Answer:
6.914miles (to 3 decimal places)
Step-by-step explanation:
Length of an arc = θ/360 *2πr
angle subtended by arc at the center of the earth = 6 minutes
1 minute =1/60 degree
6 minute= 6/60 degree =0.1°
θ=0.1°
radius of earth = 3960 miles
distance along the arc = [tex]\frac{0.1}{360}*2\pi *3960[/tex]
=6.9142857143miles
The distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles
The length of an arc that subtends with a central angle of Θ in degree is given by:
arc length = (Θ/360) * 2πr
where r is the radius of the circle
Given that r = 3960 miles, θ = 6 minutes = (1/60 degree) * 6 = 1/10 degree
Therefore:
arc length = (1/10 ÷ 360) * 2π(3960) = 6.912 miles
Hence the distance along an arc on the surface of the earth that subtends a central angle of 6 minutes is 6.912 miles
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(40 pts) Corresponding parts of similar triangles are congruent.
True
False
The answer is True.
Step-by-step explanation:
Corresponding parts of similar triangles are congruent, if the two triangles are similar and then the ratio of corresponding sides is equal to the ratio of angle bisectors, altitudes and the medians of the two triangles.Consider two triangles ABC and DEF which is proportional to each other and their corresponding altitudes, medians and angle bisectors are also proportional. There are many types of triangles some of them are equilateral triangles, right triangles, obtuse triangles, acute triangles, etc.Answer:
True
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are congruent
Which could be used to solve this equation? 3 1/5 +n =9
Answer:
A
Step-by-step explanation
You need to subtract the 3 1/5 from both sides, which gives you 29/5
Answer:
A
Step-by-step explanation:
You always to the opposite of the opporation already given.
A can of soda is placed inside a cooler. As the soda cools, its temperature T(x)
in degrees Celsius is given by the following function, where x
is the number of minutes since the can was placed in the cooler.
T(x)=−12+28e-0.38x
Find the initial temperature of the soda and its temperature after 18
minutes.
Round your answers to the nearest degree as necessary.
Answer:
The initial temperature of the soda is 16°C
The temperature of the soda after 18 minutes is -12°C
Step-by-step explanation:
T(x) = -12+28e^-0.38x
When x = 0
T(0) = -12+28e^-0.38(0) = -12+28e^0 = -12+28(1) = -12+28 = 16°C
Initial temperature of the soda is 16°C
When x = 18
T(18) = -12+28e^-0.38(18) = -12+28e^-6.84 = -12+28(0.0011) = -12+0.0308 = -11.9692°C = -12°C (to the nearest degree)
The temperature of the soda after 18 minutes is -12°C
According to the Uniform Commercial Code, a ________ requires a seller to get the goods to be shipped and delivered to a specific place of business designated by the buyer.
Answer:
destination contract
Step-by-step explanation:
Destination contract is invented to assure the goods to be shipped by the seller and to be delivered to the buyer to the location the buyer has selected. It can be a specific place of delivery or a business location.
Destination contract is meant as mean of assurance to avoid each side to take a risk.
n the sentence below identify the type of pronoun which the italicized word is.
It can stand by itself .
reflexive
intensive
interrogative
demonstrative
indefinite
relative
ITSELF is italicized
Answer:
Itself is a Reflexive Pronoun.
Step-by-step explanation:
The reflexive pronouns are words that end with prefixes "self or selves".When the object and the subject in the sentence are same then reflexive pronoun is used. That is It is to denote that the subject is doing something by or to itself .These reflexive pronoun can act either as a direct object or indirect object . It is preceded by the adverb, adjective, pronoun, or noun to which it refers to. They also allow us to point back to, or reflect on, the subject of the sentence with clarity. The nine English reflexive pronouns are
Myself Yourself Himself Herself Oneself ItselfOurselves Yourselves Themselves.A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a small square from each corner and bending up the sides. What size square should be cut from each corner for the box to have the maximum volume?
