Answer:
The number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Step-by-step explanation:
We will use the sin function for the height of the Ferris wheel.
[tex]y=A\ sin(B(x+C))+D[/tex]
A = amplitude
C = phase shift
D = Vertical shift
2π/B = period
From the provided information:
A = 15/2 = 7.5 m
[tex]Period=2\\\\\frac{2\pi}{B}=2\\\\B=\pi[/tex]
Compute the Vertical shift as follows:
D = A + Distance of wheel from ground
= 7.5 + 1
= 8.5
The equation of height is:
[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]
Now at t = 0 the height is, h (t) = 1 m.
Compute the value of C as follows:
[tex]h(t)=7.5\cdot sin(\pi (t+C))+8.5[/tex]
[tex]1=7.5\cdot sin(\pi (0+C))+8.5\\\\-7.5=7.5\cdot sin\ \pi C\\\\sin\ \pi C=-1\\\\\pi C=sin^{-1}(-1)\\\\\pi C=\frac{3\pi}{2}\\\\C=\frac{3}{2}[/tex]
So, the complete equation of height is:
[tex]h(t)=7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5[/tex]
Compute the number of minutes of the ride that are spent higher than 15 meters above the ground as follows:
h (t) ≥ 15
[tex]h(t)=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))=6.5\\\\sin(\pi (t+\frac{3}{2}))=\frac{6.5}{7.5}\\\\(\pi (t+\frac{3}{2}))=sin^{-1}[\frac{13}{15}]\\\\\pi (t+\frac{3}{2})=60.074\\\\t+\frac{3}{2}=19.122\\\\t=17.622\\\\t\approx 18[/tex]
Thus, the number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.
Two competing gyms each offer childcare while parents work out. Gym A charges $9.00 per hour of childcare. Gym B charges $0.75 per 5 minutes of childcare.
Answer:
Gym A and B offers the same price
Step-by-step explanation:
[tex]\huge\bold\color{steelblue}{\colorbox{white}{Answer:}}[/tex]
Both of them has the same price
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each system of equations to its graph.
Answer:
1) y = 2x + 1
y = x + 2 Corresponding with the third graph
2) y = 3x
y = x + 3 Corresponds with the first graph
3) y = 2x - 2
y = x - 2
4) y = 2x + 3
y = x + 5
Likely correspond with the fourth graph
5) y = 4x + 2
y = 2x + 2 Corresponding with the second equation
Step-by-step explanation:
The groups of equation are;
1) y = 2x + 1
y = x + 2
The y-intercept of equation (1) = 1
The x-intercept of equation (1) = -1/2
The slope of equation (1) = 2
So at x = 0 y = 1 and at y = 0 x = -1/2 and at x = 2 y = 3
Corresponding with the third graph
The same can be shown with the second equation
2) y = 3x
y = x + 3
The y-intercept of equation (1) = 0
The x-intercept of equation (1) = 0
The slope of equation (1) = 3
So at x = 0 y = 0 and at x = 2 y = 6
Corresponds with the first graph
The same can be shown with the second equation
3) y = 2x - 2
y = x - 2
4) y = 2x + 3
y = x + 5
Likely correspond with the fourth graph
5) y = 4x + 2
y = 3x + 2
The y-intercept of equation (1) = 2
The x-intercept of equation (1) = -1/2
The slope of equation (1) = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
Corresponding with the second equation
The same can be shown with the second equation
We have to determine, The tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each system of equations to its graph.
The groups of equation are as follows;
The given system of equation is,
[tex]y = 2x + 1\\y = x + 2[/tex]
The y-intercept of equation = 1
The x-intercept of equation = -1/2
And The slope of equation = 2
Then,
At x = 0, y = 1
And at y = 0, x = -1/2
And at x = 2, y = 3
The first and second equation Corresponding with the third graph.
