Answer:
2538
2.5%
Step-by-step explanation:
The population equayio since year 2000 can be modeled mathematically as :
P = 2538(1.025)^t
This is an exponential growth function which is represented by the general formula :
y = a(b)^t
Where, a is the initial population ;
b = growth factor ; b = (1 + r) where r = growth rate
Comparing the equations, the population in year 2000 represents the initial population, a = 2538
The percentage Rate of increase in population is :
(1 + r) = 1.025
r = 1.025 - 1
r = 0.025 ; 0.025 * 100% = 2.5%
if √3CosA = sin A , find the acute angle A
Answer:
Here is your answer.....
Hope it helps you....
The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation
p = −0.00051x + 5 (0 ≤ x ≤ 12,000)
where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by
C(x) = 600 + 2x − 0.00002x2 (0 ≤ x ≤ 20,000).
Hint: The revenue is
R(x) = px,
and the profit is
P(x) = R(x) − C(x).
Find the revenue function,
R(x) = px.
R(x) =
Answer:
[tex]R(x) = -0.00051x^2 + 5x[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
Step-by-step explanation:
Given
[tex]p = -0.00051x + 5[/tex] [tex]\to[/tex] [tex](0 \le x \le 12,000)[/tex]
[tex]C(x) = 600 + 2x - 0.00002x^2[/tex] [tex]\to[/tex] [tex](0 \le x \le 20,000)[/tex]
Solving (a): The revenue function
We have:
[tex]R(x) = x * p[/tex]
Substitute [tex]p = -0.00051x + 5[/tex]
[tex]R(x) = x * (-0.00051x + 5)[/tex]
Open bracket
[tex]R(x) = -0.00051x^2 + 5x[/tex]
Solving (b): The profit function
This is calculated as:
We have:
[tex]P(x) = R(x) - C(x)[/tex]
So, we have:
[tex]P(x) =-0.00051x^2 + 5x - (600 + 2x - 0.00002x^2)[/tex]
Open bracket
[tex]P(x) =-0.00051x^2 + 5x -600 - 2x +0.00002x^2[/tex]
Collect like terms
[tex]P(x) = 0.00002x^2-0.00051x^2 + 5x - 2x-600[/tex]
[tex]P(x) = -0.00049x^2 + 3x-600[/tex]
Which is an x-intercept of the graph of the function?
Answer:
D
Step-by-step explanation:
X intercept=y=0. 0=tan(x-5pi/6). x-5pi/6=0, x=5pi/6
What is the equation of the line that passes through the point (-4, 2) and has a
slope of -2?
Step-by-step explanation:
use the equation of the straight line
y-y1=m (x-x1)
y-2=-2(x+4)
y-2= -2x-8
y= -2x-8+2
y= -2x-6
I hope this helps
What is 1/2 of 1/3 of 1/5 of 60?
IT supposed to be 2 because 1/2 1/3 of 1/5 of 60 is "2".
Answer:
2
Step-by-step explanation:
Of means multiply
1/2 * 1/3* 1/5 * 60
1/6 * 1/5*60
1/30 *60
60/30
2
Solve the equation 10 + y√ = 14
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Answer:
y = 16
Step-by-step explanation:
Perhaps you want to solve ...
10 +√y = 14
√y = 4 . . . . . . subtract 10
y = 4² = 16 . . . square both sides
Which statement is true about the slope of the graphed line?
Answer: positive
Step-by-step explanation: because it is going up from the left to the right
Triangles ABC and DEF are similar. The height of
triangle DEF is 4 cm. Find the area of triangle ABC.
a. 1.5 cm
b. 2 cm
c. 6 cm
d. 3 cm
Option C
Height of DEF = 4cm
Therefore ratio = 1:2
Base = 3cm
Height of ABC = 2cm
Area of ABC = 1/2×b×h
= 1/2×3×4
= 6cm²
Option C
Answered by Gauthmath must click thanks and mark brainliest
David can receive one of the following two payment streams:
i. 100 at time 0, 200 at time n, and 300 at time 2n
ii. 600 at time 1 0
At an annual effective interest rate of i, the present values of the two streams arc equal. Given v^n = 0.75941.
