Answer:
The population of this country in 11 years will be 76972702.82
Step-by-step explanation:
The population of this country in 11 years can be calculated using the formula
Population in 11 years = Starting population x [tex](1+growth rate)^{period}[/tex]
Thus
Population in 11 years =50000000×[tex](1+0.04)^{11}[/tex] =76972702.82
The population of this country in 11 years will be 76.97 million.
In order to determine the population of a country in 11 years, this formula would be used:
FV = P (1 + r)^n
FV = Future value of the population = 50 million P = Present population R =rate of growth = 4% N = number of years = 1150 million x (1 + 0.04)^11
= 50 million x (1.04)^11
= 76.97 million
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On October 1, 2014, Hess Company places a new asset into service. The cost of the asset is $80,000 with an estimated 5-year life and $20,000 salvage value at the end of its useful life. What is the book value of the plant asset on the December 31, 2015, balance sheet assuming that Hess Company uses the double-declining-balance method of depreciation?
Answer:
$43,200
Step-by-step explanation:
Data provided in the question:
Cost of the asset = $80,000
Useful life of the machine = 5 years
Salvage value at the end of useful life = $20,000
Now,
Using the double declining method of depreciation
Annual depreciation rate = 2 × [1 ÷ useful life ]
= 2 × [ 1 ÷ 5 ]
= 2 × 0.2
= 0.4 or 40%
thus,
The depreciation from October 1, 2014 to December 31, 2014
= Annual Depreciation rate × duration × Book value for 2014
= 0.4 × 3 months × $80,000
= 0.4 × 0.25 year × $80,000
= $8,000
Book value for 2015
= Cost - depreciation till December 31, 2014
= $80,000 - $8,000
= $72,000
Therefore,
Depreciation for the year 2015
= Annual Depreciation rate × Book value for 2015
= 0.4 × $72,000
= $28,800
Therefore,
the book value of the plant asset on the December 31, 2015
= Book value for 2015 - Depreciation for the year 2015
= $72,000 - $28,800
= $43,200
If anyone knows this can you please help i have about an hour left to submit this (:
Find the area of a triangle with the given vertices.
Part I: Graph the following points on the coordinate grid below.
(1, -3), (3, -1), (5, -3)
Part II: Find the area of the triangle. Show your work.
Answer:
Part 1 : Figure show the graph of triangle
Part 2 : The area of triangle is 4 sqaure units
Step-by-step explanation:
Given points A(1, -3), B(3, -1) and C(5, -3) make triangle.
Part 1:
Figure show the graph of triangle with A(1, -3), B(3, -1) and C(5, -3) as vertices.
Part 2: Find the area of the triangle.
The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]
From figure, Take base as length of AC
Length of line is given by L=[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]
Now, Base = length of AC
Base =[tex]\sqrt{(X1-X2)^{2}+(Y1-Y2)^{2} }[/tex]
=[tex]\sqrt{(1-5)^{2}+((-3)-(-3))^{2}}[/tex]
=[tex]\sqrt{(-4)^{2}+(0)^{2}}[/tex]
=[tex]\sqrt{16}[/tex]
=4units
and Height as difference of y-component of point A and point B
Height = (y of component of point B)- (y of component of point A)
= (-1)- (-3)
= 2units
Therefore, The area of triangle is given by A=[tex]\frac{(Base)(height)}{2}[/tex]
A=[tex]\frac{(4)(2)}{2}[/tex]
A=4 sqaure units
Kyle says 3/5 is equal to 60%. Which statement explains Kyle is correct?
A) Kyle is correct because 3/5 is equivalent to 10/6 .
B) Kyle is correct because 3/5 is equivalent to 60/100 .
C) Kyle is incorrect because 3/5 is less than 1 and 60% is greater than 1.
D) Kyle is incorrect because 3/5 is not a whole number and 60 is a whole number.
Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.
Explanation:Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.
