Solving the trigonometric equation, it is found that during the first 11 years, the population size will be of 4700 in 3.62 and 7.24 years.
What is the trigonometric equation for the population?It is given by:
[tex]p(t) = 4096 - 1269\cos{\left(\frac{2\pi}{11}t\right)}[/tex]
It will be of 4700 when p(t) = 4700, hence:
[tex]p(t) = 4096 - 1269\cos{\left(\frac{2\pi}{11}t\right)}[/tex]
[tex]4700 = 4096 - 1269\cos{\left(\frac{2\pi}{11}t\right)}[/tex]
[tex]604 = - 1269\cos{\left(\frac{2\pi}{11}t\right)}[/tex]
[tex]\cos{\left(\frac{2\pi}{11}t\right)} = -\frac{604}{1269}[/tex]
[tex]\cos{\left(\frac{2\pi}{11}t\right)} = -0.47596532702[/tex]
[tex]\cos^{-1}{\cos{\left(\frac{2\pi}{11}t\right)}} = cos^{-1}{-0.47596532702}[/tex]
Then:
[tex]\frac{2\pi}{11}t = 2.06685766[/tex]
[tex]t = \frac{11 \times 2.06685766}{2\pi}[/tex]
[tex]t = 3.62k, k = 1, 2, ...[/tex]
Thus:
t = 3.62 x 1 = 3.62
t = 3.62 x 2 = 7.24.
The population size will be of 4700 in 3.62 and 7.24 years.
More can be learned about trigonometric equations at https://brainly.com/question/24680641
Tanya is training a turtle for a turtle race. For every 3 of an hour that the turtle is crawling, he can travel 25 of a mile. At what unit rate is the turtle crawling? A 7 of a mile per hour 75 B. of a mile per hour C 37 } miles per hour D. 7 of a mile per hour
Answer:
D. but there should be an 8.33
Step-by-step explanation:
The answer should be 8.33 but in here it only says 7 which is the closest because the unit rate would be 8.33 miles an hour.
The model represents an equation. What value of x makes the equation true?
A) 29/8
B) 29/2
C) − 29/2
D) − 29/8
Answer:
A) 29/8
Step-by-step explanation:
Identify the blocks. As you can see there are 5 x blocks on the left, and 9 -1 blocks on the left. On the right there are 3 -x blocks and 20 1 blocks. With this, form the equation.
5x - 9 = -3x + 20
Add 3x to both sides.
8x - 9 = 20
Add 9 to both sides.
8x = 29
Divide both sides by 28 to get:
x = 29/8.
You work with 3 other students on a project for science class. Your group
zarns 329 points, or 94%, of the total possible points. How many points are
possible for the project?
Answer:
350 points are possible
Step-by-step explanation:
You take 329 divided by 94% or .94 to get 350.
100% of 350 is 350
To double check, 94% of 350 is 329 & 6% of 350 is 21. 329 +21 = 350
Write 0.000299 in scientific notation
Answer:
0.000299 in scientific notation
2.99 × 10-4
Step-by-step explanation:
To convert 0.000299 into scientific notation also known as standard form, follow these steps:
Move the decimal 4 times to right in the number so that the resulting number, m = 2.99, is greater than or equal to 1 but less than 10
Since we moved the decimal to the right the exponent n is negative
n = -4
Write in the scientific notation form, m × 10n
= 2.99 × 10-4
Answer:
0.000299
2.99 × 10^-4.
Step-by-step explanation:
solve for x: x^3 + x^2 + x = 3
Please help! I cannot figure this out, I have no idea what to do.
3. First you should identify which line corresponds to which equation.
x + 2y = -8 ⇒ y = -x/2 - 4
is the line with slope -1/2 and intercept (0, -4), so the first inequality refers to the lower line in the graph.
For the inequality itself, the solution set that satisfies it is either the region above or below it. To decide which, pick any point in the plane and plug its coordinates into the inequality. The origin is a natural choice, since it's not on the line and working with 0s is easy.