The given system of equation is,
[tex]y = 3x\\y = x + 3[/tex]
The y-intercept of equation = 0
The x-intercept of equation = 0
The slope of equation = 3
So at x = 0, y = 0 and at x = 2, y = 6
The equation Corresponds with the first graph
The given system of equation is,
[tex]y = 2x - 2\\y = x - 2[/tex]
The y-intercept of equation = -2
The x-intercept of equation = 2
The slope of equation = 2
So at x = 0, y = -2 and at x = 2, y = 0
The equation Corresponds with the first graph.
The given system of equation is,
[tex]y = 2x + 3\\y = x + 5[/tex]
The y-intercept of equation = 3
The x-intercept of equation = -2
The slope of equation = 2
So at x = 0, y = 3 and at x = -5, y = 0
The equation Corresponds with the fourth graph.
The given system of equation is,[tex]y = 4x + 2\\y = 3x + 2[/tex]
The y-intercept of equation = 2
The x-intercept of equation = -1/2
The slope of equation = 4
So at x = 0 y = 2 and at y = 0 x = -1/2 and at x = 0.5 y = 4
The equation Corresponding with the second graph.
For more information about Equation click the link given below.
https://brainly.com/question/17267403
describe fully the single transformation that takes shape A to shape B
Answer:
Divide by 2 or -2
Step-by-step explanation:
The edges lengths have decreased:
4/2=2
2/2=1
6/2=3
Transformation involves changing the position and size of a shape.
The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
From the figure, we have:
The side lengths of shape A are twice as large as the side lengths of shape BShape A can be rotated 180 degrees to map onto shape B, after dilation.So, the scale of dilation from shape A to B is:
[tex]\mathbf{Scale = \frac{1}{2}}[/tex]
Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
Read more about transformations at:
https://brainly.com/question/11707700
Solve for F:
-3/4f =5/4
If your answer is wrong you're getting blocked
Answer:
f = -5/3
Step-by-step explanation:
-3/4f = 5/4
Multiply both sides by -4/3.
-3/4f × -4/3 = 5/4 × -4/3
f = -20/12
f = -5/3
Please answer it now in two minutes
Answer:
47
Step-by-step explanation:
It's just aligning each number / line to each matching one.
Answer:
47 degrees
Step-by-step explanation:
The angle that matches the angle U is angle C
The measure of angle U is 47 degrees
Jessica can paint 12 rocks in 8 minutes. How many rocks can she paint in 48 minutes
Answer:
72 rocks.
Step-by-step explanation:
A "easier" way to find out the answer, is to find how much rocks Jessica paints in 1 minute.
Divide 12 with 8:
12/8 = 1.5
Next, multiply the number you got (1.5) with 48:
48 x 1.5 = 72
Jessica can paint 72 rocks in 48 minutes.
~
Answer:
72 rocks
Step-by-step explanation:
So let’s create the following ratio 12:8
The 12 is the amount of rocks and the 8 is the time in minutes.
So we have to find how many rocks she can paint in 48 minutes.
So we make the following ratio x:48.
So we need to find x the amount of rocks she can paint in 48 minutes.
So to find x we have to divide 48 by 8 = 6.
So if the ratio is x6 we can just do 12 * 6 which is 72.
So she can paint 72 rocks in48 minutes.
The number of kilometers traveled by a bus is represented by x. If a train traveled 200 kilometers farther than the bus, represent the number of kilometers traveled by the train.
Answer:
The train travelled x + 200 km
Answer:
The number of kilometres traveled by the bus is x kilometres. The train travels 200 kilometres farther than the bus, meaning that the train traveled x kilometres, and an additional 200 kilometres.
So, the number of kilometres traveled by the train would be the x km traveled by bus, plus 200 km; or x + 200 km.
Hope this helps!
Evaluate function from a graph i need help URGENT!
