Answer:
1. 75 feet
2. 27 seconds
Step-by-step explanation:
1. If six seconds is equal to 10 feet that means that 42 seconds is equal to 70 feet (6 X 7 = 42) It also means that 3 seconds is equal to 5 feet. (42 + 3 = 45)
2. If 6 seconds is 10 feet, then 6 X 4 is 40 feet (24) And since 5 feet is equal to 3 seconds then we get 24 + 3 = 27
Use the figure below to complete the following problem.
Given:
ZH=2x+60
LT=x+30
HALT is a
H
2T=
1. 30
2. 60
3. 90
Answer:
Step-by-step explanation:
ascxne rdsjazs bcbnnnncccd
Solve the differential equation
[tex]y {}^{(5)} -4y {}^{(4)} +4y'''-y''+4y'-4y=69[/tex]
The given differential equation has characteristic equation
[tex]r^5 - 4r^4 + 4r^3 - r^2 + 4r - 4 = 0[/tex]
Solve for the roots [tex]r[/tex].
[tex]r^3 (r^2 - 4r + 4) - (r^2 - 4r + 4) = 0[/tex]
[tex](r^3 - 1) (r^2 - 4r + 4) = 0[/tex]
[tex](r^3 - 1) (r - 2)^2 = 0[/tex]
[tex]r^3 - 1 = 0 \text{ or } (r-2)^2=0[/tex]
The first case has the three cubic roots of 1 as its roots,
[tex]r^3 = 1 = 1e^{i0} \implies r = 1^{1/3} e^{i(0+2\pi k)/3} \text{ for } k\in\{0,1,2\} \\\\ \implies r = 1e^{i0} = 1 \text{ or } r = 1e^{i2\pi/3} = -\dfrac{1+i\sqrt3}2 \text{ or } r = 1e^{i4\pi/3} = -\dfrac{1-i\sqrt3}2[/tex]
while the other case has a repeated root of
[tex](r-2)^2 = 0 \implies r = 2[/tex]
Hence the characteristic solution to the ODE is
[tex]y_c = C_1 e^x + C_2 e^{-(1+i\sqrt3)/2\,x} + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
Using Euler's identity
[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]
we can reduce the complex exponential terms to
[tex]e^{-(1\pm i\sqrt3)/2\,x} = e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) \pm i \sin\left(\dfrac{\sqrt3}2x\right)\right)[/tex]
and thus simplify [tex]y_c[/tex] to
[tex]y_c = C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
For the non-homogeneous ODE, consider the constant particular solution
[tex]y_p = A[/tex]
whose derivatives all vanish. Substituting this into the ODE gives
[tex]-4A = 69 \implies A = -\dfrac{69}4[/tex]
and so the general solution to the ODE is
[tex]y = -\dfrac{69}4 + C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}[/tex]
what is the range if the given function?
Answer:
Second option
Step-by-step explanation:
The range is the set of output values a function can take. As shown in the table, as x is substituted in, y is the corresponding value.
Asap I need a answer please
Answer:
-4
Step-by-step explanation:
in order to get from -6 to 24, you need to multiply x by -4 since -6* -4 is 24
Nine and one-half less than four and one-half times a number is greater than 62.5. Which of the following represents the solution set of this problem?
A (16,+infinity)
B (-16,+infinity)
C (-infinity, 16)
D (-infinity,-16)
The solution set that represent the solution to the inequality is (16,+infinity)
Solving linear equationThe mathematical representation of the statement given is expressed as shown below;
4 1/2 x - 9 1/2 >62.5
Convert to improper fraction to have:
9/2 x - 19/2 > 62.5
Find the LCM
9x-19/2 > 62.5
9x-19 > 125
9x > 125 + 19
9x > 144
x > 16
Hence the solution set that represent the solution to the inequality is (16,+infinity)
Learn more on inequality here: https://brainly.com/question/11613554
#SPJ1
The measure of the second angle of a triangle is twice as large as the measure of the first measure of the third angle is 30° less than the sum of the measures of the other two angles find measure of each angle
Applying the triangle sum theorem, we have:
First angle measure = 35°
Second angle = 70°
Third angle = 75°
What is the Triangle Sum Theorem?According to the triangle sum theorem, all angles in a triangle will give a sum of 180 degrees.