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Please answer this question correctly I need it today please show work
Answer:
1: C(n) = 2.50 + 16n
2: $66.50
Step-by-step explanation:
Part 1
Each ticket costs $16 per person. If tickets for n persons were purchased, the total cost would be 16n.
There is also a one-time service fee of $2.50 that must be paid. Thus, for n tickets the total cost is
C(n) = 2.50 + 16n
Part 2
For n = 4, the expression evaluates to
C(4) = 2.50 + 16 (4) = $66.50
Pattern A follows the rule "add 2" and Pattern B follows the rule "subtract 2." Pattern A: 1, 3, 5, 7, 9 Pattern B: 10, 8, 6, 4, 2 Which ordered pairs are formed from combining a term in Pattern A with its corresponding term in Pattern B? Select all correct answers. A (1, 3) B (1, 10) C (3, 6) D (5, 4) E (5, 6) F (7, 4)
Answer:
B, E, F
Step-by-step explanation:
Simply write the terms out and match them.
Final answer:
The correct ordered pairs formed from combining a term in Pattern A with its corresponding term in Pattern B are:
(1, 10), (5, 6), and (7, 4), which are Options B, E, and F, respectively.
Explanation:
The question involves creating ordered pairs from two different number patterns, Pattern A and Pattern B. To find the correct ordered pairs, we match each term in Pattern A with its corresponding term in Pattern B.
Pattern A: 1, 3, 5, 7, 9Pattern B: 10, 8, 6, 4, 2To identify the corresponding terms, we look at the positions: the first term in Pattern A pairs with the first in Pattern B, the second with the second, and so on. Here are the resulting pairs:
(1, 10)(3, 8)(5, 6)(7, 4)(9, 2)Based on the above matching, we evaluate the given options:
Option A: (1, 3) - Incorrect because the first term from Pattern A should be paired with the first term from Pattern B, which is 10.Option B: (1, 10) - Correct as it matches the first term in Pattern A with the first term in Pattern B.Option C: (3, 6) - Incorrect because the second term in Pattern A is 3, but the corresponding second term in Pattern B is 8, not 6.Option D: (5, 4) - Incorrect because the third term in Pattern A is 5, and the corresponding third term in Pattern B is 6, not 4.Option E: (5, 6) - Correct as it matches the third term in Pattern A with the third term in Pattern B.Option F: (7, 4) - Correct as it matches the fourth term in Pattern A with the fourth term in Pattern B.Therefore, the correct ordered pairs when combining a term from Pattern A with its corresponding term from Pattern B are Option B, Option E, and Option F.
An electric sale gives a reading equal to the true weight plus a random error that isnormally distributed with mean 0 and standard deviationσ=.1 mg. Suppose that the results of fivesuccessive weightings of the same object are as follows:_______ 3.142, 3.163, 3.155, 3.150, 3.141.(a) Determine a 95 percent confidence interval estimate of the true weight.
(b) Determine a 99 percent confidence interval estimate of the true weight.