Answer:
x = 1.64 in the size of the side of the square
Step-by-step explanation:
Let call x side of the square to be cut from cornes, then:
First side of rectangular base
L = 14 - 2*x
And the other side
d = 8 -2*x
Then Volume of the box
V(b) = L*d*x
V(x) = ( 14- 2*x ) * ( 8 -2*x)*x
V(x) = ( 112 - 28*x -16*x + 4*x² )*x ⇒ 4*x³ - 44*x² + 112*x
Taking derivatives on both sides of the equation we get:
V´(x) = 12*x² - 88*x +112
V´(x) = 0 ⇒ 12*x² - 88*x +112 = 0
A second degree equation, solvin it
3x² - 22*x + 28 = 0
x₁,₂ = [ 22 ± √484 - 336 ] / 6
x₁ = (22 + 12,17) /6 x₂ = ( 22 - 12.17 ) / 6
x₁ = 5.69 We dismiss this solution since it make side 8 - 2x a negative length
x₂ = 9.83/6
x₂ = 1.64
Then x = x₂ = 1.64 in
Answer:
1.64 in
Step-by-step explanation:
A cable car can safely carry n people. There are already 3/4n people on the cable car. Only 12 more people can board the cable car before it becomes unsafe. How many people at most can the cable car carry? Write an inequality then solve
Answer:
The answer is 48 people.
Step-by-step explanation:
We can write the equation like following:
[tex]n=(3n/4)+12\\4n=3n+48\\n=48[/tex]
The cable car can carry 48 people at most.
Help: Simplifying inside parenthesis first
Answer:
4th one
Step-by-step explanation:
a^-2 goes down and become a^2 and
[tex] {a}^{2} \times {a}^{2} = {a}^{4} [/tex]
b^-1 goes up and become b
[tex] {b}^{2} \times {b}^{1} = {b}^{3} [/tex]
that why answer is 4th...mark me brainliest please
Ernest and Gene have been saving coins every day for a sunny day in Arizona. Ernest has 8 more half dollars than Gene and no quarters. Gene has as many quarters as Ernest has half dollars, and each has 45 dimes. How many of each coin has each saved for the big day when $200 has been saved? Which of the following equations could represent the word problem if x is the number of half dollars that Gene has?a. 3x + 106 = 200
b. 125x + 916 = 20,000
c. 125x + 1,500 = 20,000
Answer:
1. Ernest has $82.5 and Gene has $117.5
2. c) 125x + 1500 = $20000
Step-by-step explanation:
If we mark Gene's half dollars with x, then it is given that Ernest has 8 more, which is x+8.
It is also given that Ernest has no quarters, but Gene has them as many as Ernest has half dollars, which is x+8.
And it is given that they both have 45 dimes each, which is $4.5 each.
Now, let's add up all these numbers:
Ernest: (x+8)•0.5 + 0•0.25 + 4.5 = 0.5x + 8.5
Gene: x•0.5 + (x+8)•0.25 + 4.5 = 0.75x + 6.5
They collected $200 together which means:
0.5x + 8.5 + 0.75x + 6.5 = $200
1.25x + 15 = $200
If we want to avoid decimal number, we can multiply whole equation with 100:
125x + 1500 = $20000
so, the correct answer is C.
Finally, to find x:
125x = 18500
x = 148
Ernest had 0.5x + 8.5 which is $82.5
Gene had 0.75x + 6.5 which is $117.5
The marching band in selling poinsettias and wreaths to raise money for new uniforms. Trey sold 7 poinsettias and 3 wreaths and raised $201. Molly sold 4 poinsettias and 6 wreaths and raised $252. How much is a poinsettia
The cost of 1 poinsettia is $ 15
Solution:
Let "x" be the cost of 1 poinsettias
Let "y" be the cost of 1 wreath
Trey sold 7 poinsettias and 3 wreaths and raised $201
Therefore, we frame a equation as:
7 poinsettias x cost of 1 poinsettias + 3 wreaths x cost of 1 wreath = 201
[tex]7 \times x + 3 \times y = 201[/tex]
7x + 3y = 201 ------- eqn 1
Molly sold 4 poinsettias and 6 wreaths and raised $252
4 poinsettias x cost of 1 poinsettias + 6 wreaths x cost of 1 wreath = 252
[tex]4 \times x + 6 \times y = 252[/tex]
4x + 6y = 252 ------- eqn 2
Multiply eqn 1 by 2
14x + 6y = 402 -------- eqn 3
Subtract eqn 2 from eqn 3
14x + 6y = 402
4x + 6y = 252
( - ) -----------------------
10x = 150
x = 15
Thus cost of 1 poinsettia is $ 15
The price of a poinsettia is $15.