First angle measure = x
Second angle = 2x
Third angle = (2x + x) - 30 = 3x - 30
x + 2x + 3x - 30 = 180 [triangle sum theorem]
6x - 30 = 180
6x = 180 + 30
6x = 210
x = 210/6
x = 35
First angle measure = x = 35°
Second angle = 2x = 2(35) = 70°
Third angle = 3x - 30 = 3(35) - 30 = 75°
Learn more about the triangle sum theorem on:
https://brainly.com/question/7696843
#SPJ1
10-A biased die is thrown thirty times and the number of sixes seen is eight. ( The probability of face six is 8 = 4 ) If the die is thrown a further twelve times find:
30 15
(a) the probability that a six will occur exactly twice; (b) the expected number of sixes: () = ;
(c) the variance of the number of sixes.
Using the binomial distribution, we have that:
a) There is a 0.2111 = 21.11% probability that a six will occur exactly twice.
b) The expected number of sixes is of 3.2.
c) The variance of the number of sixes is of 2.35.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the parameters are given by:
p = 8/30 = 0.2667, n = 12.
Item a:
The probability is P(X = 2), hence;
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2667)^{2}.(1-0.2667)^{10} = 0.2111[/tex]
Item b:
The expected number of the binomial distribution is:
E(X) = np.
Hence:
E(X) = 12 x 8/30 = 3.2.
Item c:
The variance of the binomial distribution is:
V(X) = np(1-p).
Hence:
E(X) = 12 x 8/30 x 22/30 = 2.35.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
#SPJ1
Question 15 of 15
Convert 1,056 yards into miles. Round your answer to the nearest tenth.
Hint. There are 1,760 yards in a mile.
A. 150 miles
O B. 1.6 miles
O C. 0.6 miles
SUBMIT
Answer:
0.6
Step-by-step explanation:
Given what we know, we can set up a proportion to convert 1,056 yards into miles
[tex]\frac{1760 yd}{1mi} =\frac{1056 yd}{x mi} \\\\1760x=1056\\\\x=0.6[/tex]
23 1/2% as a mixed decimal (as a percent)
Answer: 23,5%
Step-by-step explanation:
[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%
In the figure above, if l is a line, a+b=120 and b+c=100, then what is the value of b?
Based on the angles of a + b and b + c, the value of b can be calculated to be 40°.
How many degrees is B?As this is a triangle, all the internal angles must add up to 180°.
This means that:
a + b + c = 180°
As we have the value of b + c, this becomes:
a + 100 = 180
a = 80°
b is therefore:
a + b = 120
80 + b = 120
b = 120 - 80
= 40 °
Full question is:
If in triangle abc, angle a + angle b= 120° and angle b + angle c = 100°, then find angle b.
Find out more on the internal degrees of a triangle at https://brainly.com/question/7888180.
#SPJ1
Sam has purchased collision insurance with a $100-deductible clause, and automobile medical payments insurance in the amount of $500. In an accident in which Sam is at fault, Sam incurs injuries for a total expense of $650. Also, $1,400 worth of damage is done to Sam's car. How much does the insurance company pay Sam? Benefit payment?
The amount that the insurance company will pay is $1800.
How to illustrate the information?It should be noted that the insurance company will pay John for the expenses of his injuries and repair of the car.
For the injury, he will get:
= $500 + ($1400 - $100)
= $500 + $2300
= $1800
Therefore, the amount is $1800.
Learn more about insurance on:
brainly.com/question/2141892
#SPJ1
What do l do??? Need help
Answer:
you have to put the formula of perimeter
Answer:
12a. L+8m + 14m
12b. 10m+8m +14m
12c. 66
12d.420m
12e.252m
quick questions
volume= 288cm cubed
Which is the graph of the function f(x)= - squared x
Answer:
top left graph
Step-by-step explanation:
The function is not defined for negative x.
Eliminate top middle and top rightAlso, the range should not include positive numbers.
Eliminate bottom left.So, the answer is the top left graph.
A family has two cars. The first car has a fuel efficiency of miles 15 per gallon of gas and the second has a fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 975 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the first car consumption and y represent the second car consumption, hence:
x + y = 55 (1)
Also:
15x + 20y = 975 (2)
From both equations:
x = 25, y = 30
The first car consumed 25 gallons of fuel while the second car consumed 30 gallons of fuel.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
pls helpppp a gurllll outtttt : )))))))))
Answer:
2
Step-by-step explanation:
[tex]\frac{3[2(-2)-6] + (-2)^{2} +4[2(-2)+1]}{3[(-2)-5]+2}[/tex]
[tex]\frac{3(-10) - 4 + 4(-3)}{-16}[/tex]
[tex]\frac{-30-4-12}{-16}[/tex]
[tex]\frac{-46}{-16}[/tex]
okay you know what i dont know what im doing but i know the answer is for sure 2..
