Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
How to get the rate of each jet?
Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:
R + 80mi/h
Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:
S = R + R + 80mi/h
We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:
(R + R + 80mi/h)*8h = 11,392 mi
Now we can solve that for R:
2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h
R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h
So Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
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The following scatterplot shows the percentage of the vote a candidate received in the 2016 senatorial elections
according to the voter's income level based on an exit poll of voters conducted by a news agency. The income
levels 1-8 correspond to the following income classes:
1 = Under $15,000; 2 = $15-30,000; 3 = $30-50,000; 4 = $50-75,000; 5 = $75-100,000;
6 = $100-150,000; 7 = $150-200,000; 8 = $200,000 or more.
Use the election scatterplot to the find the critical values corresponding to a 0.01 significance level used to test
the null hypothesis of ρs = 0.
A) -0.881 and 0.881
B) -0.881
C) -0.738 and 0.738
D) 0.881
The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
How to determine the critical values corresponding to a 0.01 significance level?The scatter plot of the election is added as an attachment
From the scatter plot, we have the following highlights
Number of paired observations, n = 8Significance level = 0.01Start by calculating the degrees of freedom (df) using
df =n - 2
Substitute the known values in the above equation
df = 8 - 2
Evaluate the difference
df = 6
Using the critical value table;
At a degree of freedom of 6 and significance level of 0.01, the critical value is
z = 0.834
From the list of given options, 0.834 is between -0.881 and 0.881
Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881
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SOMEONE PLEASE HELLPPPP
Answer:
93.39
Step-by-step explanation:
So the sum of exterior angles of the convex octagon is: 360 degrees
This means if we add all the equations that represent each angle, we can set it equal to 360 and solve for x
[tex](x+14) + (2x-3) + (3x+8) + (3x+16) + (2x-17) + (3x-4) + (3x-12) + (6x)[/tex]
Group like terms
[tex](x+2x+3x+3x+2x+3x+3x+6x) + (14-3+8+16-17-4-12)[/tex]
Add like terms
[tex]23x+2[/tex]
Now let's set the sum of exterior angles to 360
[tex]23x+2 = 360[/tex]
Subtract 2 from both sides
[tex]23x=358[/tex]
Divide both sides by 23
[tex]x\approx 15.565[/tex]
So by looking at all these, it appears that 6x is the highest value, given that x is positive. The way I estimated, is approximately 15.5, whenever I saw an equation like x+14, I estimated it's about 2x, since 14 is not exactly, but close to 15.5. I did this with each polynomial given. You could also manually check each one
Original equation
6x
Subsitute
6(15.565)
Simplify
[tex]93.39[/tex]
with the law of indices simplify 3a²b×2ab
Answer:
6a³b²
Step-by-step explanation:
3 × 2 = 6
a²× a¹ = a³
b × b = b²
how do you compare and contrast the steps of two different constructions using a compass?
In order to compare and contrast the steps of two different constructions using a compass, we simply take a note of the different steps followed in both the constructions.
How to compare and contrast the steps?
For both the constructions, observe the corresponding steps steps that have been performed in order.
Then, note down what similarity you find while constructing the two different constructions in the first step.
Once you know the the similarities, you can further trace down the differences in the procedure of the two constructions by observing the first step. This is how you can compare and contrast the first step of two different constructions using a compass.
This process can be followed for all the steps for comparing and contrasting two different constructions.
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The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?
the height of the pentagonal pyramid is 5. 70 meters
Volume of a regular pentagonal pyramidThe formula for determining the volume of a regular pentagonal pyramid is given as;
V=5/12tan(54°)ha^2
Where
a is the base edgeh is the heightWe have the volume to be;
volume = 82. 5 cubic centers
height = h
a = 5m
Substitute the values
[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]
[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]
Make 'h' subject of formula
[tex]h = \frac{82. 5}{14. 45}[/tex]
h = 5. 70 meters
The height of the pentagonal pyramid is 5. 70 meters
Thus, the height of the pentagonal pyramid is 5. 70 meters
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Steve took a 300 mile business trip and decided to travel by car. He drove the speed limit for half the trip until an accident occurred and he had to stop for a few hours in traffic. Steve then decided to drive slower than the speed limit the rest of the way to be safe. This situation models which type of function?