Determine i.
Answer:
3.51%
Step-by-step explanation:
From the given information:
For the first stream, the present value can be computed as:
[tex]= 100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}}[/tex]
Present value for the second stream is:
[tex]=\dfrac{600}{(1+i)^{10}}[/tex]
Relating the above two equations together;
[tex]100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}} =\dfrac{600}{(1+i)^{10}}[/tex]
consider [tex]v = \dfrac{1}{1+i}[/tex], Then:
[tex]\implies 100+200v^n + 300v^{2n} = 600 v^{10}[/tex]
where:
[tex]v^n = 0.75941[/tex]
Now;
[tex]\implies 100+200(0.75941) + 300(0.75941))^2 = 600 (v)^{10}[/tex]
[tex](v)^{10} = \dfrac{100+200(0.75941) + 300(0.75941))^2 }{600}[/tex]
[tex](v)^{10} = 0.7082[/tex]
[tex](v) = \sqrt[10]{0.7082}[/tex]
v = 0.9661
Recall that:
[tex]v = \dfrac{1}{1+i}[/tex]
We can say that:
[tex]\dfrac{1}{1+i} = 0.9661[/tex]
[tex]1 = 0.9661(1+i) \\ \\ 0.9661 + 0.9661 i = 1 \\ \\ 0.9661 i = 1 - 0.9661 \\ \\ 0.9661 i = 0.0339 \\ \\ i = \dfrac{0.0339}{0.9661} \\ \\ i = 0.0351 \\ \\ \mathbf{i = 3.51\%}[/tex]
establish this identity
Answer:
see explanation
Step-by-step explanation:
Using the identities
tan x = [tex]\frac{sinx}{cosx}[/tex] , sin²x = 1 - cos²x
sin2x = 2sinxcosx
Consider left side
cosθ × sin2θ
= [tex]\frac{sin0}{cos0}[/tex] × 2sinθcosθ ( cancel cosθ )
= 2sin²θ
= 2(1 - cos²θ)
= 2 - 2cos²θ
= right side , then established
Which of the following numbers could not be used to describe a distance walked?
129 feet
12 feet
- 140 feet
|-125 feet
Answer:
-140 ft is not a distance
Step-by-step explanation:
Distance must be a positive number
-140 is negative
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a diameter of 10 feet and a height of 8 feet. Container B has
a diameter of 12 feet and a height of 6 feet. Container A is full of water and the water
is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the
pumping is complete?
Container A
play
Container B
10
d12
8
h6
O
Answer: Volume of Cylinder A is pi times the area of the base times the height
π r2 h = (3.1416)(4)(4)(15) = 753.98 ft3
Volume of Cylinder B is likewise pi times the area of the base times the height
π r2 h = (3.1416)(6)(6)(7) = 791.68 ft3
After pumping all of Cyl A into Cyl B
there will remain empty space in B 791.68 – 753.98 = 37.7 ft3
The percentage this empty space is
of the entire volume is 37.7 / 791.68 = 0.0476 which is 4.8% when rounded to the nearest tenth
.
Step-by-step explanation: I hope that help you.
Note: you may not need to type in the percent sign.
===========================================================
Explanation:
Let's find the volume of water in container A.
Use the cylinder volume formula to get
V = pi*r^2*h
V = pi*5^2*8
V = 200pi
The full capacity of tank A is 200pi cubic feet, and this is the amount of water in the tank since it's completely full.
We have 200pi cubic feet of water transfer to tank B. We'll keep this value in mind for later.
-----------------------
Now find the volume of cylinder B
V = pi*r^2*h
V = pi*6^2*6
V = 216pi
Despite being shorter, tank B can hold more water (since it's more wider).
-----------------------
Now divide the results of each section
(200pi)/(216pi) = 200/216 = 25/27 = 0.9259 = 92.59%
This shows us that 92.59% of tank B is 200pi cubic feet of water.
In other words, when all of tank A goes into tank B, we'll have tank B roughly 92.59% full.
