac{7\sqrt{2} }{2}\\\\x=\frac{\frac{7\sqrt{2} }{2}}{\frac{\sqrt{2} }{2}} =\frac{7\sqrt{2} }{2}*\frac{2}{\sqrt{2}} =7[/tex]
Use the Pythagorean Theorem to find y[tex]y^{2} +(\frac{7\sqrt{2} }{2} )^{2} =x^{2} \\\\y^{2} =7^{2}-(\frac{7\sqrt{2} }{2} )^{2} \\\\y^{2}=49-\frac{49(2)}{4} =49-\frac{49}{2}=\frac{49(2)}{2}-\frac{49}{2}=\frac{98-49}{2}=\frac{49}{2} \\\\y=\sqrt{\frac{49}{2} } =\frac{7}{\sqrt{2} } =\frac{7\sqrt{2}}{\sqrt{2}(\sqrt{2})} =\frac{7\sqrt{2}}{2}[/tex]
After carrying out an ANOVA procedure where the decision is made to reject the null hypothesis, we can test for differences between treatment means by ______.
Answer:
Doing an additional ANOVA
Explanation:
Analysis of variance(ANOVA), developed by Ronald Fisher is a method used to statistically measure the difference between means of different variables. While the t test measures difference between two population means, analysis of variance measures the difference for more than two population means. There is the one way ANOVA and two way ANOVA that test the difference between means.
What is |-2.24|? i need this question answered quickly
i think the answer is 2.24
help pls ik the answers i just don’t k is how to show work :(
include the notation and just do the work on the page
If a square shaped lot measures 200’ on one side, what is the square footage of the lot
Answer:
40,000 ft²
Step-by-step explanation:
area = 200 ft * 200 ft = 40,000 ft²
this is what i need help with[tex](1/5)^3[/tex]
Let the probability of success on a Bernoulli trial be 0.26. a. In five Bernoulli trials, what is the probability that there will be 4 failures
Answer:
0.3898 = 38.98% probability that there will be 4 failures
Step-by-step explanation:
A sequence of Bernoulli trials forms the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Let the probability of success on a Bernoulli trial be 0.26.
This means that [tex]p = 0.26[/tex]
a. In five Bernoulli trials, what is the probability that there will be 4 failures?
Five trials means that [tex]n = 5[/tex]
4 failures, so 1 success, and we have to find P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{5,1}.(0.26)^{1}.(0.74)^{4} = 0.3898[/tex]
0.3898 = 38.98% probability that there will be 4 failures
What proportion of the students scored at least 23 points on this test, rounded to five decimal places
This question is incomplete, the complete question is;
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.
What proportion of the students scored at least 23 points on this test, rounded to five decimal places?
Answer:
proportion of the students that scored at least 23 points on this test is 0.30850
Step-by-step explanation:
Given the data in the question;
mean μ = 22
standard deviation σ = 2
since test closely followed a Normal Distribution
let
Z = x-μ / σ { standard normal random variable ]
Now, proportion of the students that scored at least 23 points on this test.
P( x ≥ 23 ) = P( (x-μ / σ) ≥ ( 23-22 / 2 )
= P( Z ≥ 1/2 )
= P( Z ≥ 0.5 )
= 1 - P( Z < 0.5 )
Now, from z table
{ we have P( Z < 0.5 ) = 0.6915 }
= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850
P( x ≥ 23 ) = 0.30850
Therefore, proportion of the students that scored at least 23 points on this test is 0.30850
I need help with this question
Answer:
Step-by-step explanation:
Expression that defines the number of words per minute that an average person can type is,
[tex]W(t)=47-20e^{-0.6t}[/tex]
a). For t = 0,
[tex]W(0)=47-20e^{0}[/tex]
[tex]W(0)=47-20[/tex]
[tex]=27[/tex]
b). For w = 1,
[tex]W(1)=47-20e^{-0.6(1)}[/tex]
[tex]=47-20e^{-0.6}[/tex]
[tex]=40-10.98[/tex]
[tex]=36.02[/tex]
≈ [tex]36[/tex]
c). For w = 6,
[tex]W(6)=47-20e^{-0.6(6)}[/tex]
[tex]=47-20(0.0273)[/tex]
[tex]=47-0.55[/tex]
[tex]=46.45[/tex]
≈ [tex]46.5[/tex]
d). For w = 12,
[tex]W(12)=47-20e^{-0.6(12)}[/tex]
[tex]=47-0.015[/tex]
= [tex]46.985[/tex]
≈ [tex]47[/tex]
A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting the given result. [Binomail Probability] Less than four twos
Answer:
0.5665 = 56.65% probability of less than four twos.
Step-by-step explanation:
For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 20 times
This means that [tex]n = 20[/tex]
One out of six sides is 2:
This means that [tex]p = \frac{1}{6} = 0.1667[/tex]
Probability of less than four twos:
This is:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]
[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]
[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]
[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]
So
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]
0.5665 = 56.65% probability of less than four twos.