Answer:
a) 95% confidence interval estimate of the true weight is (3.026, 3.274)
b) 99% confidence interval estimate of the true weight is (2.944, 3.356)
Step-by-step explanation:
Confidence Interval can be calculated using M±ME where
M is the mean of five successive weightings (3.150)ME is the margin of error from the meanAnd margin of error (ME) can be calculated using the formula
ME=[tex]\frac{t*s}{\sqrt{N} }[/tex] where
t is the corresponding statistic in the given confidence level and degrees of freedom(t-score) s is the standard deviation of the random error (0.1)N is the sample size (5)Using the numbers 95% confidence interval estimate of the true weight is:
3.150±[tex]\frac{2.776*0.1}{\sqrt{5} }[/tex]≈3.150±0.124
And 99% confidence interval estimate of the true weight is:
3.150±[tex]\frac{4.604*0.1}{\sqrt{5} }[/tex]≈3.150±0.206
An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3
Answer:
easey
Step-by-step explanation:
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region, Decision to Reject (RH0) or Failure to Reject (FRH0)]
A. [ z < -1.65, RHo]
B. [ z < -1.65 and z > 1.65, FRHo
C. [z > 1.65, FRHo]
D. [z < -1.65 and z > 1.65, FRHo]
E. [z > -1.65 and z < 1.65, RHo]
F. None of the above
One of the roots of the equation 2x^2−bx−20=0 is −2.5. Find the other root
Answer:
The answer to your question is x = 4
Step-by-step explanation:
2x² - bx - 20 = 0
One root is -2.5
Process
Get the value of the equation when x = -2.5
2(-2.5)² - b(-2.5) - 20 = 0
2(6.25) + 2.5b - 20 = 0
12.5 + 2.5b - 20 = 0
2.5b = 20 - 12.5
2.5b = 7.5
b = 7.5 / 2.5
b = 3
Then
2x² - 3x - 20 = 0
Factor the polynomial
2 x -20 = -40
2x² -8x + 5x - 20 = 0
2x(x - 4) + 5(x - 4) = 0
(x - 4)(2x + 5) = 0
x₁ - 4 = 0 2x₂ + 5 = 0
x₁ = 4 x₂ = -5/2
x₂ = -2.5
Answer:
The "other" or "second" root is 4.
Step-by-step explanation:
We are told that -2.5 is a root of the equation. The coefficient b of the x term is unknown, and must be determined. Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.
Setting up synthetic division, we arrive at:
-2.5 / 2 -b -20
-5 +12.5 + 2.5b
-------------------------------------
2 -5-b -7.5 + 2.5b
The remainer, -7.5 + 2.5b, must be zero (0). Thus, 2.5b = 7.5, and b = 3.
Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.
The other factor is 2x - 8, which, if set equal to 0, yields x = 4. This is the "other root."
Abigail is making flower bouquets. She has 16 roses and 20 carnations. She wants to make identical bouquets and use all the flowers.What is the greatest number of bouquets she can make?
Answer:
four bouquets
Step-by-step explanation:
The way of solving this problem is tell Abigail to keep the relation between flowers constant, that is
We have 16 roses and 20 carnations
16 2 16 = 2⁴ 20 2 20 = 2² * 5
8 2 10 2
4 2 5 5
2 2 1
1
So we will make bouquets of 4 roses and 5 carnations
so we will have 4 bouquets using all flowers
Help those 3 multiple choice questions correctly and show work please I need it today
A municipality wanting to use integrated waste management methodologies for its citizens would do all of the following EXCEPT: A. pay for each individual's tipping fees at landfills with taxes B. offer curbside recycling to its residents C. attract businesses that utilize source reduction in their manufacturing processes D. offer mulch to its residents at no cost E. maintain a hazardous waste collection site for its residents
Answer:
A. pay for each individuals tipping fee at landfills with taxes
Step-by-step explanation:
Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a municipality wanting to waste management so Curbside recycling can be used.
Municipal should attract business that utilize source reduction in their manufacturing.
They should offer much to its resident.
They maintain a hazardous waste collection site for its residents as well.
A stone is thrown straight up from the edge of a roof, 775 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is −32ft/sec2, how high is the stone 4 seconds later?
Final answer:
The stone is approximately 583 feet high 4 seconds later.
Explanation:
To find the height of the stone 4 seconds later, we can use the equation of motion for an object in free fall:
h = h0 + v0t + (1/2)gt^2
Where:
h = height at time t
h0 = initial height
v0 = initial velocity
g = acceleration due to gravity
t = time
Substituting the given values:
h = 775 + 16(4) + (1/2)(-32)(4)^2
h = 775 + 64 - 256
h = 583 feet
Therefore, the stone is approximately 583 feet high 4 seconds later.
The equation d=11cos(8pi/5 t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. According to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? Assume that right of center is a positive distance and left of center is a negative distance. A. 0.625 seconds B. 0.8 seconds C. 1.25 seconds D. 1.6 seconds
Answer:
The time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Step-by-step explanation:
Given the equation
[tex]d = 11cos( \frac{8\pi}{5}*t)[/tex]-----------Equation 1
where d, in inches of the pendulum of a grandfather clock from the center.