To determine the price of a poinsettia, we need to set up and solve a system of linear equations based on the given information.
Trey sold 7 poinsettias and 3 wreaths and raised $201. Let's denote the price of a poinsettia as 'P' and the price of a wreath as 'W'. Thus, the equation is:7P + 3W = 201
Molly sold 4 poinsettias and 6 wreaths and raised $252. Therefore, the equation is:4P + 6W = 252
To eliminate one variable, we can multiply the first equation by 2 to get:14P + 6W = 402Now, subtract the second equation from the new equation:(14P + 6W) - (4P + 6W) = 402 - 25210P = 150P = 15Therefore, the price of a poinsettia is $15.
At 1:30 Marlon left his house to go to the beach a distance of 6.75 mi. He rode his skateboard until 2:15 and then walked the rest of the way. He arrived at the beach at 3:00. Marlins speed on his skateboard is 2 times his walking speed. Find his speed when skateboarding and when walking
Answer: his speed when skateboarding is 6 mph and when walking is 3 mph
Step-by-step explanation:
Let x represent Marlon's walking speed.
Marlins speed on his skateboard is 2 times his walking speed. This means that his skating speed would be 2x.
At 1:30 Marlon left his house to go to the beach a distance of 6.75 mi. He rode his skateboard until 2:15. This means that the total time he spent skating is 45 minutes = 45/60 = 0.75 hours
Distance = speed × time
Distance covered while skating would be
2x × 0.75 = 1.5x
He walked the rest of the way. He arrived at the beach at 3:00. This means that the time that he spent walking is 45 minutes = 0.75 hours.
Distance covered while walking would be
x × 0.75 = 0.75x
Total distance covered is 6.75 miles. Therefore
1.5x + 0.75x = 6.75
2.25x = 6.75
x = 6.75/2.25
x = 3 miles per hour
His skating speed = 2 × 3 = 6 miles per hour.
In a school one-third of all 240 students play soccer. Forty four students play both soccer and basketball and sixty students do not play any of these games. How many students play only basketball?
Answer:
100 students play only basketball.
Step-by-step explanation:
We are given the following information in the question:
Total number of students in school = 240
Number of students that play soccer =
[tex]\dfrac{1}{3}\times \text{Total number of students}\\\\=\dfrac{1}{3}\times 240 = 80[/tex]
n(S) =80
[tex]n(S\cap B) = 44[/tex]
[tex]n(S'\cap B') = 60[/tex]
Formula:
[tex]n(S\cup B) = \text{Total} - n(S' \cap B')\\n(S\cup B) = n(S) + n(B) - n(S\cap B)[/tex]
Putting the values, we get,
[tex]n(S\cup B) =240-60=180\\n(S\cup B) = 180 = 80 - 44 + n(B)\\n(B) = 180 - 80 + 44= 144[/tex]
Thus, 144 students play basketball.
Out of these 144, 44 plays soccer as well.
[tex]\text{Student only playing basketball} = 144 -44 = 100[/tex]
Thus, 100 students play only basketball and not soccer.
Create an explicit equation for each recursively defined sequence below:
Part A
This is an arithmetic sequence with starting term a(1) = 17 and common difference d = -7.
a(n) = a(1) + d(n-1)
a(n) = 17 + (-7)(n-1)
a(n) = 17-7(n-1)
a(n) = 17-7n+7
a(n) = -7n+24 is the final answer========================================================
Part B
We have a geometric sequence here because we multiply by the same quantity (5) each time. This makes the common ratio be r = 5.
The starting term is t1 = 3
The nth term of this geometric sequence can be expressed as...
t(n) = t1*(r)^(n-1)
t(n) = 3*(5)^(n-1) is the final answerTerry pays £635.71 a year on his car insurance. The insurance company reduces the price by 5.3%. How much does the insurance cost now? Give your answer rounded to 2 DP.
The insurance costs £602.02 now.
