Answer:
the distance between the ships is changing at 21.4 km/h
Step-by-step explanation:
Given;
distance between ship A and ship B = 150 km
speed of ship, A = 35 km/h
speed of ship B = 25 km/h
at 4 pm, the time difference = 4 hours
let the distance between A and B = C
The position of A after 4 hours = 35 km/h x 4 h = 140 km
The distance covered by A, a = 150 km - 140 km = 10 km
The distance covered by B, b = 25 km/h x 4 h = 100 km
The distance between A and B;
c² = a² + b²
c² = 10² + 100²
c² = 10100
c = √10100
c = 100.5 km
The change in the distance between A and B is calculated as;
[tex]c^2 = a^2 + b^2\\\\2c\frac{dc}{dt} = 2a\frac{da}{dt} + 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = a\frac{da}{dt} + b\frac{db}{dt} \\\\100.5(\frac{dc}{dt}) = -10(35) + 100(25) \\\\(the \ negative \ sign \ indicates \ decrease \ in \ distance \ of \ A \ from \ B \ with \ time)\\\\100.5(\frac{dc}{dt})= 2150\\\\\frac{dc}{dt} = \frac{2150}{100.5} \\\\\frac{dc}{dt} = 21.39 \ km/h\\\\\frac{dc}{dt} \approx 21.4 \ km/h[/tex]
Therefore, the distance between the ships is changing at 21.4 km/h
Evaluate the functions
Answer:
Step-by-step explanation:
The following are on a parabola defining the edge of a ski
(-4, 1), (-2, 0.94), (0.1)
The general form for the equation of a parabola is:
Ax^2+ Bx +C= y
Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Repeat this process with 1 of the other to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
9514 1404 393
Answer:
a) 16A -4B +C = 1
b) 4A -2B +C = 0.94
c) C = 1
Step-by-step explanation:
Substitute the x- and y-values into the general form equation.
a. A(-4)² +B(-4) +C = 1
16A -4B +C = 1
__
b. A(-2)² +B(-2) +C = 0.94
4A -2B +C = 0.94
__
c. A(0)² +B(0) +C = 1
C = 1
_____
Additional comment
Solving these equations gives A=0.015, B=0.06, C=1. The quadratic is ...
0.015x² +0.06x +1 = y
Please help out explanation need it
Answer:
[tex] \sin(θ) = \frac{19}{41} \\ θ = 27.6 \\ θ = 28[/tex]
What is the inverse of the function ? f(x)=x+1 over x?
plato
Answer:
[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]
Step-by-step explanation:
bxhrrrhi5u44ftj7gttjoy
Answer:
x = (y+1)/y
xy = (y+1)
xy -y = 1
y(x-1)=1
y = 1/(x-1)
Step-by-step explanation:
Write an equation for the graph below in terms of x
Answer:
x = -2
Step-by-step explanation:
the line goes through -2 on the x-axis
the line also goes through -3 on the y-axis
HELP ME PLEASE I NEED HELP
Answer:
1. 3-5
2. 5-3
3. 3-5
4. 5-3
Step-by-step explanation:
This is simple! Just get rid of the parenthesis for each of the expressions shown.
3 + (-5)
the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes
3 - 5
Now do the same for the rest!
For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]
Hope this helps !!
-Ketifa
There are 160 pages in a book.15% of the pages having pictures on them. How many
Pages do not have pictures on them?
Answer:
136
Step-by-step explanation:
15/100×160
=24
pages that doesn't have pictures=160-24
=136
90 units needed 8per case
The total cost, C, for running an advertisement in a local newspaper, The Free Press, is made up of an initial cost of $12 plus a charge of $5 per day. A rival newspaper, The Banner, is currently running a special on advertisements at $8 per day with no initial cost.
a) Write an equation representing the cost in The Free Press.
b) Write an equation representing the cost in The Banner.
c) For each newspaper, create a table of values.
d) Use Rapid Tables (will need to select 2 lines from the drop down - see example in relation to the Jason's Trip graph below) to graph each cost on the same set of coordinate axis. Your two lines will represent The Free Press and The Banner. You are also able to create the graph on other technology or a piece of paper.
e) Which newspaper would you use for an ad that ran 1 day?
f) Which newspaper would you use for an ad that ran 12 days?
Answer:
(a) [tex]C(x) = 12 + 5x[/tex]
(b) [tex]C(x) = 8x[/tex]
(c) Tables
(d) See attachment for graph
(e) Banner newspaper
(f) Free press newspaper
Free Press
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
Banner
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
Step-by-step explanation:
Given
Free Press
[tex]Initial = 12[/tex]
[tex]Rate =5[/tex]
Banner
[tex]Initial=0[/tex]
[tex]Rate =8[/tex]
Solving (a): Free Press Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 12 + 5x[/tex]
Solving (b): Banner Equation
This is calculated as:
[tex]C(x) = Initial + Rate * x[/tex]
Where
[tex]x \to[/tex] days
So, we have:
[tex]C(x) = 0 + 8x[/tex]
[tex]C(x) = 8x[/tex]
Solving (c): Table of values
For free press, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {17} & {22} & {27} & {32} & {37} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 12 + 5* 1 =17[/tex]
[tex]x = 2;\ C(2) = 12 + 5* 2 =22[/tex]
..
