Maya travels [tex]4.19 feet/sec[/tex] faster than Kelly !
Difference in distance is : [tex]106.76-56.52 = 50.24 feet[/tex]
Step-by-step explanation:
Here we have , The Carousel in the National Mall has 4 rings of horses. Kelly is riding on the inner ring, which has a radius of 9 feet. Maya is riding on the outer ring, which is 8 feet farther out from the center than the inner ring is. We need to find In one rotation of the carousel, how much farther does Maya travel than Kelly . Let's find out:
Kelly is riding on the inner ring, which has a radius of 9 feet
Total distance traveled by Kelly is circumference of circle with radius 9 feet i.e.
⇒ [tex]Distance = 2\pi r[/tex]
⇒ [tex]Distance = 2(3.14) 9[/tex]
⇒ [tex]Distance = 56.52feet[/tex]
Maya is riding on the outer ring, which is 8 feet farther out from the center than the inner ring .
Total distance traveled by Maya is circumference of circle with radius (8+9=17) feet i.e.
⇒ [tex]Distance = 2\pi r[/tex]
⇒ [tex]Distance = 2(3.14) 17[/tex]
⇒ [tex]Distance = 106.76feet[/tex]
Therefore , Difference in distance is : [tex]106.76-56.52 = 50.24 feet[/tex]
Now , Speed of both is give by
⇒ [tex]Speed_k_e_l_l_y=\frac{56.52}{12} = 4.71 feet/sec[/tex] And ,
⇒ [tex]Speed_M_a_y_a=\frac{106.76}{12} = 8.90 feet/sec[/tex]
Faster Maya travels = 8.90-4.71 = 4.19
So , Maya travels [tex]4.19 feet/sec[/tex] faster than Kelly !
How long is AB please explain how you answered
Answer:
AB = [tex]4\sqrt{3}[/tex]
Step-by-step explanation:
30-60-90 theorem, usually x is used to explain but I will use y since x is in your problem, just substitute any variable for y
in a 30 -60 -90 triangle
the length opposite the 30 degrees is y
the length opposite the 60 degrees is y[tex]\sqrt{3}[/tex]
the length opposite the 90 degrees is 2y
since y[tex]\sqrt{3}[/tex] = 6
y = 6/[tex]\sqrt{3}[/tex]
rationalizing the denominator
[tex]\frac{6}{\sqrt{3} } *\frac{\sqrt{3}}{\sqrt{3}}[/tex] = [tex]\frac{6\sqrt{3} }{3} = 2\sqrt{3}[/tex]
if y = [tex]2\sqrt{3}[/tex], 2y = [tex]4\sqrt{3}[/tex]
Slope of the line passing through the points (-3,3) and (5,9)
Answer:
m=3/4
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
m=change in y/change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).
m=y2−y1/x2−x1
Substitute in the values of x and y into the equation to find the slope.
m=9−(3)/5−(−3)
Simplify.
m=3/4
The slope of the line passing through the points (-3,3) and (5,9) is 3/4
The formula for calculating the slope of a line is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Given the coordinate (-3,3) and (5,9), substitute the coordinates into the formula as shown below;
[tex]m=\frac{9-3}{5-(-3)}\\m=\frac{6}{5+3} \\m=\frac{6}{8}\\m=\frac{3}{4}[/tex]
Hence the slope of the line passing through the points (-3,3) and (5,9) is 3/4
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An airplane flies a constant speed of 720 km/hour.
e Ilies a constant speed of 720 km/hour. How far can it travel in 4 hours?
Answer:
2880 km
Step-by-step explanation:
(distance) = (rate)*(time).
Here we have:
(distance traveled) = (720 km/hr)(4 hrs) = 2880 km
What is 1099 divided by 54
Answer:
20.4
Step-by-step explanation:
20.35185185185185
You have to round it because in the hundredth place #5 is over 5 so, it rounds so the answer is 20.4.
Anything more than 5, 6, 7, 8, 9 ^ rounds.
you are asked to draw a triangle with side length of 10in,7in and 2in how many triangles like this can you draw
In dealing with surface area what is net?
Answer:
Step-by-step explanation:
A net is a drawing that shows the edges and faces of a solid in two dimensions. You can think of a net as what you would get if you “unfolded” a solid. ... The net is made of three congruent rectangles and two congruent equilateral triangles. The surface area is the sum of the areas of the five shapes.
Answer:
three-dimensional figure that represents a cylinder
Step-by-step explanation:
genas new outfit originally cost 75. she received 20% off how much did genas outfit cost
Answer:
$75 x .20=$15
75-15=$60
To find out how much Gena's outfit cost after the 20% discount, subtract the discount amount from the original price.
