The required Mark has completed 38.46% of the race.
To calculate the percentage of the race completed by Mark, we can divide the number of miles he has run by the total length of the race and then multiply by 100 to convert the result to a percentage.
So, Mark has run 5 miles out of a total of 13 miles:
Percentage of race completed = (5/13) x 100%
Calculating this expression, we get:
Percentage of race completed = 38.46%
Therefore, Mark has completed 38.46% of the race.
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A show box measures 15 in. by 7 in. by 4 1/2 in. What is the surface of the box?
The surface area of the box is 408 square inches whose dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in.
The formula for the surface area of a rectangular box is:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the box.
Given that the dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in., we have:
l = 15 in.
w = 7 in.
h = [tex]4\frac{1}{2}[/tex] in. = 9/2 in.
Substituting these values into the formula, we get:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(15)(7) + 2(15)(9/2) + 2(7)(9/2)
Surface Area = 210 + 135 + 63
Surface Area = 408
Therefore, the surface area of the box is 408 square inches.
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Keng adds a 3-inch-wide frame around all sides of his canvas.
Answer:
That statement describes an action taken by Keng to add a 3-inch-wide frame around all sides of his canvas, likely for artistic or aesthetic purposes. This would result in the canvas being extended by 3 inches in each direction, effectively increasing its overall dimensions and adding a border or frame around the original artwork. The purpose and effect of adding a frame may vary depending on the artistic intention of the artist, but it is a common practice in art and design to enhance the presentation and visual appeal of the artwork.
Step-by-step explanation:
Explain the J curve effect when domestic currency is appreciated?
The J curve impact is an financial wonder that happens when domestic currency increases in value in esteem relative to other monetary forms within the remote trade advertise. The J curve impact is named for the shape of the bend that's made when the adjust of exchange and the esteem of a country's currency are plotted against time.
What occur to the J curve effect when domestic currency is appreciated?Within the brief run, when a country's money increases in value, its sends out ended up more costly and imports ended up cheaper. This implies that the request for a country's sends out will diminish, whereas the request for imports will increase. As a result, the adjust of exchange will at first
compound, which implies that the nation will have a exchange shortfall.
Be that as it may, within the long run, the J curve impact predicts that the adjust of exchange will in the long run progress, and the exchange shortage will turn into a exchange overflow. This happens because the increment within the cost of sends out due to the appreciation of the currency will in the long run lead to a diminish within the amount of trades requested. At the same time, the diminish within the price of imports due to the appreciation of the money will in the long run lead to an increment within the amount of imports requested. Over time, these changes in request will cause a move within the adjust of exchange, coming about in a exchange excess.
In this manner, the Jcurve impact portrays the short-term weakening within the adjust of exchange that happens when a money increases in value, taken after by a long-term enhancement within the adjust of exchange. This impact is named after the shape of the bend that's shaped when the adjust of exchange and the esteem of a country's cash are plotted against time, which looks like a "J" shape.
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Drag the tiles to the correct boxes to complete the pairs.
Match each system of linear equations with the correct number of solutions.
One solution
62
地址
3x - y
-
y =
Infinitely many solutions
-
= 4
2y = 8
-4x - 5
-4x + 1
-3x + y
2x
ee
4y
= 7
=
-8
Reset
Next
No solution.
In the given system of linear equations we get,
3x - y = 4, 6x - 2y = 8 has no solution.
y = -4x - 5, y = -4x + 1 has infinitely many solutions.
- 3x + y = 7, 2x - 4y = -8 has exactly one solution.
System of linear equations can have one solution or infinitely many solution or no solution based on their form.
If two lines are parallel to each other (that is, both linear equations have same slope) then the system of linear equations has no solutions.
A system of linear equation with infinitely many solutions has both the sides of equations equal.
When a system of linear equation has exactly one value of the variables which makes the equations satisfy is said to have one solution.
Here the system of linear equations are as,
3x - y = 4
6x - 2y = 8
The two equations of the system of linear equations are parallel to each other and hence has no solution.
y = -4x - 5
y = -4x + 1
The two equations of the system of linear equations has both the sides equal to each other and hence has infinitely many solutions.