Comparing with the standard equation of an oscillating pendulum bob.
[tex]d = Acos (wt + \alpha )[/tex] ----------Equation 2
where ω = angular velocity
t = time taken
α = The angular displacement when t = 0
Comparing equation 1 and 2,
α = 0
[tex]w =\frac{8\pi }{5}[/tex]
Recall that [tex]w = 2\pi f
Therefore,
[tex]2\pi f = \frac{8\pi }{5} \\\\f = \frac{4}{5}[/tex][/tex]
f = 0.8 Hertz
Recall that [tex]f = \frac{1}{T}[/tex]
[tex]T = \frac{1}{0.8}[/tex]
T = 1.25 seconds
Therefore, the time it takes for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
A truck costs $16,000 with a residual value of $1,000. It has an estimated useful
life of five years. If the truck was bought on July 3, what would be the book
value at the end of year 1 using straight-line rate?
A. $1,500
B. $16,000
C. $12,500
D. $14,500
Answer:
Option D.
Step-by-step explanation:
Cost of truck = $16000
Residual value after 5 years = $1000
Depreciated value of a truck in 5 year is
[tex]Depreciation=16000-1000=15000[/tex]
In straight-line method, the value of a fixed asset depreciate by a constant rate.
Since depreciation of truck in 5 years is $15000, therefore, the depression of one year is
1 year Depreciation = [tex]\dfrac{15000}{5}=3000[/tex]
From July 3 to end of fist year = 1/2 year
1/2 year Depreciation = [tex]\dfrac{3000}{5}=1500[/tex]
So, the value at the end of year 1 using straight-line rate is
[tex]Value=16000-1500=14,500[/tex]
Therefore, the correct option is D.
Choose the word or phrase that completes each sentence. helps businesses allocate resources for their best and most productive uses. The more a resource, the more costly it will be. A manufacturer that requires scarce and costly resources is likely to charge for its products.
Answer:
1. Value helps businesses allocate resources for their best and most productive uses.
2. The more Scarce a resource, the more costly it will be.
3. A manufacturer that requires scarce and costly resources is likely to charge more for its products.
Step-by-step explanation:
Given:
Three sentences are given we need to add a word or phrase to complete it
First Sentence:
helps businesses allocate resources for their best and most productive uses.
It the above sentence Value will be the word which will complete the sentence because when a resource is valued for his work he provides his best in his work and can be assured as productive too.
Hence we can say,
Value helps businesses allocate resources for their best and most productive uses.
Second Sentence:
The more a resource, the more costly it will be.
It the above sentence Scarce will be the word which will complete the sentence because Scarce Resource always considered to be more costly.
Hence we can say;
The more Scarce a resource, the more costly it will be.
Third Sentence.
A manufacturer that requires scarce and costly resources is likely to charge for its products.
It the above sentence more will be the word which will complete the sentence because A manufacture who has Scarce and costly resource is said to have less production and hence its product would be more costly too.
Hence we can say;
A manufacturer that requires scarce and costly resources is likely to charge more for its products.
Answer: Value, scarce , more
Step-by-step explanation:
those are correct
The radius of a spherical is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5cm.
The rate of change of the volume of a ball when the radius is 5cm is -300π cubic centimeters per second.
Explanation:To find the rate of change of the volume of a ball, we can use the formula for the volume of a sphere, which is V = (4/3)πR³. We are given that the radius is decreasing at a constant rate of 3 cm per second. So, the rate of change of the volume can be found using the derivative of the volume function with respect to time.
First, we differentiate the volume function with respect to time:
dV/dt = (4/3)π×3R²×(-3)
dV/dt = -12πR²
Then we substitute the given value of the radius when it is 5 cm:
dV/dt = -12π×5²
dV/dt = -12π×25
dV/dt = -300π
Therefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic centimeters per second.
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A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.