This means the percentage of empty space (aka air) in tank B at this point is approximately 100% - 92.59% = 7.41%
Then finally, this value rounds to 7.4% when rounding to the nearest tenth of a percent.
A pharmaceutical company conducted an experiment to test a drug for managing morning sickness for school children. The
company enrolled students for the experiment in the age group of 10 to 15 and divided them into two groups. One group
received sugar pills and the other group received pills that have compounds to manage morning sickness. Which group
receives the placebo?
Answer:
In an experiment, one group receives a new antidepressant medication and the other group receives a sugar pill. the group receiving the new antidepressant medication is called the ________ group.
a. dependent
b. placebo
c. experimental
d. control.
Evaluating functions (pic attached)
f(x) = 2x³ - 3x² + 7
f(-1) = 2(-1)³ - 3(-1)² + 7
=> f(-1) = 2(-1) - 3(1) + 7
=> f(-1) = -2 -3 + 7
=> f(-1) = 2
f(1) = 2(1)³ - 3(1)² + 7
=> f(1) = 2(1) - 3(1) + 7
=> f(1) = 2 -3 + 7
=> f(1) = 6
f(2) = 2(2)³ - 3(2)² + 7
=> f(2) = 2(8) - 3(4) + 7
=> f(2) = 16 - 12 + 7
=> f(2) = 11
In the Fuel Economy Guide for 2018 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles. There are a number of outliers, mainly hybrid gas electric vehicles. If we ignore outliers, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.
Required:
a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?
b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?
Answer:
a) The probability is the p-value of [tex]Z = \frac{X - 22.6}{5.2}[/tex], in which X is the gas mileage of the 2020 Honda Civic.
b) Your dad's truck is 1.65 standard deviations below the mean.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.
This means that [tex]\mu = 22.6, \sigma = 5.2[/tex]
a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?
This is the p-value of Z, given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - 22.6}{5.2}[/tex]
In which X is the gas mileage of the 2020 Honda Civic.
b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?
This is Z when X = 14. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14 - 22.6}{5.2}[/tex]
[tex]Z = -1.65[/tex]
Your dad's truck is 1.65 standard deviations below the mean.
10v-6v=28
Simplify your answer as much as possible
Step-by-step explanation:
10v-6v=28
4v=28
v=28/4
v=7
Answer:
10v-6v=28
or, 4v = 28
or, v = 28/4
or, v = 7
hence 7 is the required value of v
A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answer:
67^2+76+2
that's my answer towards this question
convert 657 as binary form in computer language
Answer:
1010010001
Step-by-step explanation:
Keep dividing 657 by 2, and record the quotient and remainder
657
328,1
164,0
82,0
41,0
20,1
10,0
5,0
2,1
1,0
So chain the remainders from bottom up to get the binary number:
1010010001
Check:
1+16+128+512=657 checks.
"when reading a cd-rom disk 2.8 cm from its center the rotational speed is 726 rpm what is the rpm at 5.2cm
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Answer:
726 rpm
Step-by-step explanation:
The angular speed is not dependent upon the radius. The rotational speed is 726 rpm at any radius.
t^2 +11t+30/t^2+5t-24 ÷ t^2+4t-21/t^2+10t+25
Answer:
t^2 + 30t - 15/t^2 + 25
Step-by-step explanation:
If in 1 month you can make 6 carpets, how many days will it take for making 10 carpets?
Si en 1 mes puedes hacer 6 alfombras, ¿cuántos días se necesitarán para hacer 10 alfombras?
Step-by-step explanation:
6 carpets=1month
10 carpets=?
1month=31 days
10 /6*31
51
Step-by-step explanatio
the bath tap was left dripping at 18 :00. The water dripped out at a rate of 3 drops per minute. each drop contains 2ml of water. how much water had been lost by 06 :00 the next morning
The length of a rectangle is 4 in longer than its width.
If the perimeter of the rectangle is 32 in, find its area.