Based on the fact that Steve was originally driving the speed limit and then stopped a few hours and drove slower, the situation models a piecewise defined function.
What is a piecewise defined function?This is a type of function where there are two or more parts joined together. In other words, there are two equations to represent the different parts of the function.
In this case, Steve was driving at a certain speed. This is one function. Then he stopped for a couple of hours which is another function. Then the last function has him driving slower than the speed limit.
In conclusion, this is a defined piecewise function.
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Harry took a loan from the bank.
DDD represents Harry's remaining debt (in dollars) after ttt months.
D=-200t+9000D=−200t+9000D, equals, minus, 200, t, plus, 9000
What was the size of Harry's loan?
The amount of Harry's loan is $9000.
A loan is when money is lent to another person with the understanding that it would be repaid, along with interest.
According to the question,
A bank loan is taken up by Harry.
After t months, D indicates Harry's outstanding debt (in dollars).
D=-200t+9000
In order to find the initial size of Harry's loan, the time(t)=0, that is, the time when no debts had been paid.
The negative sign in the expression of D denotes the payment of debt.
Substituting t=0, we get,
D=-200*0+9000
D=9000
Thus, the amount of loan taken by Harry is $ 9000.
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Part of the arena is being turned into a public darkroom. The floor needs covering in rubber tiles before work can begin on the dark room. The tiles are 20 cm by 30 cm. The dark room floor is 6 metres by 3 metres. Are 280 tiles enough? How many more/less tiles are needed?
The number of tiles used is 300 tiles.
According to the statement
We have given that:
The tiles are 20 cm by 30 cm. And the dark room floor is 6 meters by 3 meters.
And we have to find that the number of tiles used to prepare the dark room.
So, For this purpose we have to find the area of the room floor.
The area of the floor is 6 *3.
The area of the floor is 18 meter per square.
The area of the tile is 0.2*0.3
The area of the tile is 0.06 meter per square.
Now,
The number of tiles used is 18/0.06
The number of tiles used is 300.
So, The number of tiles used is 300 tiles.
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H2 Worksheet #8
Complete the table for the following rule
y = 2x + 2.
X
1
3
9
10
y
A1
Answer:
It's easy to solve the problem.
let's start...
given equation:- y = 2x+2
X y
1 (2× 1 )+ 2 = 4 .
3 (3×2)+2 = 8 .
9 (9×2) + 2 = 20 .
10. (10× 2)+2 = 22 .( table completed)
just put the value of X in the expression.
x+2y=5 and 4x+12y=-20 elimination method
Answer:
x=25 and y=-10
Step-by-step explanation:
x+2y=5 ..........(1)
4x+12y=-20.........(2)
using elimination method.
multiply equ(1) by 4 and equ(2) by 1
so we have
x+2y=5..........*4
4x+12y=-20.........*1
4x+8y=20................(3)
4x+12y=-20.............(4)
subtract eq(4) from (3) we have
-4y=40
y=-10
substitute y=-10 in equation (1)
we have:
x+2(-10)=5
x-20=5
x=25
Which graph has a domain of -∞ < x < ∞ and a range of -∞ < y
The graph of the option in the question has a domain of -∞ < x < 3.5.
Please find attached the drawing of a graph that has a domain of -∞ < x < ∞ Which method can be used to find the graph that has a domain of -∞ < x < ∞?The domain of a graph are the possible x-values that can be obtained from the graph.
A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.
An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.
The given graph has a vertical asymptote at y ≈ 3.5
The domain of the given graph is therefore, -∞ < x < 3.5
Similarly, the graph has a horizontal asymptote at x ≈ 3
The range of the given graph is therefore, -∞ < y < 3.
A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.
A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.