[tex]x = 5;\ C(5) = 12 + 5* 5 =37[/tex]
For banner, we have:
[tex]\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} & {C(x)} & {8} & {16} & {24} & {32} & {40} \ \end{array}[/tex]
C(x) is calculated as:
[tex]x = 1;\ C(1) = 8* 1 =8[/tex]
[tex]x = 2;\ C(2) = 8* 2 =16[/tex]
..
[tex]x = 5;\ C(5) = 8* 5 =40[/tex]
Solving (d): Graph of both using rapidtable
See attachment
Solving (e) Newspaper to use for 1 day
From the graph, when [tex]x = 1[/tex]
[tex]Free\ press = 17[/tex]
[tex]Banner = 8[/tex]
So, we use Banner newspaper because it is cheaper
Solving (f) Newspaper to use for 12 days
From the graph, when [tex]x = 12[/tex]
[tex]Free\ press = 72[/tex]
[tex]Banner = 96[/tex]
So, we use free press newspaper because it is cheaper
The height of the triangle is 4 meters longer than twice its base. find the height if the area of the triangle is 80 square meters. The height must be ___meters
Answer:
The height is 20 meters
Step-by-step explanation:
First set up the equation (Area)80=bh/2 then set up another equation, (height) h=4+2b (base). After this you can substitute h in the equation to end up with 80=(b(2b+4))/2 simplify it to get 80=b^2+2b then solve. The base is 8 meters, plug into the formula that we made before and you find the height is 20 meters.
Solve the equation Axb by using the LU factorization given for A. Also solve Axb by ordinary row reduction. A , b Let Lyb and Uxy. Solve for x and y. nothing nothing Row reduce the augmented matrix and use it to find x. The reduced echelon form of is nothing, yielding x nothing.
Answer: Hello your question is poorly written attached below is the complete question
answer:
[tex]y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right][/tex]
[tex]x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right][/tex]
Step-by-step explanation:
[tex]y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right][/tex]
[tex]x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right][/tex]
attached below is the detailed solution using LU factorization
The graph f(x)=x^5 is transformed to form a new function, g(x). Which set of transformations takes f(c) to g(x) in the correct order?
- translation 2 units to right,vertical stretch by a factor 1/3, translation 1 unit up
-translation 2 units to the right, vertical stretch by a factor of 3, translation 1 unit up
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 1/3
-translation 2 units to the right,translation 1 unit up,vertical stretch by a factor of 3
Answer:
Translation 2 units to the right
Vertical stretch by a factor of 3
Translation 1 unit up
Step-by-step explanation:
Correct on plato :}
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
Learn more about the place value strategy here:
brainly.com/question/654419
#SPJ2
Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.28 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent.
Required:
a. What is the probability that both professors get their grantsfunded?
b. What is the probability that at least one of the professors will befunded?
c. What is the probability that Professor Jane is funded but ProfessorJoe is not?
d. Given at least one of the professors is funded, what is theprobability that Professor Jane is funded but Professor Joe is not?
Smart phone: Among 239 cell phone owners aged 18-24 surveyed, 103 said their phone was an Android phone. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to at least three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is .
Answer:
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
Step-by-step explanation:
The point estimate is the sample proportion.
Sample proportion:
103 out of 249, so:
[tex]p = \frac{103}{249} = 0.4137[/tex]
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
find the sum of (-260)+(-30)
Answer:
-290
Step-by-step explanation:
(-260) +(-30)
=-260-30
=-290
Answer:
the answer is -290
Step-by-step explanation:
it is telling us to add so we can see that both the numbers have the same sign which is negative
when the signs are all the same, we can add and we got -290
Banking fees have received much attention during the recent economic recession as bankslook for ways to recover from the crisis. A sample of 31 customers paid an average fee of $11.53 permonth on their checking accounts. Assume the population standard deviation is $1.50. Calculatethe margin of error for a 90% confidence interval for the mean banking fee.
Answer:
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Sample of 31:
This means that [tex]n = 31[/tex]
Assume the population standard deviation is $1.50.
This means that [tex]\sigma = 1.5[/tex]
Calculate the margin of error for a 90% confidence interval for the mean banking fee.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645\frac{1.5}{\sqrt{31}}[/tex]
[tex]M = 0.44[/tex]
The margin of error for a 90% confidence interval for the mean banking fee is of $0.44.
what is the union of these two sets? E={-1,0,4,5,6,7} G={-2,-1,1,2,3,8}
Answer:
U={-2,-1,0,1,2,3,4,5,6,7,8}
The polygons in each pair are similar. Find the missing side length.