Answer:
Part a) [tex]120\pi\ \frac{rad}{min}[/tex]
Part b) [tex]960\pi\ \frac{in}{min}[/tex]
Step-by-step explanation:
we have
60 rev/min
Part a) Find the angular speed in radians per minute
we know that
One revolution represent 2π radians (complete circle)
so
[tex]1\ rev=2\pi \ rad[/tex]
To convert rev to rad, multiply by 2π
[tex]60\ \frac{rev}{min}=60(2\pi)=120\pi\ \frac{rad}{min}[/tex]
Part b) Find the linear speed in inches per minute
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=8\ in[/tex] ----> given problem
substitute
[tex]C=2\pi(8)[/tex]
[tex]C=16\pi\ in[/tex]
Remember that
One revolution subtends a length equal to the circumference of the circle
so
[tex]1\ rev=16\pi\ in[/tex]
To convert rev to in, multiply by 16π
[tex]60\ \frac{rev}{min}=60(16\pi)=960\pi\ \frac{in}{min}[/tex]
Final answer:
The angular speed of the pulley is 120π radians per minute, and the linear speed is 960π inches per minute.
Explanation:
The question pertains to angular and linear speeds related to circular motion. Given that a belt runs a pulley with a radius of 8 inches at 60 revolutions per minute (rpm), we are tasked with finding both the angular speed in radians per minute and the linear speed in inches per minute.
Calculating the Angular Speed
The angular speed (ω) in radians per minute can be calculated using the formula ω = 2π×rpm, where rpm is the number of revolutions per minute and 2π radians is the equivalent of one full revolution.
ω = 2π × 60 = 120π radians/minute
Calculating the Linear Speed
The linear speed (v) can be determined from the radius (r) and angular speed (ω) using the formula v = r×ω. The radius of the pulley is 8 inches, so:
v = 8 inches × 120π radians/minute = 960π inches/minute
The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠A:
∠A = ∠B
6x + 12 = 3x + 63
6x - 3x = 63 - 12
3x = 51
x = 51 ÷ 3
x = 17
6(17) + 12
102 + 12
∠A = 114°
Answer:
114
Step-by-step explanation:
The total surface of the cuboid is 112cm2 find the value of x bottom length 10cm side bottom length 2cm, id prefer just an answer as im about to get an hour detention, thank you
Answer:
The value of x is 3 cm.
Step-by-step explanation:
Given,
Total surface area of cuboid = 112 cm^2
Height of cuboid = 10 cm
Breadth of cuboid = 2 cm
Length of cuboid = x cm
Solution,
Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]
∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]
Thus the length of cuboid is 3 cm.
How does the graph of g(x) = (x − 1)3 + 5 compare to the parent function f(x) = x3?
g(x) is shifted 1 unit to the right and 5 units up.
g(x) is shifted 5 units to the right and 1 unit up.
g(x) is shifted 1 unit to the left and 5 units up.
g(x) is shifted 5 units to the right and 1 unit down.
Answer:
A
Step-by-step explanation:
Given:
- The original function is:
f(x) = x^3
Find:
How does the graph of g(x) = (x − 1)3 + 5 compare to the original function.
Solution:
- We have a general form of the new function relating to parent function.
g(x) = a*( x +/- b )^n + c
Where; a, b and c are constants.
- The constant a magnitude denotes steepness of the graph relative to 1 and the sign of a will determine the mirror image of the graph about line y = 0.
- The constant b magnitude denotes shifts of the graph of every x value sign of b will determine the direction of shifts. + b : shift left , - b shift right.
- The constant c magnitude denotes shifts of the graph of every y value. sign of c will determine the direction of shifts. + c : shift up , - b shift down.
- In our g(x). a = 1 , b = -1 , c = + 5
Hence, g(x) is shifted 1 unit to the right and 5 units up.
The graph of g(x) = (x - 1)^3 + 5 is shifted 1 unit to the right and 5 units up compared to the parent function f(x) = x^3.