Answer:
-2
Step-by-step explanation:
Simply find the y-value when x = -5. Looking at the graph, we should get y = -2
Answer:
f(-5) = -2
Step-by-step explanation:
f(-5)
x=-5
Go x=-5 on the graph and see what the y value of the function is
The y value is -2
f(-5) = -2
There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities? There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
Answer:
Step-by-step explanation:
No of people using both gym and pool that is N( gup ) = 25
No of people using both track and pool that is N( tup ) = 30
No of people using both track and gym that is N( tug ) = 17
No of people using all that is N( gutup) = 6
No of people using two or three facilities
= 25+30+17- 2 x 6
= 60
Total no of people = 125
No of people using only one facility
= 125 - 60
= 65 .
Ratio of people using only one facility
= 65 / 125
.52
Required probability
= .52 .
probability that the person uses exactly one of the facilities
= .52
Bridget and Caroline win some money and share it in the ratio 7:3. Bridget gets £40 more than Caroline. How much did they get all together?
Answer:
£100
Step-by-step explanation:
if the ratio is 7:3, the difference between them is 7-3 . = 4.
So,
4x = £40
Now, calculate x
x = £10
Now,
we are able to calculate:
7x (Bridget's share) = £70
3x (Caroline's share) = £30
Sum = £100
Hope this helps.
Good Luck
Evaluate the expression. 56 Divided by (-8)
Answer:
-7
Step-by-step explanation:
Plz help!! Brainleist answer will be given if explanation is performed
Answer:
x = 76 roses
Step-by-step explanation:
Step 1: Define variables
x = # of roses
y = # of tulips
Step 2: Write systems of equations
x = 4y + 8
5x + 2y = 414
Step 3: Use Substitution
5(4y + 8) + 2y = 414
20y + 40 + 2y = 414
22y = 374
y = 17
Step 4: Plug in y to find x
x = 4(17) + 8
x = 68 + 8
x = 76
Answer:
x = 76
Step-by-step explanation:
x = Roses
y = Tulips
x = 4y + 8
5x + 2y = 414
5(4y + 8) + 2y = 414
20y + 40 + 2y = 414
22y = 374
y = 17
x = 4(17) + 8
x = 68 + 8
x = 76
Which arrow would most likely represent the phase change that involves the same amount of energy as arrow 1?
2
3
4
5
Answer:
arrow 4
Step-by-step explanation:
The amount of energy needed in the transformation from liquid to gas is equal to the gas to liquid transition.
Boiling is the mechanism by which a substance passes from the liquid phase to the gaseous form.
Like water diagram in phase:
Evaporisation is a method of phase shift in which the water transitions from a liquid to a gas (water vapour).
Condensation is the process of phase shift in which water transitions from a gas to a liquid, and the vapour becomes a cloud.
Answer:
4
Step-by-step explanation:
ya boy did the test
Help plzzzzzzzz do these two questions and I’ll mark Brainlynest
Answer:
Step-by-step explanation:
Q1: <B = 150 °
If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
8x-10 = 3x+90
5x=100 (subtract 3 from both sides)
x=20 (divide both sides by 5)
x = 20
<B= 3x +90
<B = 3 (20) +90
<B = 60 + 90
<B = 150
Q2: 62
An angles complement (not compliment, haha) is what the number that added to the angle equals 90°.
An angle is 34 more than its complement.
Let x represent the angle.
Let y represent its complement.
x= 34 +(90-x)
y= (90-x)
x + y = 90
34 + (90-x) + (90-x) =90
x= 62
Check the answer.
x= 34 more than complement.
62-34=28
62+28=90
Checked!
Words of encouragement:
Good luck!
what is the slope and y-intercept (−6,5),(-3,-3)
Answer:
Step-by-step explanation:
The values of the slope and y-intercept are
m =- 8/3
and b = − 11
could someone please answer 1 and 7:)
Answer:
1- %50
0.2008
Step-by-step explanation:
0.0008 1/5
(0.0008*5)+1=0.004+1=1.004/5
0.2008
→Answer:
1) 50%
7) 5.02
→Step-by-step explanation:
1)
Even if a coin is tossed many times and its still heads there is still 50% it is tails. It doesn't change.
7)
.0008 1/5 as a fraction.