An example is, y = x
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Evaluate each expression if A=2
B=-3. C=-1. D=4
2d-a/b
Answer:
2 × 4 - 2 / -3
8-2/-3
6/-3
-2
Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)
The difference of squares is:
(x+i√3)(x-i√3)
So the correct option is the last one, D.
Which expression gives x^2 + 3?For a complex number:
[tex]Z = a + b*i[/tex]
We define the complex conjugate of Z as:
[tex]Z' = a - b*i[/tex]
Such that the product between the complex number and its complex conjugate gives:
[tex]Z*Z' = a^2 + b^2[/tex]
Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:
[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]
Which is what we wanted to get, so that is the correct option.
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How many milliliters are contained in 3 liters of fluid?
Answer:
3000Step-by-step explanation:
1 liter = 1000 milliliters
so
3 liters = 3000 milliliters
------------------------
1 : 1000 = 3 : x
x = 3 * 1000 : 1
x = 3000
Answer: 3000 mL
Step-by-step explanation:
1 L = 1000 mL
3x1000 = 3000
Donna is putting 9 books in a row on the bookshelf she will put one of the books gullivers travel in the first spot she will put in another of the bucks a tale of two cities in the last spot in how many ways can she put the books on the shelf
There are 5,040 different ways in which she can order the books.
In how many ways can she put the books on the shelf?We know that Donna has 9 books, but 2 of these books already have fixed positions (the first one and the last one).
So we only need to order the remaining 7 books in 7 positions.
On the first position, we have 7 options (7 books to put there).On the second position, we have 6 options (because one book is already in the first position).On the third position, we have 5 options.And so on for the remaining positions.
The total number of different combinations in which she can order the books is given by the product between the numbers of options above, so we will get:
C = 7*6*5*4*3*2*1 = 5,040
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pls help me!!! #18-19
Answer:
18. Sqrt40 goes between 6 and 7.
19. Sqrt83 ~= 9
Step-by-step explanation:
For both of these problems, it's really useful to be very familiar with the perfect squares on the times table. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225...
On #18, we're looking at the sqrt40. This will be between sqrt36 and sqrt49, because 40 is between 36 and 49. But sqrt36 is 6 and sqrt49 is 7. So sqrt40 is between 6 and 7.
For #19, the sqrt83 is far closer to sqrt81 than it is to sqrt100. Sqrt81 = 9. So sqrt83 is very close to 9, it would round to 9 and not 10.
domain of f(x)=(1/4)^x
What is the domain of f(x)
O A. x>0
OB. All real numbers
O C. y>0
O D. x<0
? Need help asap
Answer: B
Step-by-step explanation:
The domain of a function is the set of x-values.
Nisha collects comic books, and she convinced her friend Hakim to start collecting as well. Every week, they go to the store together, and they each buy a new comic book. This table shows how many books they each have:
By using the given table, we will get the linear equation:
h = n - 9
How to find the equation for Hakim?
We know that they always get comic books together, so always that Nisha's collection increases by one, Hakim's collection will also increase by one, so we will have a linear equation.
Now, if you look at the given table, you can see that Hakim's collection is always 9 units less than Nisha's collection, then the linear equation that models the relation between the two collections, h and n, is really straightforward, it will be:
Hakim's collection = Nisha's collection - 9
Using the variables, we get:
h = n - 9
That is the linear equation Hakim wanted.
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Answer:
h=n-9
Step-by-step explanation:
find the critical value for the given confidence level c and sample size n c=.90 n=21
The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].
How to calculate the critical value for t-distribution?The critical value is calculated as follows:
For the given sample size n, find the degree of freedom (d.f)Where d.f = n - 1Using the t-distribution table, the critical value is obtained for the obtained d.f and the confidence level.Calculation:It is given that,
confidence level c = 0.90
sample size n = 21
Then,
degree of freedom,
(d.f) = n - 1 = 21 - 1 = 20
So, from the t-distribution table,
at d.f = 20 and the confidence level 0.90, the critical value is 1.725.