Explanation:To find out how much Gena's outfit cost after the 20% discount, we can use the formula:
The discount amount = original price x discount percentage
In this case, the discount amount = $75 x 0.20 = $15.
Therefore, Gena's outfit cost after the discount is:
Original price - discount amount = $75 - $15 = $60.
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An athlete plans to row upstream a distance of 6 kilometers and then return to his starting point in a total time of 4 hours. If the rate of the current is 2 km/hr, how fast should he row.
Answer:
3.5 kilometers per/hour
Step-by-step explanation:
6/4= 1.5
1.5+2=3.5
Which expression is equivalent to 30 divided by (3+x )
The expression 30 divided by (3+x) is already presented in its simplest form which is 30 / (3 + x).
The question which expression is equivalent to 30 divided by (3+x) pertains to the simplification of algebraic expressions, a basic concept in algebra. To solve or simplify this expression directly, it remains 30 / (3 + x), as there is no further simplification that can be done without additional context or constraints on the variable x. In algebra, expressions are simplified or manipulated using algebraic rules, but in this case, the expression is already in its most simplified form unless specific values are provided for x.
Cylinder is 9 inches high, and has a base with a radius of 5 inches. If you fill half the cylinder with water, what volume of water would that be?
What is the constant of proportionality in the equation, Y=4.50x?
Solution:
Given that,
[tex]y = 4.50x[/tex]
We have to find the constant of proportionality in the equation
We know that,
When y varies directly with x, then
[tex]y \propto x\\\\y = kx ---- eqn\ 1[/tex]
Where, "k" is constant of proportionality
From given,
y = 4.50x
Compare the above equation with eqn 1,
k = 4.50Thus, constant of proportionality in the equation y = 4.50x is 4.50
please help ty!
Alex swims in a 400-m freestyle competition at an average speed of 1 1/3 m/s. If he increases his average speed to 1.6 m/s, how much less time will he take?
50 seconds
Recall the equation
d=rt
Distance = rates times time.
We have a single distance, 400m
We have two different rates 1 1/3 m/s and 1.6 m/s
Let's calculate the time for each rate
t = d/r
t = 400/(1 1/3) = 300 seconds
t = 400/1.6 = 250 seconds
By increasing his average speed, Alex will reduce his time by
300-250 = 50 seconds.
I could use some help on this, please! :)
i dont wanna just give away the answer so heres a hint
#x stands for # X x or # times x
x is a vairable so the x+13 part will be #+13
figure out what the number is then if you still need help ask me again
15 points: can someone help me with this thank you. (all separate equations)
solve for y: 6x+3y=12
solve for k: 2p-k=3
solve for w: 6v-2w=10
Step-by-step explanation:
[tex]6x+3y=12\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x-6x+3y=12-6x\\\\3y=12-6x\qquad\text{divide both sides by 3}\\\\\dfrac{3y}{3}=\dfrac{12}{3}-\dfrac{6y}{3}\\\\\large\boxed{y=4-2y}\\\\===================[/tex]
[tex]2p-k=3\qquad\text{subtract}\ 2p\ \text{from both sides}\\\\2p-2p-k=3-2p\\\\-k=3-2p\qquad\text{change the signs}\\\\k=-3+2p\\\\\large\boxed{k=2p-3}\\\\===================[/tex]
[tex]6v-2w=10\qquad\text{subtract}\ 6v\ \text{from both sides}\\\\6v-6v-2w=10\\\\-2w=10-6v\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2w}{-2}=\dfrac{10}{-2}-\dfrac{6v}{-2}\\\\w=-5+3v\\\\\large\boxed{w=3v-5}\\\\===================[/tex]
linear, exponential, or neither?
Answer:
A) Linear
Step-by-step explanation:
For a linear relation, there will be a constant rate of change
For an exponential relationship, there will be a multiplicative rate of change.
For x-values, there is a constant difference of
[tex]d = 4 - - 3 = 11 - 4 = 18 - 11 = 7[/tex]
For the y-values, there is a constant difference of
[tex]b = 1 - - 3 = 5 - 1 = 9 - 5 = 4[/tex]
The rate of change of the function represented by the table is
[tex]m = \frac{change \: in \: y}{change \: in \: x} = \frac{4}{7} [/tex]
The equation can be derived as:
[tex]y + 3 = \frac{4}{7} (x + 3)[/tex]
This is a linear relationship
i need help ASAP please
Answer:
plot the first point on -3 3/4 which is 1 line to the left of -3 and the second on 3/2 which is 1 1/2 or 1 1 2/4 which is in the middle of 1 and 2
Step-by-step explanation:
Chase plans to buy a new car and determines he can budget $725 monthly for four years. His bank is
offering an 8.25% annual interest rate. What is the maximum loan he can afford to stay in his budget?