Explanation:The graph of g(x) = (x - 1)3 + 5 is obtained by shifting the graph of f(x) = x3 one unit to the right and five units up. Shifting a function horizontally is done by replacing x with (x - h), where h is the amount of units you want to shift.
In this case, g(x) = (x - 1)3 + 5 is equivalent to f(x - 1) + 5. So the graph is shifted 1 unit to the right. Shifting a function vertically is done by replacing f(x) with f(x) + k, where k is the amount of units you want to shift.
Since f(x - 1) + 5 is obtained by shifting f(x) one unit to the right and five units up, the correct answer is: g(x) is shifted 1 unit to the right and 5 units up.
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Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:
Select one:
a. -2.101
b. -1.980
c. -1.960
d. -1.728
Answer:
lyrics d - 1.782
Step-by-step explanation:
Assume Normal Distribution
we have μ₀ = 40 (from Dullco claims)
And from sample μ = 37.8 and standard deviation of 5.4
random sample n = 18
We have to use t-student for testing the hypothesis
and we have a one tail test (left) since Dullco claims : " at least" meaning (always bigger or at least ) not different.
Then
t (s) =( μ - μ₀) / (σ/√n) ⇒ t (s) = [(37.8 - 40 )* √18 ]/5.4
t (s) = - 1.7284
Using the t-distribution, as we have the standard deviation for the sample, it is found that the test statistic is given by:
d. -1.728
What are the hypothesis tested?At the null hypothesis, it is tested if the batteries last at least 40 hours, that is:
[tex]H_0: \mu \geq 40[/tex]
At the alternative hypothesis, it is tested if they last less than 40 hours, that is:
[tex]H_1: \mu < 40[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the parameters are given by:
[tex]\overline{x} = 37.8, \mu = 40, s = 5.4, n = 18[/tex]
Hence:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{37.8 - 40}{\frac{5.4}{\sqrt{18}}}[/tex]
[tex]t = -1.728[/tex]
Hence option d is correct.
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Enter the equation of the parabola in vertex form that has its vertex at (4,–13) and passes through the point (6,–5).
Answer:
Step-by-step explanation:
If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is
[tex]y=a(x-h)^2+k[/tex]
We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:
[tex]-5=a(6-4)^2-13[/tex] which simplifies to
-5 = 4a - 13 and
8 = 4a so
a = 2
That means that the paraobola in vertex form is
[tex]y=2(x-4)^2-13[/tex]
A model rocket has upward velocity v(t) = 10t2 ft/s, t seconds after launch. Use the interval [0, 6] with n = 6 and equal subintervals to compute the following approximations of the distance the rocket traveled. (Round your answers to two decimal places.
(a) Left-hand sum = _____ ft
(b) Right-hand sum = _____ ft
(c) average of the two sums = ______ ft
Answer:
a)550
b)910
c)730
Step-by-step explanation:
The given model is
[tex]v(t) = 10t^2 ft/s[/tex]
Use the interval [0,6], with n=6 rectangles
Then, the interval width is
[tex]\Delta t = \frac{b-a}{n}[/tex]
[tex]\Delta t = \frac{6-0}{6}[/tex]= 1
so, the sub intervals are
[0,1], [1,2], [2,3], [3,4],[4,5],[5,6]
Now evaluating the function values
[tex]f(t_0)= f(0) = 0[/tex]
[tex]f(t_1)= f(1) = 10[/tex]
[tex]f(t_2)= f(2) = 40[/tex]
[tex]f(t_3)= f(3) = 90[/tex]
[tex]f(t_4)= f(4) = 160[/tex]
[tex]f(t_5)= f(5) = 250[/tex]
[tex]f(t_6)= f(6) = 360[/tex]
a) left hand sum is
L_6 = [tex]\Delta t [f(t_0)+ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)][/tex]
=[tex]1 [0+ 10+40+90+160+250][/tex]
= 550
b) right hand sum
R_6 = [tex]\Delta t [ f(t_1)+f(t_2)+f(t_3)+f(t_4)+f(t_5)+f(t_6)][/tex]
= [tex]1 [10+40+90+160+250+360][/tex]
= 910
c) average of two sums is
[tex]\frac{L_5+R_5}{2}[/tex]
= [tex]\frac{550+910}{2}[/tex]
=730
Which point lies on the graph of the line? (5, 8) (1, 6) (–3, 3) (–4, 2)
Answer:
the answer is (-4,2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is (-4,2)
If the coefficient of determination is a positive value, then the regression equation a. must have a negative slope b. must have a positive slope c. could have either a positive or a negative slope d. must have a positive y intercept
If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.