In the first inequality, we have
x = 0 and y = 0 ⇒ 0 + 2•0 = 0 < -8
which is not true. So (0, 0) is not in the solution set, and it stands to reason that any point in the same region will not be a solution. In other words, the region above the line x + 2y = -8 does not satisfy the inequality, while the one below it does.
In the second inequality,
x = 0 and y = 0 ⇒ 2•0 + 0 = 0 ≥ -1
which is true. This means the region containing (0, 0) above the upper line solves the second inequality.
The solution to the system of inequalities is then the intersection of these two regions. (See attached; I've labeled the solution to the first inequality in blue, the solution to the second one in red, and the solution to both in green.)
All this work is kind of overkill for this particular question, though. All you really need to do is check if the given point satisfies the inequalities:
• (-5, 5) :
x = -5 and y = 5 ⇒ -5 + 2•5 = 5 < -8 ⇒ NO
• (2, -5) :
x = 2 and y = -5 ⇒ -2 + 2•5 = 8 < -8 ⇒ NO
• (-4, -6) :
x = -4 and y = -6 ⇒ -4 + 2•(-6) = -16 < -8 ⇒ MAYBE
x = -4 and y = -6 ⇒ 2•(-4) + (-6) = -14 < -8 ⇒ YES
• (5, -7) :
x = 5 and y = -7 ⇒ 5 + 2•(-7) = -9 < -8 ⇒ MAYBE
x = 5 and y = -7 ⇒ 2•5 + (-7) = 3 < -8 ⇒ NO
4. x is the number of candy boxes with chocolates and y is the number of boxes without chocolates. Each of the x boxes cost $27.50, so if you have x boxes, their total cost is $27.5x. Each of the y boxes cost $25.00, so y boxes cost $25y. The sponsor doesn't want to order more than 100 boxes total, so
x + y < 100
but wants to raise at least $2000, so
27.5x + 25y ≤ 2000
Now do the same thing as before; plug in the listed x- and y-coordinates and pick the point that satisfies both inequalities. You will find that (50, 30) is the correct choice.
5. Consult the "overkill" part of problem 3. The line y = -3x + 6 has a negative slope, so it's the downward sloping one. Check if the origin satisfies the inequality:
x = 0 and y = 0 ⇒ 0 ≤ -3•0 + 6 ⇒ 0 ≤ 6 ⇒ YES
This means Regions II and III solve the first inequality.
Do the same with the other inequality:
x = 0 and y = 0 ⇒ 0 ≥ 1/2•0 + 1 ⇒ 0 ≥ 1 ⇒ NO
This tells us that Regions I and II solve the second inequality.
The intersection of these regions is of course Region II.
6. One of the plotted lines is apparently y = x + 4, which has a positive slope, so this must be the upper line. The shaded region below it corresponds to the solution of either y < x + 4 or y ≤ x + 4 and we eliminate B.
The other line has negative slope, which eliminates A and D since
3x - 4y = 20 ⇒ y = 3/4x - 5
has positive slope. This leaves D.
What is the IQR for 79 85 98 125 140
Hi there!
We have the numbers:
79 85 98 125 140
From the data, we can see that '98' is the median value as it is exactly in the middle. We can then split the data into equal groups on both sides of the median.
79 85
125 140
Since there are only two numbers, we can find the median of EACH sub-group (Q1 and Q3 respectively) by taking the average.
Q1 = (79 + 85)/2 = 82
Q3 = (140 + 125)/2 = 132.5
The IQR is simply the difference between Q3 and Q1, so:
IQR = 132.5 - 82 = 50.5
The probability that a couple will havenbaby boys in a row is given by the formula
2
Find the probability that a couple will have Sbaby boys in a row.
Answer:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
Step-by-step explanation:The probability that a couple will havenbaby boys in a row is given by the formula2Find the probability that a couple will have Sbaby boys in a row.
is your correct answer
Let x1 = 36, y1 = −6, and y2 = 8, and let y vary inversely as x. Find x2.
Answer:
-30
Step-by-step explanation:
Using 'y' is vary inversely to 'x', the value of x₂ = -27.