Answer:
60 sq in
Step-by-step explanation:
Perimeter = 2l + 2w
If l = w+4
Perimeter = 2(w+4) + 2w
Perimeter = 4w+8
32 = 4w + 8
24 = 4w
6 = w
If w = 6, l = 6+4 = 10
Area = l * w
Area = 10 * 6
Area = 60
2 squared plus b squared equal 256
Answer:
[tex]2^2+b=256[/tex]
b=252
Step-by-step explanation:
[tex]2^2+b=256[/tex]
4+b=256
b=252
I wasn't very sure about what you are asking, but I hope this helps!
1 1/5 + 17/2 - 3/2 Helppppp
Answer:
[tex]\frac{82}{10}[/tex]
Step-by-step explanation:
[tex]1\frac{1}{5} +\frac{17}{2} -\frac{3}{2}[/tex]
→ Convert the mixed number into an improper fraction
[tex]\frac{6}{5} +\frac{17}{2} -\frac{3}{2}[/tex]
→ Complete the takeaway operation
[tex]\frac{6}{5} +\frac{14}{2}[/tex]
→ Make the denominators the same
[tex]\frac{12}{10}+\frac{70}{10}[/tex]
→ Simplify
[tex]\frac{82}{10}[/tex]
Answer:
8.2
Step-by-step explanation:
I have 3 questionssss
∠A and ∠T are supplementary. Given m∠T = (7x+11)° and m∠A = (8x+19)°, what is m∠T?
The other two are in the pics attached! PLS!
Answer:
<T = 81
x = 10, angle = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
Step-by-step explanation:
Supplementary angles add to 180
(7x+11) + (8x+19) = 180
Combine like terms
15x + 30 = 180
Subtract 30 from each side
15x +30-30 = 180-30
15x= 150
Divide by 15
15x/15 = 150/15
x = 10
We want angle T
T = 7x+11 = 7(10)+11 = 70+11 = 81
The two angles add to 90
5x+10 + 30 = 90
Combine like terms
5x+40 = 90
5x+40-40 = 90-40
5x = 50
Divide by 5
5x/5 = 50/5
x=10
5x+10 = 5(10) +10 = 50+10 = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
Midpoint for
(-2,3) and (4,-1)
Midpiont=(_2+3\2), (4+_1/2)
=2/2,6/2
=1,3
How long will it take for a home improvement loan for 22,800to earn interest of 608.00at 8 %ordinary interest
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Answer:
120 days
Step-by-step explanation:
Using the formula for simple interest, we can solve for t:
I = Prt
t = I/(Pr) = 608/(22800×.08) = 608/1824 = 1/3 . . . . year
For "ordinary interest", a year is considered to be 360 days, so 1/3 year is ...
(1/3)(360 days) = 120 days
It will take 120 days for the loan to earn 608 in interest.
A subcommittee of six is to be selected from a committee containing 10 democrats and 12 republicans. In how many ways can at least 1 democracy be selected for the subcommittee?
Answer:
the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
Step-by-step explanation:
Given;
number of the subcommittee, = 6
number of democrats = 10
number of republicans, = 12
The number of ways to select at least 1 democrat in the subcommittee is calculated as follows;
Let D represent Democrats
let R represent Republicans
= (1D & 5R) or (2D & 4R) or (3D & 3R) or (4D & 2R) or (5D & 1R) or (6D)
= 10C₁ x 12C₅ + 10C₂ x 12C₄ + 10C₃ x 12C₃ + 10C₄ x 12C₂ + 10C₅ x 12C₁ + 10C₆
[tex]=( \frac{10!}{9!1!} \times \frac{12!}{7!5!} )+ (\frac{10!}{8!2!} \times \frac{12!}{8!4!})+ (\frac{10!}{7!3!} \times \frac{12!}{9!3!})+ (\frac{10!}{6!4!} \times \frac{12!}{10!2!})+ (\frac{10!}{5!5!} \times \frac{12!}{11!1!}) \\\\ +(\frac{10!}{4!6!})\\\\= (7,920) + (17,820) + (26,400) + (13,860)+ (3,276) + (210)\\\\= 69,486 \ ways[/tex]
Therefore, the number of ways to select at least 1 democrat in the subcommittee is 69,486 ways
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