So first we need to put .0008 into 1/5.
To do that we do .0008*5 which is .004.
So the fraction is now 1.004/5
To make that a decimal we do 1.004 divided by 5 which is 5.02
What is the sum of the series represented by:
Answer:
70
Step-by-step explanation:
n =2 ; 3n + 2 = 3*2 + 2 = 6 + 2 = 8
n = 3 ; 3n + 2 = 3*3 + 2 = 9 + 2 = 11
n =4 ; 3n+ 2 = 3*4 + 2 = 12 + 2 = 14
n= 5; 3n +2 = 3*5 + 2 = 15 + 2 = 17
n = 6; 3n + 2 = 3*6 + 2 = 18 + 2 = 20
∑ (3n + 2) = 8 + 11 + 14 + 17 + 20 = 70
Answer:
70
Step-by-step explanation:
TTT
Can someone attempt part A) for me, or at least explain it.
Step-by-step explanation:
if AB and CD are parallel then
90 -x +83 +46 = 180 --> x= 39
Answer:
x = 39
Step-by-step explanation:
Using the properties of parallel lines, then
x + 44 = 83 ( subtract 44 from both sides )
x = 39
Claire is designing a banner that will hang in her classroom. The length of one diagonal of the banner is 48 inches, and the sides are 25 inches long. Is the banner a square?
Answer: No the banner is not square.
Step-by-step explanation:
If it were square, the diagonal would be about 35.36 inches.
Pythagorean Theorem: a² + b² + = c²
?25² + 25² = 48² ?
625 + 625 ?=? 2304
1250 ≠ 2304
√1250 ≈ 35.3553
Answer:
The second option
Step-by-step explanation:
Source: trust me bro
Jayden measured a community college and made a scale drawing. He used the scale 22 millimeters : 9 meters. The actual length of a building at the college is 99 meters. How long is the building in the drawing?
Hey there! :)
Answer:
x = 242 mm.
Step-by-step explanation:
Begin by setting up a proportion between the actual college building and the drawing.
[tex]\frac{22mm}{9m} = \frac{x}{99m}[/tex]
Cross multiply:
99 × 22 = 9 × x
2178 = 9x
Divide both sides by 9:
2178/9 = 9x/9
x = 242 mm.
Someone..... I beg you!!! I will definitely mark you as a brainliest if you give me the correct answer!
Answer :
[tex]x = - 6 \\ x = 1[/tex]
Find the area of this triangle..
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the altitude.
h^2 = 9^2 - 6.4^2
h^2 = 40.04
h = 6.328
area = base * height/2
area = (2 * 6.4) * 6.328/2
area = 40.5 square units
Urgent pls. The diagram shows a parallelogram. Work out the area of the parallelogram. Give your answer to 2 significant figures.
Answer:
54.88 square cm
Step-by-step explanation:
If d1 and d2 are the diagonal of parallelogram and [tex]\alpha[/tex] is the angle between then
then its area is given by
area = d1*d2 sin [tex]\alpha[/tex]
given
in the problem
for one diagonal one part is 7cm
we know that diagonal intersects each other to divide each part of same diagonal equally.
hence if one part is of length 7 then other part is also of 7cm length
hence full length of this diagonal is 7+7 = 14cm
similarly full length of other diagonal is 4+4 = 8cm
now area of this parallelogram
area = d1*d2 sin [tex]\alpha[/tex] = 14*4 sin100
we know sin100 = 0.98
area = 56*0.98
area = 54.88
Thus, area of given parallelogram is 54.88 square cm.
Nick has fraction 1 over 2 cup of syrup. He uses fraction 1 over 6 cup of syrup to make a bowl of granola. How many bowls of granola can Nick make with fraction 1 over 2 cup of syrup?
Answer:
3
Step-by-step explanation:
1/2 is 3 times 1/6, because 3/1 [tex]\frac{3}{1} * \frac{1}{6} = \frac{3}{6}[/tex] and 3/6 is the same as 1/2. Thus, he can make 3 bowls of granola.
what number must you add to complete the square x^2+4x=5
Answer:
You should add 4 to both sides because that would make the left side a perfect square which is what you are intending to do when you complete the square.