Find the integral
∫(cos(1/x)) /x^2 dx
Answer:
Step-by-step explanation:
∫(cos(1/x)/x² dx
[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]
What is the area of a desktop that is 2 1/2 feet by 5 feet?
The area of the desktop is 12. 5 feet square
How to determine the area
The formula for area of a rectangle;
Area = length × width
Length = 2. 5 feet
Width = 5 feet
Area = 2. 5 × 5
Area = 12. 5 feet square
Thus, the area of the desktop is 12. 5 feet square
Learn more about area of a rectangle here:
https://brainly.com/question/14137384
#SPJ1
A study showed that low intenstisy vibration therapy reduce pain levels in patients with fibromyalgia. During each session in the study, vibration pads were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session. Another study is being design to examine whether low intensity vibration therapy also reduces pain in patients suffering from ruptured disks at the lumbar region of the back. Three hundred male patients are subjects the new study. Part A: What is an appropriate design for the new study? Include treatments used, method of. treatment assignment, and variables that should be measure
Part b: if the study consists of 150 male and 150 female patients instead of 300 male patients would you change the study design if so, how would you modify your design? if not, why not?
Part c: could your design be double blind
Answer:
I didn't got the question well
Need an detailed step by step answer and solution again
Answer:
12u²
Step-by-step explanation:
area of a regular quadrilateral is always base x vertical height.
the base here is clearly 4 (just count the squares)
draw an imaginary line connecting the bottom right corner to the line before the top right corner (the line should be vertical)
count the squares here too and you get 3.
so the area = 3 x 4,
the area is 12u²
Solve equation 1102 Base 3= 212 Base n
Answer: 4
Step-by-step explanation:
[tex]1102_{3}=2+0(3)+1(9)+1(27)=38\\\\212_{n}=2+1(n)+2(n^2)=2n^2 + n+2\\\\\implies 2n^2 + n+2=38\\\\2n^2 + n-36=0\\\\(n-4)(2n+9)=0\\\\n=-\frac{9}{2}, 4[/tex]
However, as the base must be positive, n=4.
An international company has 21,700 employees in one country. If this represents 17.7% of the company's employees, how many employees does
it have in total?
Round your answer to the nearest whole number.
Answer:
122,599
Step-by-step explanation:
In words, what I am is asking is 17.7% of what number is 21,700. I will need to change 17.7% to a decimal. To do that, I move the decimal 2 places to the left. Then solve.
.177 x w = 21700 Divide both sides by .177
w = 122,599
Refer to your course materials to answer the following questions regarding " energy vampires ":
help (energyvampires)
a) How much electricity is used, on average, by a security system in 2 years?
Express your answer rounded to the nearest hundredth of a kilowatt-hour.
kW-hr
b) How much carbon dioxide is emitted into the atmosphere to produce this electricity?
Express your answer rounded to the nearest tenth of a pound of carbon dioxide.
lb of CO2
The electricity that is used, on average, by a security system in 2 years is 4.3Kw.
How to illustrate the information?The average power consumption of the security system given is 2.7 watt.
(a) Electricity consumption in 2 years
in KW-h = (24*365*2.7)/1000 = 4.304 KWh
(b) As per US data CO2 emissions = 0.99 pound per kilowatt-h.
Hence here CO2 emissions = 4.3 × 0.99 = 4.2610 pounds / KW-h.
= 4.3 pound / KW-h.
Learn more about electricity on:
https://brainly.com/question/776932
#SPJ1
Use two formulas for volume to find the volume of the figure. Express the volume in terms of 3.14 and than round to the nearest whole number. Note that the figure may not be drawn to scale
The volume of the figure to the nearest whole number = 756π m³.
How to estimate the volume of the given figure?The figure shown exists composed of a cone and a cylinder.
The volume of the figure = volume of cone + volume of the cylinder
Height of cone = 12 - 8 = 4
Radius (r) of cone = 18/2 = 9 m
The volume of the cone V = 1/3hπr²
= 1/3 [tex]*[/tex] 4π [tex]*[/tex] 9² = 108π
The volume of the Cylinder = πr²h
radius (r) = 18/2 = 9 m
height (h) = 8 m
Volume of cylinder = π [tex]*[/tex] 9² [tex]*[/tex] 8 = 648π m³
Volume of the figure = 108π + 648π = 756π
The volume of the figure to the nearest whole number = 756π m³.