Step-by-step explanation:
Amount paid for car insurance = £635.71
Price reduce = 5.3%
Amount of reduce = 5.3% of amount paid
Amount of reduce = [tex]\frac{5.3}{100}*635.71[/tex]
Amount of reduce = [tex]0.053*635.71[/tex]
Amount of reduce = £33.69263
Rounding off to two decimal place
Amount of reduce = £33.69
Reduced price = Amount paid - Amount of reduce
Reduced price = 635.71 - 33.69 = £602.02
The insurance costs £602.02 now.
Keywords: subtraction, division
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Original price × (1 - reduction percentage) = Reduced price. £635.71 × (1 - 0.053) ≈ £602.97 (rounded to 2 DP).
let's break it down step by step:
1. Calculate the reduction amount:
Multiply the original price (£635.71) by the reduction percentage (5.3% or 0.053).
Reduction Amount = £635.71 * 0.053
2. Subtract the reduction amount from the original price:
Subtract the reduction amount from the original price to find the reduced price.
Reduced Price = £635.71 - Reduction Amount
Now, let's plug in the values:
1. Calculate the reduction amount:
Reduction Amount = £635.71 * 0.053
≈ £33.73763
2. Subtract the reduction amount from the original price:
Reduced Price = £635.71 - £33.73763
≈ £602.97237
Rounded to two decimal places:
Reduced Price ≈ £602.97
So, after the 5.3% reduction, Terry's car insurance costs approximately £602.97.
Find the angle that the line through the given pair of points makes with the positive direction of the x-axis
(1,4) and (-1,2)
Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt
[tex]Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the values we get
[tex]Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1[/tex]
Also Slope of line when angle ' θ ' is given as
[tex]Slope=\tan \theta[/tex]
Substituting Slope = 1 we get
[tex]1=\tan \theta[/tex]
[tex]\tan \theta=1\\\theta=\tan^{-1}(1)[/tex]
We Know That for angle 45°,
tan 45 = 1
Therefore
[tex]\theta=45\°[/tex]
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
In triangle ABC, a = 2, c = 6, and cos B = . Find b.
Answer:
Use Law of Cosines, which is ß² = α² + c² - 2αccos(B) where <B is opp. to side ß.
Let α = 2, c = 6 and cos(B) = 1/6, so
ß = √(2² + 6² - 2(2)(6)(1/6))
= √(4 + 36 - 4)
= √36 = 6
Find a function of the form
y=Asin(kx)+C or y=Acos(kx)+C whose graph matches this one:
Answer:
y = 2sin((π/7)x)
Step-by-step explanation:
The graph goes through (0, 0) and has a range of ±2. This matches a sine function with an amplitude (A) of 2 and a vertical offset (C) of zero.
The half-period is 7, so the value of k is such that 7k = π, or k = π/7.
The desired function is y = 2·sin((π/7)x).
What is the difference?
2x + 5/x 2 - 3x - 3x + 5/x3 - 9x - x + 1/x2 - 9
(x + 5)(x + 2)/x3 - 9x
(x + 5)(x + 4)/x3 - 9x
-2x + 11/x3 - 12x - 9
3(x + 2)/x2 - 3x
Edit: It's A
Answer:
The option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct
The difference of the given expression is
[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]
To find the difference of the given expression as below :
[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-9)})-({\frac{x+1}{x^2-9})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-3^2)})-({\frac{x+1}{x^2-3^2})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x-3)(x+3)})-({\frac{x+1}{(x-3)(x+3)})[/tex]
( using the formula [tex]a^2-b^2=(a+b)(a-b)[/tex] )
[tex]=\frac{2x+5(x+3)-(3x+5)-x(x+1)}{x(x-3)(x+3)}[/tex]
[tex]=\frac{2x^2+6x+5x+15-3x-5-x^2-x}{x(x-3)(x+3)}[/tex] (adding the like terms)
[tex]=\frac{x^2+7x+10}{x(x^2-9)}[/tex] ( by factoring the quadratic polynomial )
[tex]=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore the difference of the given expression is
[tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct
Answer:
A
Step-by-step explanation:
____________is the practice of putting students into specific curriculum groups based on their test scores and other factors.
Answer: Tracking is the practice of putting students into specific curriculum groups based on their test scores and other factors.
Tracking is the practice of grouping students based on their abilities and test scores. It involves sorting students into different curriculum groups. Ability grouping and tracking are used to place students on specific educational tracks.