Answer:
4
Step-by-step explanation:
x² + 4x = 5
b = 4
We need to add (b/2)² to both sides to complete the square.
(4/2)² = 4
x² + 4x + 4 = 5 + 4
x² + 4x + 4 = 9
(x + 2)² = 9
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)? (4 points)
If the plane is flying at an altitude of 21,000 feet, it is perpendicular to the observer's horizontal line of sight. Thus, I concluded that the given information be assigned to the attachment below.
Given -
( Observer at point O, plane flying at point P
( Plane at 55° angle to horizontal line of sight, altitude of 21,000 feet
The distance ( x ), is represented by the line segment OP, with which we have to determine the length of. Therefore we can conclude the following -
[tex]Sin( 55 ) = Altitude / Distance,\\Sin( 55 ) = 21,000 / x,\\----------------\\x = \frac{21,000}{Sin( 55 )},\\x = 21,000 / 0.81915204428\\\\x = ( About ) 25636 feet\\[/tex]
As you can see, the distance from the plane to the observer is about 25,636 ft!
Answer:
25,636 feet
Step-by-step explanation:
I took the test on FLVS and got 100%
What is the difference of the fractions below 5/2 - 3/5
Answer:
19/10 or 1 9/10
Step-by-step explanation:
you first put them into common denominators
so the least common denominator is 10
so 5/2= 25/10
and 3/5= 6/10
so 25/10 minus 6/10= 19/10
hope this helps
Answer:
1 9/10
Step-by-step explanation:
5/2 - 3/5
Get a common denominator of 10
5/2 *5/5 - 3/5 *2/2
25/10 - 6/10
19/10
10/10 + 9/10
1 9/10
Use the vertical line test to determine if the relation whose graph is provided is a function
Answer:
the graph represents a function.
Step-by-step explanation:
The vertical line test is a test to check if a graph represents a function.
To proceed, draw (imaginary) vertical lines through the entire domain of the graph. If any of the line intersects the graph at any value of x, then the graph does not represent a function.
Here it is not possible to draw a vertical line to intersect the red curve at any point, therefore the graph represents a function.
Answer:
Yes, the graph represents a function.
Step-by-step explanation:
The vertical line test is a test you can do to determine if a graph is a function. Basically, you draw straight vertical lines, and if it intersects with the line more than once, the graph is not a function.
This is because in a function, each input can only have one output.
So, we can draw vertical lines through the graph, and you'll find that each line will only intersect with the line once.
Based on this, the given graph would represent a function.
What is the next number in the pattern below?
3, 5, 9, 15, 23, ___
A.
31
B.
33
C.
35
D.
37
Answer:
the answer you are looking for is the letter B. 33
Which could be the graph of f(x) = |x - h| + k if h and k are both positive? On a coordinate plane, an absolute value graph has a vertex at (2, 1). On a coordinate plane, an absolute value graph has a vertex at (1, negative 4). On a coordinate plane, an absolute value graph has a vertex at (negative 3, 2). On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 5).
Answer:
Step-by-step explanation:
f(x) = |x - h| + k has a vertex at (h, k), where both h and k are positive. Only
"On a coordinate plane, an absolute value graph has a vertex at (2, 1)" satisfies those requirements.
The vertex of an absolute function is the minimum or the maximum point of the graph
The graph that could be [tex]f(x) = |x - h| + k[/tex] is (a) an absolute value graph has a vertex at (2, 1)
The function is given as:
[tex]f(x) = |x - h| + k[/tex]
And the coordinates of the vertex (h,k) are said to be positive.
From the list of given options, only the first option has both coordinates of the vertex to be positive i.e. (2,1)
Hence, the graph that could be [tex]f(x) = |x - h| + k[/tex] is (a)
Read more about absolute value functions at:
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