What is inverse?The word inverse in mathematics "a function or operation which reverses the order or operation of another function or operation".
According to the question,
x₁ = 36, y₁ = -6, y₂ = 8 and x₁ is inversely proportional to y₁ which mean
(x₁) (y₁) = k
(36)(-6) = -216.
Formula for inverse is x = k([tex]\frac{1}{y}[/tex]).
In order to find x₂, x₂ = -216(1/8)
x₂ = -27
Hence, the value of x₂ = -27.
Learn more about inverse proportional here
https://brainly.com/question/20026843
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Multiply: (x−4)(x+5)
Simplify and write your answer in Standard Form.
HINT
Standard Form: ax2+bx+c
Answer:
x^2 + x -20
Step-by-step explanation:
First, Multiply
(x)(x) + (x)(5) + (-4)(5) + (-4)(x)
Second, Add The Like Terms Together
X^2 + x + -20
Answer: Its x^2 + 9x -20
Step-by-step explanation:
I did the test and got it wrong
3827 x 8/8 lees than equal to or greater than 3827 asap
Answer:
It's equal to itself. Here are the two ways to do this problem. ↓
[tex](3,827 * 8) / 8 = 3,827[/tex][tex]3,827 * 100~percent(8/8) = 3,827[/tex]Triangle ABC is similar to triangle XYZ. Find side a.
Answer:
If ABC and XYZ are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths. ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z AB/XY = BC/YZ = AC/XZ
Math test Farley easy
Answer:
417.831823 [tex]in^{2}[/tex]
Step-by-step explanation:
surface area of cone ;
[tex]=\pi r^{2}+\pi rl\\ =\pi (7^{2}) +\pi (7)(12)=417.831823 in^{2}[/tex]
Answer:417.831823
Step-by-step explanation:
Tickets to games of a local basketball team cost $12 for students and $16 for adults. For one game, $3700 was collected and 250 tickets were sold. How many of each kind of ticket were sold? Write and solve a system of equations.
Answer:
12x + 16y = 3700
x + y = 250
x = 75 students
y = 175 adults
Step-by-step explanation:
y = 250 - x
12x + 16(250-x) = 3700
12x + 4000 - 16x = 3700
-4x = -300
x = 75
y = 250 - 75
y = 175
A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The
function P(d) measures the pressure exerted by water, where d represents the depth of water in
meters. Which of the following would be a possible domain?
A
d is the set of all integers.
B
d is the set of all integers where d > 0.
d is the set of all rational numbers.
D
d is the set of all rational numbers where 0 sds depth of sea floor).
994
Answer:
the correct answer is D.
Step-by-step explanation:
d is the set of all rational numbers where (0 ≤ d ≤ depth of seafloor).
i just took the test on math nation and got it correct.
hope this helped! :)
the area of a parallelogram measures 171 cm the base of the parallelogram is 18 cm in length which of the following best represents the height of the parallelogram A. 11cm B. 9.5 C. 13.5 D. 8cm give step by step explanation
Answer:
A=bxh
171 cm=18cmxh
h=171/18
= 9.5 cm
which is B no.
1/3(6x-3)-1/4(20x+8)=-6
Answer:
x = 1.
Step-by-step explanation:
[tex]\frac{1}{3}(6x-3)-\frac{1}{4}(20x+8)=-6\\\\[Distribute the first fraction into the parenthesis.]\\((\frac{1}{3}*6x)-(\frac{1}{3}*3))-\frac{1}{4}(20x+8)=-6\\\\2x-1-\frac{1}{4}(20x+8)=-6\\\\[Distribute the second fraction into the parenthesis.]\\2x-1-((\frac{1}{4}*20x)+(\frac{1}{4}*8))=-6\\\\2x-1-5x-2=-6\\\\[Combine like terms.]\\-3x-3=-6\\\\[Add 3 to both sides.]\\-3x=-3\\\\[Divide both sides by -3.]\\x=1[/tex]
add the following integers {3 +(-7)}+(-6)
Answer:
-10
Step-by-step explanation:
Answer:
-10
Step-by-step explanation:
(3+(-7))+(-6)
=3-7+-6
=3-7-6=-10
Find the reciprocal of 6.