Let missing one be x
If both are similar
[tex]\\ \sf\longmapsto \dfrac{20}{25}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{4}{5}=\dfrac{16}{x}[/tex]
[tex]\\ \sf\longmapsto 4x=16(5)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{16(5)}{4}[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
If 8 bags of chips cost 10.32;how much will you pay for 20 bags?
Answer:
$25.80
Step-by-step explanation:
First, let's find the cost of one bag of chip:
10.32/8 = 1.29
If one bag costs $1.29, simply multiply the number of bags (20) by 1.29
1.29 x 20 = 25.80
= $25.80
Answer:
25.80
Step-by-step explanation:
We can use a ratio to solve
8 bags 20 bags
------------- = ----------------
10.32 x dollars
Using cross products
8x = 10.32 * 20
8x =206.40
Divide each side by 8
8x/7 = 206.40/8
x =25.80
Solve for x then measure to find A
Answer:
[tex]125 \: \: degrees[/tex]
Step-by-step explanation:
As the 2 lines are parallel
<A = <B ( Alternative Angles)
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = 20[/tex]
[tex]<A = 6x + 5 \\ = 6 \times 20 + 5 \\ = 120 + 5 \\ = 125[/tex]
<A=6x+5
=6×20+5
=120+5
=125
<B=4x+45
=4×20+45
=80+45
=125
it is alternate angle they are equal each other
<A = < B
[tex]6x + 5 = 4x + 45 \\ 6x - 4x = 45 - 5 \\ 2x = 40 \\ x = \frac{40}{2} \\ x = 20 \\ \\ [/tex]
Which polynomial is prime?
a. x³+3x²+2x+6
b. x³+3x²-2x-6
c. 10x²-4x+3x+6
d. 10x²-10x+6x-6
Which statement is true about the value of Start Absolute Value negative 5 End Absolute Value?
Statements? At least look for one that says it is equivalent to positive 5.
__ (5 + 4) = 2 * 5 + 2 * 4
PLEASE EXPLAIN HOW YOU GOT THE ANSWER
Answer:
x = 2
Step-by-step explanation:
→ Simplify
x × ( 9 ) = 10 + 8
→ Further simplify
9x = 18
→ Divide both sides by 9
x = 2
Choose the correct answer.
The History Activities were about ___ and ___. They were both from ___. One of them had a ___ named after him. The other had a ___ named after him. The work they did together on a problem they got from a ___ laid the foundation for probability theory.
A. Pascal, Decartes, England, graph, book, relative
B. Luniz, Kolmogrov, Germany, church, square, teacher
C. Fermat, Luniz, England, law, diagram, priest
D. Pascal, Fermat, France, triangle, theorem, gambler
Answer:
I say Its letter d
Step-by-step explanation:
I hope this help
A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate, 10 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?
Answer:
340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Step-by-step explanation:
Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:
480 x 20 = 9600
400 x 28 = 11200
350 x 33 = 11550
300 x 38 = 11400
310 x 37 = 11470
320 x 36 = 11520
330 x 35 = 11550
340 x 34 = 11560
Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
A plumber had two pipes. The ratio of the length of the longer pipe to the
shorter pipe was 9 : 2. When he
cut 1.65 m from the longer pipe, the
remaining length was 3 times that of the shorter
pipe. Find the length of
the shorter pipe in metres.
Answer:
4.95m
Step-by-step explanation:
Let the length of longer and shorter pipe be x and y respectively..
given,
x/y=9/2...(i)
x-1.65=3y ...(ii)
in eqn ii..
x-1.65=3y
or, x/y - 1.65/y = 3
or, 9/2-1.65/y =3
or, 4.5-3 = 1.65/y
or, y=1.65/1.5
•°• y = 1.1m
now,
x/y = 9/2
or, x/1.1 = 4.5
x= 4.5×1.1
•°• x= 4.95m
thus, the length of the longer pipe is 4.95m
find the missing side length in the image below
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto 9x=7(27)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
CAN SOMEBODY ANSWER MY QUESTIONS !!!!
9514 1404 393
Answer:
A''(-1, 2)B''(3, 5)C''(4, 3)Step-by-step explanation:
Reflection over the line x=a is the transformation ...
(x, y) ⇒ (2a -x, y)
Then the double reflection over x=a and x=b is the transformation ...
(x, y) ⇒ (2b -(2a -x), y) = (2(b-a) +x, y)
That is, the result is translation by twice the distance between the lines. For a=1 and b=3, the transformation is ...
(x, y) ⇒ (x +4, y) . . . . . . . translation to the right by 4 units.
A(-5, 2) ⇒ A''(-1, 2)
B(-1, 5) ⇒ B''(3, 5)
C(0, 3) ⇒ C''(4, 3)
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