Use the formula, A – P/(1+) -11
, where P is the month payment, r is the annual interest rate, n is
the nur
the number of times interest is compounded in one year, and t is the number of years.
O A. $26,000.50
B. $29,555.50
C. $37.425.75
O
D. $52,500.00
Answer:
The correct answer is B. $ 29,555.50
Step-by-step explanation:
Let's calculate A, using the formula provided, this way:
A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ, where:
P is the month payment = 725
r is the monthly interest rate = 0.0825/12 = 0.006875
n is the the number of months to pay = 4 * 12 = 48
Replacing with the values we know, we have:
A = P * [(1 + r)ⁿ - 1]/r * (1 + r)ⁿ
A = 725 * [(1 +0.006875 )⁴⁸ - 1]/0.006875 * (1 +0.006875 )⁴⁸
A = 725 * 0.38939833/0.006875 * 1.38939833
A = 282.313789/0.009552114
A = 29,555.50
The correct answer is B. $ 29,555.50
The correct option is B. [tex]\$29555.50[/tex]. The maximum loan Chase can afford, while making monthly payments of [tex]\$725[/tex] for [tex]4[/tex] years at an [tex]8.25\%[/tex] annual interest rate.
Given:
Monthly payment [tex]\( P = $725 \)[/tex]
Annual interest rate [tex]\( r = 8.25\% \)[/tex] or [tex]\( 0.0825 \)[/tex] as a decimal
Number of payments per year [tex]\( n = 12 \)[/tex] (since monthly payments)
Number of years [tex]\( t = 4 \)[/tex]
The formula to calculate the present value [tex]\( A \)[/tex] of the loan is:
[tex]\[ A = P \times \frac{1 - (1 + \frac{r}{n})^{-nt}}{\frac{r}{n}} \][/tex]
Now, substitute the given values
[tex]\[ A = 725 \times \frac{1 - (1 + \frac{0.0825}{12})^{-12 \times 4}}{\frac{0.0825}{12}} \][/tex]
First, calculate [tex]\( \frac{r}{n} \)[/tex]
[tex]\[ \frac{0.0825}{12} = 0.006875 \][/tex]
Next, calculate [tex]\( (1 + \frac{r}{n})^{-nt} \)[/tex]
[tex]\[ (1 + 0.006875)^{-48} = 0.7221 \][/tex]
Now substitute these values into the formula for [tex]\( A \)[/tex]
[tex]\[ A = 725 \times \frac{1 - 0.7221}{0.006875} \][/tex]
[tex]\[ A = 725 \times \frac{0.2779}{0.006875} \][/tex]
[tex]\[ A = 725 \times 40.4218 \][/tex]
[tex]\[ A = 29555.50 \][/tex]
You jump off a 24 foot high cliff and your fall is modeled by the function:
h(t) = -16t2 + 8t + 24
When would you reach 16 feet above the water?
A. 1/4 second
B. 1 second
C. 1/2 second
D. 8 seconds
Answer: B) 1 second
Step-by-step explanation:
plug 16 (final height) into the equation given:
16=-16t^2+8t+24, and solve for t.
x will equal -1/2 or 1
disregard the negative because you can’t have time.
To reach 16 feet above the water, you would reach that height after approximately 1/2 second. Option C
To find when you would reach 16 feet above the water, set the function h(t) equal to 16 and solve for t:
-16t2 + 8t + 24 = 16
Combine like terms to get:
-16t2 + 8t + 8 = 0
Now, you can use the quadratic formula to solve for t:
t = (-b ± √(b2 - 4ac)) / (2a)
Plug in the values of a, b, and c from the equation:
t = (-8 ± √(82 - 4(-16)(8))) / (2(-16))
Simplify the expression inside the square root and solve for t to get the answer:
t ≈ 1/2 second
Option C
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Solve.
The answer must be a fraction. Solve by substituting.
Answer: x = -14/5
Step-by-step explanation: We shall begin by expanding the brackets for both sides of the equation
-2/3 (x + 2) = 1/6 (x + 6)
(-2x/3) -4/3 = (x/6) + 1
By collecting like terms we now have
(-2x/3) - (x/6) = 1 + 4/3
(-4x - x)/6 = 7/3
-5x/6 = 7/3
By cross multiplication we now have
-5x (3) = 7 (6)
-15x = 42
x = -(42/15) {simplify further by dividing the RHS by 3}
x = -14/5
Therefore x equals, minus fourteen over five (-14/5)
Ture or False
The median better represents
the data than the mean.
Answer:
False
Step-by-step explanation:
-10 + 20p + 6p = -16
Answer: p = 0.23
Step-by-step explanation:
-10 + 20p + 6p =-16
To find the value of p
Step 1: combine like terms
20p + 6p = -16 + 10
26p = 6
Divide both sides by 26
p = 6/26
P= 0.23
I hope this helps.