- 3x + y = 7
2x - 4y = -8
The two equations of the system of linear equations has exactly one value of x and y which satisfies the conditions and hence has one solution.
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geometry please help fast
questions 1 and 2
What is the meaning of "there is some [tex]k \in I[/tex] such that [tex]D_{i}\subseteq D_{k}[/tex] and [tex]D_{j}\subseteq D_{k}[/tex]?
The given statement "there is some k∈I such that [tex]D_{i}[/tex]⊆[tex]D_{k}[/tex] and [tex]D_{j}[/tex]⊆[tex]D_{k}[/tex]means that there is a set [tex]D_{k}[/tex] in a collection of sets I that contains all the elements of both sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex].
For example, let's say we have a collection of sets I that includes sets A, B, C, D, E, and F. If we have two sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex], where [tex]D_{i}[/tex] is the set of all even numbers, and [tex]D_{j}[/tex] is the set of all positive integers less than or equal to 10, then we can say that there exists a set [tex]D_{k}[/tex] in I that contains both [tex]D_{i}[/tex]and [tex]D_{j}[/tex] as subsets.
In this case, the set [tex]D_{k}[/tex] could be the set of all even positive integers less than or equal to 10. This set contains all the elements of [tex]D_{i}[/tex] and [tex]D_{j}[/tex], making them both subsets of [tex]D_{k}[/tex]. The statement "there is some k belongs I such that [tex]D_{i}[/tex] is a subset of [tex]D_{k}[/tex] and [tex]D_{j}[/tex] is a subset of [tex]D_{k}[/tex]" is a way to express this relationship between the sets.
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Help please on this one i need help
∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.
option A.
What is a supplementary?Supplementary angles are the two angles that sum up to 180 degrees.
That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.
From the given diagram we can form the following equation;
∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )
∠ AFE = 180 - ∠ AFB
∠ AFE = 180 - 78
∠ AFE = 102⁰.
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Two cars left Sunnyside City at the same time and traveled for 5 hours. The average speed of the faster car was 10 kilometers per hour greater than the average speed of the slower car. In the 5 hours, the two cars traveled a total of 550 kilometers
The velocity of the two cars are 50km/hr and 60km/h
What is velocity?Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.
let the faster car be A and slower car be B
V(A) = V(B) +10
S( A) = v × t
S(B) = v(b) × t
S( A) = 5( v(b) +10)
S(A) +S(B) = 550
5v(b) +50+5vb = 550
10v(b) = 550-50
v(b) = 500/10
v(b) = 50km/h
v(a) = 50 +10
v(a) = 60km/h
Therefore the velocity of the two cars are 50km/h and 60 km/h
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math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
first option
Step-by-step explanation:
differentiate using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{dt}[/tex] × [tex]\frac{dt}{dx}[/tex] = [tex]\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
y = t² + 4t
[tex]\frac{dy}{dt}[/tex] = 2t + 4
x = t - 3
[tex]\frac{dx}{dt}[/tex] = 1
then
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{2t+4}{1}[/tex] = 2t + 4
Answer:
2t + 4
Step-by-step explanation:
A parametric equation is one where x and y are defined separately in terms of a third variable (often the parameter t).
To find dy/dx from parametric equations, differentiate each equation with respect to the parameter t, then use the chain rule:
[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}}[/tex]
Differentiate the two parametric equations with respect to t:
[tex]x=t-3 \implies \dfrac{\text{d}x}{\text{d}t}=1[/tex]
[tex]y=t^2+4t \implies \dfrac{\text{d}y}{\text{d}t}=2t+4[/tex]
Use the chain rule to combine them:
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{\text{d}y}{\text{d}t} \times \dfrac{\text{d}t}{\text{d}x}\\\\&=(2t+4) \times \dfrac{1}{1}\\\\&=2t+4\end{aligned}[/tex]
Therefore:
[tex]\boxed{\dfrac{\text{d}y}{\text{d}x}=2t+4}[/tex]
Find the value of x
Will mark as brainliest if correct
Provide explanation.
I've been struggling a lot with interpreting what this problem wants me to find.