Tracking is the practice of putting students into specific curriculum groups based on their test scores and other factors. This process involves classifying students based on academic merit or potential and is a formalized sorting system that places students on 'tracks' that perpetuate inequalities. Ability grouping and tracking are strategies used to group students according to their perceived abilities for educational purposes.
A community center has adopted two miles or 3520 wide of a highway to pick up trash along the side of the road falling tears are divided into 7 groups each group is a sign of equal length of Highway to clean up how many yards will each group clean up explained
Answer:
no it is 8 more so do it one more time and you will get the answer 352? fine the number
Step-by-step explanation:
Jean has a ride metro card. It costs $2.50 to get on the tram plus $0.75 for each stop. If Jeans metro card allows her 8 rides and costs $44 how many stops can she make?
Answer: she can make 32 stops
Step-by-step explanation:
Let x represent the number of stops that she can make.
Jean has a ride metro card. It costs $2.50 to get on the tram plus $0.75 for each stop.
If Jeans metro card allows her 8 rides and costs $44, it means that if she makes x stops, then
2.5 × 8 + 0.75 × x = 44
20 + 0.75x = 44
0.75x = 44 - 20 = 24
x = 24/075 = 32
What function is represented by the graph?
F(x) = (3/4)^x + 6
F(x) = (3/4)^x + 5
F(x) = (4/3)^x + 5
F(x) = (4/3)^x + 6
Answer:
[tex]\displaystyle f(x) = [\frac{3}{4}]^x + 5[/tex]
Explanation:
All you have to do is plug in some intervals into the function based off of the graph, to make sure your function is authentic.
* Anytime that [tex]\displaystyle a < 1,[/tex]the graph will be falling from the left.
I am joyous to assist you anytime.
Abby has a collection of 61 dimes and nickels worth $4.40. How many nickels does she have? Show steps
Answer:
34 nickels
Step-by-step explanation:
First, consider the value if they were all dimes. That would be 61×$0.10 = $6.10. Next, realize this is more than the actual amount by 1.70. Of course, replacing one of the 61 dimes by a nickel reduces the total amount by $.05, so we must have ...
$1.70/$0.05 = 34
nickels in the mix.
Abby has 34 nickels.
_____
Alternate solution methods
I like to solve these using number sense, as above. Equivalently, an equation can be written using n to represent the number of nickels. The total value is then ...
.05n + .10(61 -n) = 4.40
-.05n +6.10 = 4.40 . . . . . . eliminate parentheses
-.05n = -1.70 . . . . . . . . . . . subtract 6.10
n = -1.70/-.05 = 34
Hopefully, you notice some similarities between this solution and the one in words, above.
__
Often, you will see this sort of problem formulated using two equations.
n + d = 61 . . . . . . . . . . number of coins (d=#of dimes)
.05n +.10d = 4.40 . . . .value of coins
If we solve this by substitution, we can use d=61-n, and get ...
.05n +.10(61-n) = 4.40 . . . . . . looks like our equation in the previous section
By creating two equations for the total value of coins and the total number of coins Abby has, we can solve for both the number of dimes and nickels she holds. After doing the required calculations, we find that Abby has 34 nickels.
Explanation:The subject of this question is algebra and it involves solving a system of equations. This is a classic problem that can be solved using two equations because we have two unknowns: the number of dimes and the number of nickels.
Since each dime is worth 10 cents and each nickel is worth 5 cents, and total value of Abby's coins is $4.40 or 440 cents, we can write the value equation as:So, Abby has 34 nickels.
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Mike and Kim invest $18,000 in equipment to print yearbooks for school. Each yearbook costs $5 to print and sells for $15. How many yearbooks must they sell before their business breaks even?a. 1,100 yearbooksb. 1,200 yearsbooksc. 3,600 yearbooksd. 1,800 yearsbooks
Answer:
1800yearbook(D)
Step-by-step explanation:
Cost of printing a year book = $5
A year book is sold at $15
The profit on each year book = $15 - $5 = $10
Let y represent the number of year books sold for a break even to occur.
A break even occurs when the amount sold is equals the amount invested
10y = 18000
y = 18000/10
y = 1800 yearbooks
An airplane flies horizontally from east to west at 320 mph relative to the air. If it flies in a steady 40-mi/hr wind that blows horizontally toward the southwest (45 degrees south of west). find the speed and direction of the airplane relative to the ground.