To learn more about volume refer to:
https://brainly.com/question/18959925
#SPJ9
please help I've been trying to figure it out but I can't
answer : 2 1/2
divide y by x
divide 2 1/2 by 1
its 2 1/2
10 divided by 4 is also
2 1/2
17 1/2 divided by 7 is also
2 1/2
The average weight of the passengers of an airline has increased from 150 pounds in 2000 to 170 pounds in 2010. If an airline used to transport 270 passengers in a plane in 2000, and the total passenger weight is fixed, approximately how many passengers can travel with the same plane in 2010?
There are 238 passengers in the plane in 2010
How to determine the number of passengers?The given parameters are:
Weight = 150 pounds and Passenger = 270 --- Year 2000
Weight = 170 pounds --- Year 2010
Represent the parameters using the following inverse proportion
Weight * Passenger= Fixed
So, we have:
150 * 270 = 170 * Passenger
Divide both sides by 170
150 * 270/170 = Passenger
Evaluate
238 = Passenger
Rewrite as
Passenger = 238
Hence, there are 238 passengers in the plane in 2010
Read more about variation at:
https://brainly.com/question/6499629
#SPJ1
You throw a ball at a height of 6 feet above the
ground. The height h (in feet) of the ball after t seconds can be modeled by the equation
h=-16t² +62t +6. After how many seconds does the ball reach a height of 27 feet?
Answer:
0.375 second and 3.5 second
Step-by-step explanation:
The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:
[tex]\displaystyle{27=-16t^2+62t+6}[/tex]
Solve for t:
[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]
Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:
[tex]\displaystyle{t=0.375, 3.5}[/tex]
After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.
Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.
Find the inverse function of
f(x)=20x-4
Domain of f(x)
Domain of f^-1(x)
Range of f(x)
Range of f^-1(x)
help can you show work for question please
Answer:
[tex]f(x) = 20x - 4 \\ substitute \: y \: for \: f(x) \\ y = 20x - 4 \\ interchange \: x \: and \: y \\ x = 20y - 4 \\ swap \: the \: sides \: of \: the \: equation \\ 20y - 4 = x \\ move \: the \: constant \: to \: the \: right \: hand \\ 20y = x + 4 \\ divide \: both \: sides \: by \: 20 \\ y = \frac{1}{20} x + \frac{1}{5} \\ substitute \: f {}^{ - 1} (x) \: for \: y \\ f {}^{ - 1} (x) = \frac{1}{20} x + \frac{1}{5} [/tex]
The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.
Thus, domain of f(x): x∈R = range of f¯¹(x)
and range of f(x): x∈R =domain of f¯¹(x)
A restaurant hands out a scratch-off game ticket with prizes being worth
purchases at the restaurant. The back of the ticket lists the odds of winning
each dollar value: 0.4 for $5, 0.3 for $25, 0.2 for $50, and 0.004 for $75. What
are the odds that the ticket is worth at least $25?
Answer:
0.7
Step-by-step explanation:
Because 0.4 is $5 and 0.3 is $25. So 0.3+0.4=0.7
what is the answer to 20÷ 1683 pls
two candles of the same height are lighted at the same time. the first is consumed in 4 hrs and the second in 3 hrs. assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?
The height of candle 4 is twice that of candle B after 2.4 hours.
How many hours after being lighted was the first candle twice the height of the second?For candle, A time is taken for 100% bearning=4hour.
For 1 hour, it burns for 25%(100/4)
After 1 hr.[tex]\frac{25}{100}[/tex]
After x hours, the amount burnt[tex]=\frac{x}{4}[/tex]
Amount left[tex]=1-\frac{x}{4} =\frac{4-x}{4}[/tex]
Let's not presume that candle B's height will be half that of candle A after x hours.
After x hours, part vemacing [tex]=1-\frac{x}{3} =\frac{3-x}{3}[/tex]
[tex]\frac{4-x}{4} =1\frac{3-x}{3}[/tex]
Height of candle A[tex]=2[/tex]×Height of candle B.
[tex]12-3x=24-8x[/tex]
⇒[tex]5x=12[/tex]
[tex]x=\frac{12}{5}[/tex]
[tex]=2.4[/tex]
The height of candle 4 is twice that of candle B after 2.4 hours.
To learn more about the candles of equal height, refer to:
https://brainly.com/question/15493665
#SPJ9