The plane departs an airport at 9:00 AM and flies 200 mph southwest. A second plane ldeparts the same airport at 9:30 AM and flies 320 mph northwest. Find the bearing of the second plane from the first one at 10:00 AM.
The reason: I've heard some people say a bearing has to be in one direction (north). I've also heard that a bearing has to be an acute angle and some insist there is an answer to this greater than 90º.
I drew out a diagram with a right triangle, legs of 200 and 160 (320 ÷ 2 for the half hour), separated my right triangle into two triangles with 45º angles, and went from there.
Where the hypotenuse and the 160 side meet, the angle is 51.34º. The 200 side makes a 38.66º angle (both came from arctan). I know for a fact there is an 83.66º angle that can be found.
Trouble is, I'm not sure if that's the actual bearing or not. Everything SEEMS correct there, but I've just heard so many other answers on this that I'm not sure who or what to believe!
Figured I'd see what everyone else thought. It's the "second from the first" that I'm struggling with semantically too. I can do the math just fine here.
Answer:
6.34°
Step-by-step explanation:
You want to know the bearing of a second plane from the first at 10 a.m. when the first leaves at 9 a.m. and flies 200 mph SW, while the second leaves at 9:30 a.m. and flies 320 mph NW.
LocationsThe first plane flies for an hour at 200 mph, so is 200 miles from the airport on a bearing of 180° + 45° west of south, or 225°.
The second plane flies for half an hour at 320 mph, so is 160 miles from the airport on a bearing of 360° -45° west of north, or 315°.
DirectionThe vector in the direction of the second plane from the first is found by subtracting the location of the first plane from the second:
vector of interest = (160∠315°) -(200∠225°)
A suitable calculator can tell you the difference is ...
vector of interest = 256∠6.34°
The second plane is on a bearing of 6.34° from the first.
__
Additional comment
You are correct that an angle of 83.66° is involved. That would be the measure of the direction vector counterclockwise from the +x axis. You want the bearing angle, measured clockwise from the +y axis (North), so the angle you're looking for is 90° -83.66° = 6.34°.
If you work enough of these problems, you will find that it doesn't matter how you measure the angles, as long as you do it consistently. The second attachment shows the arithmetic using distance∠bearing. The effect is to swap the x, and y coordinates so that they are (N, E) coordinates, rather than the usual (E, N) coordinates. This doesn't have to be confusing. A diagram usually helps.
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If sin 0 = 3/4 and angle 0 is in quadrant I, what is the exact value of tan20 in simplest radical form?
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Which of the following equations describes the
graph below?
Answer:
5x + 3y = - 15
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line
m = [tex]\frac{-5-0}{0-(-3)}[/tex] = [tex]\frac{-5}{0+3}[/tex] = - [tex]\frac{5}{3}[/tex]
the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5
y = - [tex]\frac{5}{3}[/tex] x - 5 ← in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 5x - 15 ( add 5x to both sides )
5x + 3y = - 15 ← in standard form
Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answer:
25000
Step-by-step explanation:
The amount of pollution entering the atmosphere varies directly as the number of people living in an area. If 35,000 people create 21,350 tons of pollutants, how many tons enter the atmosphere in a city with a population of 500,000?
Please Help
The city with a population of 500,000 would produce 305,000 tons of pollutants.
We have,
Let's call the unknown amount of pollutants in the second city "x".
According to the problem,
The amount of pollution is directly proportional to the number of people. This means that we can set up a proportion:
Pollution/number of people
= pollution/number of people
Using the values we know:
= 21350/35000
= x/500000
Simplifying:
0.61 = x/500000
To solve for x, we can cross-multiply:
0.61 x 500000 = x
x = 305000
Therefore,
The city with a population of 500,000 would produce 305,000 tons of pollutants.
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the permieter of object A is 94cm. What the value of x
The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The permieter of object A is 94cm
Assuming the object is a square
So, we have
4x = 94
Divide both sides by 4
So, we have
x = 94/4
Evaluate
x = 23.5
Hence, the value of x is 23.5cm
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12. An inequality is given, where r is a positive rational number.
r.9 <09/1
Jala:
bo
true?