Explanation:If the coefficient of determination is a positive value, then the regression equation could have either a positive or a negative slope.
The coefficient of determination, denoted as r², is equal to the square of the correlation coefficient, r. It represents the percentage of variation in the dependent variable, y, that can be explained by variation in the independent variable, x, using the regression line. When r² is positive, it indicates a positive relationship between x and y, but it does not specify the direction of the slope.
Therefore, if the coefficient of determination is positive, the regression equation could have either a positive or a negative slope.
How much is a $26,000 automobile car worth after 1 year if the depreciation is 15% per year
Answer:
The worth of the automobile after an year with 15% depreciation is $22,100.
Step-by-step explanation:
The current cost of the automobile car = $26,000
The percentage of depreciation = 15%
Now, calculating the depreciated amount:
15% of $26,000 = [tex]\frac{15}{100} \times 26,000 = 3,900[/tex]
So, the depreciated amount of the car in the next year = $3,900.
Now, the worth of the car after an year
= CURRENT WORTH - THE DEPRECIATED AMOUNT
= $26,000 - $3,900.
= $22,100
Hence, the worth of the automobile after an year is $22,100.
According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected.
(a) What is the probability that 11 or more are serving time for drug dealing? (Round your answer to three decimal places.)
(b) What is the probability that 2 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)
(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)
Answer:
a)[tex]P(X\geq 11) = 0.198[/tex]
b)[tex]P(X\leq 2) = 0.000565[/tex]
c) Mean = 8.8
Step-by-step explanation:
1) Previous concepts
Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".
The Binomial distribution is a type of Bernoulli experiment with following properties:
a)There are two possible outcomes; success or failure.
b) Outcomes are independent on preceding result of a trial.
c) The probability of success remains constant throughout the experiment.
d)The number of successes are fixed.
The probability mass function for the Binomial distribution is given by:
[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]
Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.
[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing
[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing
[tex]n=16[/tex] random sample selected
2) Part a
The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]
On this case we want the following probability, and since says greater or equal than 11 we can express like this:
[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]
[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]
[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]
[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]
[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]
[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]
[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]
[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]
3) Part b
[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]
[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]
[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]
[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]
[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]
4) Part c
The expected value for the binomial distribution is given by the following formula:
[tex] E(X)=np=16*0.55=8.8[/tex]
So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.
Mrs. Andretti is having new drapes made for her living room. The cost of the fabric is $15 per yard. The fee to make and hang the drapes is $250. She uses the expression 15x + 250 to calculate the total cost of the drapes. Mrs. Andretti states that x represents the total cost of the fabric. Is she correct?
Answer: No
Step-by-step explanation:
X does not represent the cost of fabric. X represents the number of yards of fabric used.
15x + 250
Could be read as ($15 × # of yards) + $250
So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.
She could use an additional variable to represent the cost of fabric.
Example: Y
Y= 15x
Cost of fabric is equal to $15 per yard × # of yards.
The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.
C = 50 + 20x
Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of A after both reflections?
(-2, -7) (-2, 7) (7, -2) (7, 2)
Answer:
option C) (7, -2)
Step-by-step explanation:
By the graph, the initial coordinates of point A are ( -5, -4)
first reflection along the line x=1, only the x coordinate will change.
the new x coordinate is = x = 7
thus the point becomes (7, -4)
similarly, reflection along y= -3, only the y coordinate will change.
the new y coordinate is = y = -2
thus the final coordinates are (7, -2)