Answer:
1/6
Step-by-step explanation:
6 = 6/1
Therefore, reciprocal= 1/6
Answer:
1/6
Step-by-step explanation:
Help help help math math math
4x + 8 > -x - 7
4x + x > - 7 - 8
5 x > - 15
x > -3
x > -3
↪explanation4x + 8 > -x - 7
4x + x > -7 - 8
5x > -15
5x ÷ 5 > -15 ÷ 5
x > -3
☆...hope this helps...☆
Sawyer is 6 years older than his sister.
This year, Sawyer is also three times as
old as his sister. How old is Sawyer now?
Sawyer is 9 yrs old and his sister is 3 yrs old
hope it really helps...
Please solve with explanation high points
Answer:
k = 0, k = 4
Step-by-step explanation:
Given equation:
[tex]y=x^2+kx+3k+4x+4[/tex]
Rearrange into standard form [tex]ax^2+bx+c[/tex]:
[tex]\implies y=x^2+kx+4x+3k+4[/tex]
[tex]\implies y=x^2+(k+4)x+(3k+4)[/tex]
Therefore:
[tex]a=1, \quad b=(k+4), \quad c=(3k+4)[/tex]
If the vertex lies in the x-axis, then the quadratic has one (repeating) root at (x, 0). Therefore, we can use the discriminant to find the values of k.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
Therefore, set the discriminant to zero and solve for k:
[tex]\implies (k+4)^2-4(1)(3k+4)=0[/tex]
[tex]\implies k^2+8k+16-12k-16=0[/tex]
[tex]\implies k^2-4k=0[/tex]
[tex]\implies k(k-4)=0[/tex]
[tex]\implies k=0, k=4[/tex]
So the vertex lies in the x-axis when k = 0 or k = 4
You have two part-time jobs making $11 an hour mowing lawns and $8 an hour washing cars. You want to make at least $150 a week but work less than 20 hours per week. Write a system to represent this situation..
What is 2/3 - 5/6 divided by 3/4
A temperature of 35 degrees Fahrenheit is as cold as a temperature of -35 degrees Fahrenheit.
Answer:yes
Step-by-step explanation:
How many milliliters are in 5 liters?
500 mL
5,000 mL
50,000 mL
50 mL
Answer:
5,000 is the correct answer
Pls help me with this
1. Which drink is the most preferred by your classmates?
2. Which drink is the least preferred by your classmates?
3. Compare the percentage of students who prefer juice and coffee.
4. Compare the percentage of students who prefer water and tea.
5. Compare the percentage of students who prefer chocolate drink and other drink.
Answer:
1. Choclate Drink
2. Coffee
3. 19 % difference
4. 1 % difference
5. 42% difference
Step-by-step explanation:
For the 50 students in an art contest, there will be 1 prize for first-place, 1 prize for second-place, and 3 prizes for honorable mention. What is the probability of winning a prize?
Step-by-step explanation:
there are 50 students and 5 prizes (1 + 1 + 3).
so, already in natural language we would say "there is 1 prize for every 10 students".
formally, remember the rule of probability : desired outcomes over total possible outcomes.
this is here
5/50 = 1/10 = 0.1
your can see it also this way :
if there was only 1 prize, each student would have a chance of 1/50 of winning.
now there are 5 prizes, which gives everybody 5 times the chance of winning. which is then 5×1/50 = 5/50 = 0.1
Espanol
- 9
1
2
P4
8
3
5
6
A triangle is placed in a semicircle with a radius of 3 yd, as shown below. Find the area of the shaded region.
Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answer: 5.13 square cm
Step-by-step explanation:
Estimate the answer to
(
9.51
×
10
3
)
×
(
8.57
×
10
4
)
Give your answer in standard form.
Step-by-step explanation:
9.51 x 10^3 * 8.57 x 10^4 = ~~ 10000 * 90000 = 900, 000,000 est
Question was changed.....so answer was edited