Since r is a positive rational number, an inequality must also be true include the following: A.) q < 0.
What is a rational number?In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the square root of 11.
Next, we would solve the given inequality in order to determine all of the solutions that satisfies the variable q. This ultimately implies that, we would simplify the inequality by cancelling out the variable r as follows;
r × q/r < 0 (r is a positive rational number).
q < 0
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Complete Question:
An inequality is given, where r is a positive rational number.
r • q/r < 0
Which inequality must also be true?
A.) q < 0
B.) q > 0
C.) q < - r
D.) q/r < - r
Victoria wants to figure out if she can run faster than
an elephant. She reads that an elephant can run 100
yards in 20 seconds. She knows she can run 60 feet in
10 seconds. Victoria says, "Since 60/10 = 6 and 100/20 = 5,
my speed is faster than an elephant's!" Does her
statement make sense? Explain why or why not.
20
Answer and explanation:
Victoria's statement that her running speed is faster an elephant's does not make sense because it is based on the comparison of unlike units of measurement.
How the above conclusion is reached:Elephant's running speed = 100 yards in 20 seconds
= 5 yards per second (100 ÷ 20)
Units of Measurement:1 yard = 3 feet
5 yards = 15 feet (5 x 3)
The elephant's running speed = 15 feet per second.
Victoria's running speed = 60 feet in 10 seconds
= 6 feet per second (60 ÷ 10)
Thus, we conclude that the elephant's running speed is 15 feet per second, while Victoria does 6 feet per second, making her claim untrue.
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Classify the pair of angles. Then find the value of x.
Two angles share a side. One angle measures 4 x degrees and the other angle measures 2 x degrees. The sum of the angles is 90 degrees.
The pair of angles are complementary angles and the value of x is 15.
The pair of angles are complementary angles because their sum is equal to 90 degrees.
We can set up an equation based on the given information:
4x + 2x = 90
Simplifying this equation, we get:
6x = 90
Dividing both sides by 6, we get:
Value of x = 15
Therefore, the angle that measures 4x degrees is:
4x = 4(15) = 60 degrees
And the angle that measures 2x degrees is:
2x = 2(15) = 30 degrees
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Highschool geometry 8-12
The values of x and y in the given triangle are 41.4° and 114.5°
We have to values of x and y by using law of cosine
Using the Law of Cosines, we can find the values of x and y:
For angle x⁰:
cos(x⁰) = (a² + c² - b²) / (2ac)
cos(x⁰) = (15² + 18² - 12²) / (540)
cos(x⁰) = 0.75
x⁰ = cos⁻¹(0.75)
x⁰ = 41.4°
For angle y:
cos(A) = (b² + c² - a²) / (2bc)
cos(A) = (12² + 15² - 18²) / (360)
cos(A) = -0.4
A = cos⁻¹(-0.4)
y=114.5°
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In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
30% of the pennies in the roll were made before 1985.
To find the percentage of pennies made before 1985, we need to divide the number of pennies made before 1985 by the total number of pennies and then multiply by 100 to convert the answer into a percentage.
Number of pennies made before 1985 = 15
Total number of pennies = 50
Percentage of pennies made before 1985
= (15/50) x 100%
= 30%
Therefore, 30% of the pennies in the roll were made before 1985.
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HELP ME ASAP PLS. If 19,432 divided by x equals 48 with a remainder of 232. What is X?
The value of x, given that when it divides a number, there is a quotient and a remainder, is 400
How to find the value of x?To find the value of divisor, we can use a variant of the division algorithm formula :
Divisor = ( Dividend - Remainder ) / Quotient
x is the divisor
Dividend = 19, 432
Remainder = 232
Quotient = 48
This means that the value of x is:
x = ( 19, 432 - 232 ) / 48
x = 19, 200 / 48
x = 400
In conclusion, x is 400.
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 1.What did Ruskin write about Nocturne in Black and Gold: Falling Rocket?