Answer:
p = -3/13
Explanation:
1. add 10 onto right side
2. combine like terms
3. divide by 26 to get p by itself
4. simplify
At which points does the graph of y=X(squared)+3x-18 intersect the x axis??
Step-by-step explanation:
Let A be the point at which the graph y=x²+3x-18
intersect the x-axis
As the graph intersects x-axis it's coordinate will be (x,0)
putting the value of y =0
x²+3x-18=0
x²+6x-3x-18=0
x(x+6)-3(x+6)=0
(x+6)(x-3)=0
x=-6, or,x=3
The point A maybe (-6,0) or (3,0)
The formula for the surface area of a cube is S 5 6x2
where x is the length of one side. Find the length of the
side of a cube with a surface area of 150 square inches.
Interpret the y-intercept of the graph
Answer:
answer is A
Step-by-step explanation:
769.5 Divided by 142.5=5.4???
Answer: True
Step-by-step explanation:
769.5/142.5 = 5.4
company 2 charges 4600$ for the first 550 feet of fence and 29 for each additional feet.find the cost if company 2 completes the job the total fence is 660
To calculate the total cost for a 660 feet fence by Company 2, subtract the initial 550 feet covered by the flat fee from the total length, multiply the additional feet by the per-foot cost, and add the flat fee to get the final cost, which is $7790.
Explanation:The student is asking about calculating the total cost for installing fencing, which involves initial fees and additional per unit costs. In this case, Company 2 charges a flat fee for the first 550 feet of fence and then an additional fee for each foot beyond that.
To find the total cost when Company 2 installs a fence of 660 feet, we first calculate the number of feet beyond the initial 550 feet. This is 660 - 550 = 110 feet. Then, we multiply the additional feet by the cost per additional foot: 110 feet x $29/foot = $3190.
Lastly, we add the initial flat fee of $4600 to the cost for the additional feet to get the total cost: $4600 + $3190 = $7790.
Find the value of 10! / (10-2) !
Answer:
The answer is 90
The value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have given an expression:
10!/(10 - 2)!
The sign '!' represents the factorial of the number.
As we know,
If factorial of any number can be evaluated:
n! = n(n - 1)(n - 2)(n - 3)(n - 4).......1
10! = 10×9×8×7×6×5×4×3×2×1
or
10! = 90(8!)
(10 - 2)! = 8!
= 90(8!)/(8)!
90
8! is canceled out from the numerator and denominator
Thus, the value of the 10!/(10 - 2)! is 90 after simplification of the factorial option (C) 90 is correct.
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evaluate expression 5a+b for A=6 and b=3
Answer:
33
Step-by-step explanation:
5a+b
if a = 6 and b = 3, substitute these values into the expression:
5a+b
= 5(6) + 3
= 30 + 3
= 33
Hope This Helps!!!!!!!!!!!!!!
Answer:
33
Step-by-step explanation:
5a+b
if a = 6 and b = 3, substitute these values into the expression:
5a+b
= 5(6) + 3
= 30 + 3
= 33
Divide the number in the thousands place by itself and then multiply the answer by 0. Write your answer in the tenths place
To divide the number in the thousands place by itself and then multiply the answer by 0, we can follow a simple process. Let's consider an example where the number in the thousands place is 5. Dividing 5 by 5 gives us 1. Multiplying 1 by 0 gives us 0, which is the answer in the tenths place.
Explanation:To divide the number in the thousands place by itself, we can consider a specific number for better understanding. Let's say the number in the thousands place is 5. Dividing 5 by 5 gives us 1. To find the answer in the tenths place, we need to multiply 1 by 0. The product of 1 and 0 is 0. Therefore, the answer in the tenths place is 0.
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six episodes of a tv series last total of five hours, How many minutes on average does an episode last
Step-by-step explanation:
[tex]5 \: hours \: = 5 \times 60 = 300 \: min \\ minutes \: per \: episode = \frac{300}{6} \\ = 50 \\ [/tex]
Hence, each episode lasted for 50 minutes on an average.
On average, each episode of the TV series lasts 50 minutes, calculated by converting the total viewing time of five hours to 300 minutes and dividing that by the number of episodes, which is six.
To calculate the average duration of an episode, we need to convert the total time of all episodes from hours to minutes and then divide by the number of episodes.
There are 60 minutes in one hour, so five hours equates to 300 minutes (5 hours × 60 minutes/hour = 300 minutes). With six episodes in total, we divide the total minutes by the number of episodes to find the average length of one episode.
300 minutes / 6 episodes = 50 minutes per episode.
Therefore, on average, each episode of the TV series lasts 50 minutes.