Answer:Speed of airplane= 43.18mi/he
Direction of the airplane relative to the ground=4.64°. Counter-clockwise rotation from west.
Step-by-step explanation: welovity/speed is represented as magnitudes of vectors.
Let A= the vector of the airplane
Let W= the vector of the wind
From the diagram,total vector F= A + w
F= 320+ 40cos45°I +0j) + (0i + 40sin46°)
F=320+28.28i+28.28j
To calculate the magnitude
/F/=root of A2 +w2
/F/=root320+40cos45°2+40sin45°2
/F/=root 1919.5168
/F/=43.18= speed
To calculate the direction of the airplane relative to the ground, use tan function because it is a right triangle as seen in the diagram
Tan x= opp/adj=40sin45/320+40cos45
Tanx=28.28/348.28
Tanx=0.091199
×=tan-1 0.091199
×=4.64
Bacteria can multiply at an alarming rate when each bacterium splits into two new cells, thus doubling. If a single bacterium is discovered at 9 a.m. and doubles every hour, how many bacteria will there be at the end of the day (midnight)?
65,536 cells of bacterium
Answer: 135
Step-by-step explanation:
Grace started her own landscaping business. She charges $6 an hour for mowing lawns and $11 per house pulling weeds. In September she mowed lawns for 63 hours and pulled weeds for 9 hours. How much money did she make in September?
Answer:
The total money made by Grace is $477.
Step-by-step explanation:
Given:
Charge per hour for mowing lawn = $6
Charge per hour for pulling weeds = $11
Number of hours for which lawns are mowed = 63 hours
Number of hours for which weeds are pulled = 9 hours
Now, total money made by Grace in September can be calculated by adding the total money gained in mowing lawns and pulling weeds.
Total money gained in mowing lawns is given as:
[tex]C_m=\textrm{Number of hours of mowing}\times\textrm{Charge per hour}\\\\C_m=63\times 6=\$378[/tex]
Total money gained in pulling weeds is given as:
[tex]C_w=\textrm{Number of hours of pulling weeds}\times\textrm{Charge per hour}\\\\C_w=9\times 11=\$99[/tex]
Now, total money made = [tex]C_m+C_w=378+99=\$477[/tex]
Therefore, the total money made by Grace is $477.
A baseball is thrown at an angle of 30° with respect to the ground and it reaches the ground in 2 seconds. What is its initial velocity of baseball?
Answer:
The answer to your question is vo = 19.62 m/s
Step-by-step explanation:
Data
angle = α = 30°
time = t = 2 s
vo = ?
g = 9.81 m/s²
Formula
[tex]t = \frac{2vosin\alpha}{g}[/tex]
Solve for vo
[tex]vo = \frac{tg}{2sin\alpha}[/tex]
Substitution
[tex]vo = \frac{(2)((9.81)}{2sin 30}[/tex]
Simplification
[tex]vo = \frac{19.62}{2(0.5)}[/tex]
[tex]vo = \frac{19.62}{1}[/tex]
Result
vo = 19.62 m/s
The least-squares regression line is ________.
a. the line that passes through the most data points.
b. the line that minimizes the vertical distances of the data points from the line.
c. the line such that half of the data points fall above the line and half fall below the line.
d. All of the choices are correct.
Answer:
a. the line that passes through the most data points.
Step-by-step explanation:
Regression analysis, is used to draw the line of‘ best fit’ through co-ordinates on a graph. The techniques used enable a mathematical equation of the straight line form y=mx+c to be deduced for a given set of co-ordinate values, the line being such that the sum of the deviations of the co-ordinate values from the line is a minimum, i.e.
The least-squares regression lines is the line of best fit
How long would it take for a ball dropped from the top of a 576576-foot building to hit the ground? Round your answer to two decimal places.
Answer:
5.98 s
Step-by-step explanation:
576 ft = 576 / 3.28 = 175.56 m
Let g = 9.81 m/s2. The time it takes for the ball to fall from 165.56 m high to the ground is
[tex]s = gt^2/2[/tex]
[tex]t^2 = 2s/g = 2*175.56/9.81 = 35.8[/tex]
[tex]t = \sqrt{35.8} = 5.98 s[/tex]