2. How did Whistler defend his work in court? ( You need to mention the two paintings he brought with him to court.)
3. What was the outcome of the trial?
4. Why do you think the lawsuit was important in the history of art?
Two forces act at a point in the plane. the angles between the two forces are given. fidn the magnitude of the resultant force
The resultant between the two vectors is 21.17 lb
What is parallelogram law of vectors?Parallelogram law of vectors says that if two vectors acts on a point, the resultant of this vectors can be represented by the diagonal from the point of intersection.
R² = x²+y2+2xycos (tetha)
where x and y are the vectors
When x = 20.6 and y = 17.4
R² = 20.6²+17.4²+2(20.6)(17.4)cos 112.9
R² = 727.12+716.88cos 112.9
R² = 727.12 -278.95
R² = 448.17
R = √448.17
R = 21.17 lb
Therefore the resultant is 21.17lb
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determine the number and type of solutions
2x²-7x-30=0
The equation 2x² - 7x - 30 = 0 has two solutions: x = -5/2 and x = 6 and both solutions are real.
What is the number and type of solutions of the quadratic equation?Given the equation in the question:
2x² - 7x - 30 = 0
We can use the quadratic formula to to determine the number and type of solutions :
x = (-b±√(b² - 4ac)) / (2a)
2x² - 7x - 30 = 0
a = 2
b = -7
c = -30
Plugging in these values, we get:
x = (-b±√(b² - 4ac)) / (2a)
x = (-(-7) ± √((-7)² - ( 4 × 2 × -30))) / (2×2)
x = (7 ± √( 49 - ( -240))) / (4)
x = (7 ± √( 49 + 240)) / (4)
x = (7 ± √( 289)) / (4)
x = (7 ± 17) / 4
x = (7 - 17) / 4 and x = (7 + 17) / 4
x = -5/2 and x = 6
Therefore, the two solutions are x = -5/2 and x = 6.
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After paying a 20% deposit on a $300,000 home, David and Kennah finance the rest of the home cost and the closing fees for their home purchase with a 30-year loan for
$247,249 that charges an annual percentage rate of 3.94%. Calculate the total sum (NOT A SINGLE MONTHLY PAYMENT) of all monthly payments required to pay off this loan.
Round to the nearest whole number.
Answer: The total sum of all monthly payments required to pay off this loan is $410,932.
To calculate this, we need to first find the amount of the loan that is not covered by the deposit. The deposit is 20% of $300,000, or $60,000, so the remaining amount of the loan is $300,000 - $60,000 = $240,000.
Next, we need to calculate the monthly payment on the loan. We can use the formula for a fixed-payment loan to do this:
Payment = (Loan amount x Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
The monthly interest rate is the annual interest rate divided by 12, or 0.0394 / 12 = 0.003283.
The number of months is the number of years times 12, or 30 x 12 = 360.
Plugging these values into the formula gives:
Payment = ($247,249 x 0.003283) / (1 - (1 + 0.003283)^(-360)) = $1,151.80
Finally, we can find the total sum of all monthly payments by multiplying the monthly payment by the number of months:
Total payments = $1,151.80 x 360 = $410,932 (rounded to the nearest whole number).
Step-by-step explanation:
Pls tell me just the answer
The domain of the function g(x) is given as follows:
B. All values of x such that x ≥ 0.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
The function for this problem is defined as follows:
[tex]g(x) = \sqrt{8x}[/tex]
The square root function assumes values that are greater than or equals to zero, hence the domain of the function is obtained as follows:
8x ≥ 0.
x ≥ 0.
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A bag has 4 brown marbles and 12 yellow marbles. Half of the yellow marbles are made of glass. A marble is selected at random from the bag. What is the
probability that it is a yellow, glass marble?
Write your answer as a fraction in simplest form.
9
Answer: 3/8.
Step-by-step explanation: f 4 + 12 = 16, 12 / 2 = 6, 6 / 16 = 3 / 8
Simplify 6/15 x 55/10
2.2 in decimal form.
eleven fifths
The circumference of a circle is 43.96 m. What is the approximate area of this circle? Use 3.14 for TT.
O 153.86 m²
O 164.32 m²
O 138.03 m²
O 615.44 m²
Answer:
43.96 = 2πr
r = 21.98/π
A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters
A = 483.1204/3.14 = 153.86 square meters