I.e., [tex]t_c[/tex] = 1.725
For this, α = (1 - 0.90)/2 = 0.05
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25(0.3x-4)-5(1.5x-6)+100·13/4
Answer:
255 (assuming x is the variable x)
340 (assuming x is the multiplication sign)
See explanation below.
Step-by-step explanation:
I assume that x is the variable x.
25(0.3x-4)-5(1.5x-6)+100·13/4 =
= 7.5x - 100 - 7.5x + 30 + 25 × 13
= -70 + 325
= 255
If my assumption above is incorrect, and x really means the multiplication sign, then we have this:
25(0.3×-4)-5(1.5×-6)+100·13/4 =
= 25(-1.2) - 5(-9) + 100(3.25)
= -30 + 45 + 325
= 340
need heeeelp please
Answer:
1) log7 (5*8)= log7(40)
2) log2(11) -log2(9)=log2(11/9)
3)2log9 2=log9(2^2)
100 POINTS!!!!!!!!!!!!!!1 PLEASE SOLVE THESE PROBLEMS QUICKLY WITH AN EXPLANATION
In triangle ABC, if m∠B = 90°, BH = AH, and the ratio of m∠A to m∠C is 1:2, then m∠BHA = 120° (C).
In the next given equilateral triangle ABC, y = 70°.
Finding m∠BHA:
In triangle ABC, it is given that,
∠B = 90°
And m∠A : m∠C = 1:2
Let us assume m∠A is x. Then, m∠C = 2x
According to the angle sum property of a triangle,
∠A + ∠B + ∠C = 180°
90° + x + 2x = 180°
90° + 3x = 180°
3x = 90°
x = 30°
⇒ In triangle ABC, ∠A = 30° and ∠C = 60°
Now, in triangle AHB, it is also given that,
BH = AH
⇒ ∠ABH = ∠A = 30°
Thus, according to the angle sum property of a triangle,
∠ABH + ∠A + ∠BHA = 180°
30° + 30° + ∠BHA = 180°
∠BHA = 180° - 60°
∠BHA = 120°
Finding y in the Second Triangle:
Since triangle ABC is equilateral,
∠A = ∠B = ∠C = 60°
∴ x + 2x + 3x = 60°
6x = 60°
x = 10°
In triangle ABD, using angle sum property of triangle,
x + ∠B + ∠BDA = 180°
10° + 60° + ∠BDA = 180°
∠BDA = 180° - 70°
∠BDA = 110°
Now, since, ∠BDA and y are linearly adjacent angles,
∠BDA + y = 180°
110° + y = 180°
y = 180° - 110°
y = 70°
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Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
Justin recently drove to visit his parents who live 270
miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran into some bad weather). If Justin spent a total of 9 hours driving, find the two rates.
Answer:
66 mph to visit55 mph to homeStep-by-step explanation:
An equation can be set up and solved based on the relation between the two speeds and the relation between time, speed, and distance.
Setuptime = distance/speed
Let x represent the (slower) speed on the way home. Then the total time for the round trip was ...
time going + time coming home = total time
270/(x +11) +270/x = 9
Solution30x +30(x +11) = x(x +11) . . . . . . multiply by x(x+11)/9
x^2 -49x -330 = 0 . . . . . . . . rewrite in standard form
(x -55)(x +6) = 0 . . . . . . . . factor
x = 55 or x = -6 . . . . . . . solutions to this equation; x < 0 is extraneous
Justin's rate on the way there was 66 mph; on the way home, it was 55 mph.
Calculus HW , will someone please teach me how to do this problem. thanks! 10 Points
Your answers seem to be on the right track. These online homework apps can be picky about the answer they accept, though.
Given [tex]f(x) = x^4 - 2x^2 + 3[/tex], we have derivative
[tex]f'(x) = 4x^3 - 4x = 4x (x^2 - 1) = 4x (x - 1) (x + 1)[/tex]
with critical points when [tex]f'(x) = 0[/tex]; this happens when [tex]x=0[/tex] or [tex]x=\pm1[/tex].
We also have second derivative
[tex]f''(x) = 12x^2 - 4 = 12 \left(x^2-\dfrac13\right) = 12 \left(x - \dfrac1{\sqrt3}\right) \left(x + \dfrac1{\sqrt3}\right)[/tex]
with (possible) inflection points when [tex]x=\pm\frac1{\sqrt3}=\pm\frac{\sqrt3}3[/tex].
Intercept
If "intercept" specifically means [tex]y[/tex]-intercept, what you have is correct. Setting [tex]x=0[/tex] gives [tex]f(0) = 3[/tex], so the intercept is the point (0, 3).
They could also be expecting the [tex]x[/tex]-intercepts, in which case we set [tex]f(x)=0[/tex] and solve for [tex]x[/tex]. However, we have
[tex]x^4 - 2x^2 + 3 = \left(x^2 - 1\right)^2 + 2[/tex]
and
[tex]x^2-1\ge-1 \implies (x^2-1)^2 \ge (-1)^2 = 1 \implies x^4-2x^2+3 \ge 2[/tex]
so there are no [tex]x[/tex]-intercepts to worry about.
Relative minima/maxima
Check the sign of the second derivative at each critical point.
[tex]f''(-1) = 8 > 0 \implies \text{rel. min.}[/tex]
[tex]f''(0) = -4 < 0 \implies \text{rel. max.}[/tex]
[tex]f''(1) = 8 > 0 \implies \text{rel. min.}[/tex]
So we have two relative minima at the points (-1, 2) and (1, 2), and a relative maximum at (0, 3).
Inflection points
Simply evaluate [tex]f[/tex] at each of the candidate inflection points found earlier.
[tex]f\left(-\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]
[tex]f\left(\dfrac{\sqrt3}3\right) = \dfrac{22}9[/tex]
What is the length of the hypotenuse of a 45°-45°-90° triangle with legs that are 8 cm long?
Answer:
Step-by-step explanation:
Use your 45-45-90 special triangle with side lengths 1, 1, sqrt(2).
The given triangle has legs length 8 (given) which is 8 times the size of our special 1-1-sqrt(2) triangle.
Therefore the length of the hypotenuse is 8 times the length of the hypotenuse in our special triangle
= 8 sqrt(2)
1. A foot contains 12 inches. 5 inches is what fraction of a foot?
Answer:
5/12
Step-by-step explanation:
a foot =12 inches
fraction of 5 inches=5/12
If the formula r=1/n-1 .....following data, what would be the value of x?
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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Let g(x)= 18 - 3x
Find g-¹ (0). Final answer is just a number.
Answer:
g(0)⁻¹ = 6
Step-by-step explanation:
First, you must find the inverse of the function. Remember, another way of representing g(x) is with "y". To find the inverse, you must swap the positions of the "x" and "y" variables in the equation. Then, you must rearrange the equation and isolate "y".
g(x) = 18 - 3x <----- Original function
y = 18 - 3x <----- Plug "y" in for g(x)
x = 18 - 3y <----- Swap the positions of "x" and "y"
x + 3y = 18 <----- Add 3y to both sides
3y = 18 - x <----- Subtract "x" from both sides
y = (18 - x) / 3 <----- Divide both sides by 3
y = 6 - (1/3)x <----- Divide both terms by 3
Now that we have the inverse function, we need to plug x = 0 into the equation and solve for the output. In the inverse function, "y" is represented by the symbol g(x)⁻¹.
g(x)⁻¹ = 6 - (1/3)x <----- Inverse function
g(0)⁻¹ = 6 - (1/3)(0) <----- Plug 0 in for "x"
g(0)⁻¹ = 6 - 0 <----- Multiply 1/3 and 0
g(0)⁻¹ = 6 <----- Subtract
TIME REMAINING
44:36
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)?
(0,6)
(0,–6)
(6,0)
(–6,0)
Answer:
d. (-6, 0)
Step-by-step explanation:
no explanation bc u need this quick