Rounded to the nearest minute, the answer is 12 minutes.
What do you mean by equation?The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.
The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.
To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:
h(t) = 10 sin(2πt/10) + 11
To find out when h(t) is greater than 19, we solve the inequality:
10 sin(2πt/10) + 11 > 19
Subtracting 11 from both sides, we get:
10 sin(2πt/10) > 8
Dividing by 10, we get:
sin(2πt/10) > 0.8
The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:
sin(2πt/10) = 0.8
sin(2πt/10) = -0.8
Using a calculator, we find that these equations have solutions at:
t = 1.167, 8.833, 3.5, 6.5
These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.
Therefore, the total time spent higher than 19 meters is:
(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes
Rounded to the nearest minute, the answer is 12 minutes.
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If the sum of 3 consecutive numbers is 114 find the numbers? WILL MARK BRAINLIEST!:)
If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.
The sum of the three numbers is:
x + (x+2) + (x+4) = 3x + 6
We know that the sum is 114, so we can set up the equation:
3x + 6 = 114
Subtracting 6 from both sides gives:
3x = 108
Dividing both sides by 3 gives:
x = 36
Therefore, the three consecutive even numbers are 36, 38, and 40.
Answer:
37, 38, 39
Step-by-step explanation:
let the 3 consecutive numbers be
n , n + 1 , n + 2
then summing and equating to 114
n + n + 1 + n + 2 = 114
3n + 3 = 114 ( subtract 3 from both sides )
3n = 111 ( divide both sides by 3 )
n = 37
n + 1 = 37 + 1 = 38
n + 2 = 37 + 2 = 39
the 3 consecutive numbers are 37 , 38 , 39
It costs $3. 75 to buy 3/4 pound of chopped walnuts. How much would 10 pounds of chopped walnuts cost?
Ten pounds of chopped walnuts would total cost $30.00. That is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.
1. 3/4 pound of chopped walnuts costs $3.75
2. 1 pound of chopped walnuts costs $5.00 (3.75 x 1.33)
3. 10 pounds of chopped walnuts costs $50.00 (5.00 x 10)
To calculate the cost of 10 pounds of chopped walnuts, we need to first calculate the cost of 1 pound of chopped walnuts. We know that 3/4 of a pound of chopped walnuts costs $3.75. To calculate the cost of 1 pound, we can multiply 3.75 by 1.33, which gives us the result of $5.00. We then multiply $5.00 by 10, which gives us the result of $50.00. Therefore, 10 pounds of chopped walnuts would cost $50.00. This is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.
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The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?
Answer:
Step-by-step explanation:d = 14t + 21t = 35t
So, after 3 hours, the distance between the boats will be:
d = 35 * 3 = 105 miles
Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.
Write the expression as a square monomial
0.16x^2y^2
Answer: (____)^2
Answer:
0.0256x^4y^4
Step-by-step explanation:
it takes half of a yard of ribbon to make a bow how many bows can be made with 7 yards of ribbon
Answer:
14 bows
Step-by-step explanation:
.5 yards is need for one bow if you have 7 yards you have 14(.5) yards
easier way a half goes into 7, 14 times since 14 divide by two is 7
Complete the table below treat each row has a different problem.
Important : the last row is sector area (a)
The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
What is sector?The sector is essentially a section of a circle, and it may be described using the following three criteria:
The area of a disc that is surrounded by two radii and an arc is known as a circular sector.
The circle is divided into the Major Sector and the Minor Sector by a sector.
The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.
Given that,
Central angle = [tex]\frac{\pi}{6}[/tex].
The arc length is given as:
l = α/360 (2πr)
Where, α is the central angle.
Substitute the value of central angle we have:
l = (π/6)/360 2πr
l = 2π²r/ 2160
The sector area is given as:
A = α/360 πr²
A = (π/6)/360 πr²
A = π²r²/ 2160
Similarly, the arc length is given as:
l = π/3
Substituting the value of l in arc length we have:
π/3 = α/360 (2πr)
α = 360(π)/ 6πr
α = 60/r
The sector area is given as:
A = α/360 πr²
A = (60/r) 360 πr²
A = πr/60
Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
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Rashida measured the length of a beam to be 16 3/4
feet. The actual length of the beam is 17 1/2
feet.
What is the percent error in Rashida's measurement?
The percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
What is meant by percent error?
The percent error is the distinction between the estimated value and the actual value in relation to the actual value. Percent errors show the magnitude of our measurement errors during an analysis procedure. We are getting close to the accepted or original value when the percent mistakes are smaller. The relative error is multiplied by 100 to get the percent error.
Given,
The actual length of beam = 17 and 1/2 feet = 17.5 feet
The measured length of beam = 16 and 3/4 feet = 16.75 feet
The formula to find the percent error is as follows:
Percent error = [tex]|\frac{Measured\ value - Actual\ value}{Actual\ value} | * 100[/tex]
= [tex]|\frac{16.75 - 17.5}{17.5} | * 100 =[/tex] 0.75/17.5 * 100 = 4.29%
Therefore the percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
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Here is some information about some temperatures in Great Britain in January.
Maximum Temp (°C) Minimum Temp (°C)
-8
-1
0
Glasgow
Cardiff
Exeter
b)
2
6
8
a) Which city is warmest in January?
How much colder is the minimum temperature in Glasgow
than the minimum temperature in Cardiff?
Exeter
c) Which city has the biggest difference between the maximum
and minimum temperatures?
°C
The diagram shows three identical coins of
radius 1 cm.
Calculate the shaded area in the middle
of the diagram.
Shape ABCD is a rectangle.
C is the point with coordinates (0,-8)
The equation of the straight line through A and B is 2y + x = 4. Find the equations of the lines
DC, AD and BC.
Equation of line DC is y = -1/2 x - 8
Equation of line AD is y = 2x + 2
Equation of line BC is y = 2x - 8
How to find the equation of the linesThe equation of the line 2y + x = 4 is arranged in slope intercept form to have
y = -x/2 + 2
The slope is -1/2
with a slope of -/2 and points (0, -8) line DC is written as
y - -8 = -1/2 (x - 0)
y + 8 = -1/2 x
y = -1/2 x - 8
Equation of line AD
line AD is a perpendicular line to line DC hence the slope is negative reciprocal of the slope of line DC
slope = 2
point A(0, 2) line AD is written as
y - 2 = 2 (x - 0)
y - 2 = 2x
y = 2x + 2
Equation of line BC
line BC is a parallel to line AD hence the slopes are equal
slope = 2
point C (0, -8) line AD is written as
y - - 8 = 2 (x - 0)
y + 8 = 2x
y = 2x - 8
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A customer paid goods on may 12 2018. The company invioced deliver goods
As per the discount, the customer will only need to pay P4,950 on May 12.
Discounts are a common practice in business transactions, where the seller offers a reduction in the price of goods or services as an incentive for the buyer to make a purchase.
The terms of the sale are as follows: 2/10, 1/15, n/30. This means that the customer is entitled to a 2% discount if they pay within 10 days, or a 1% discount if they pay within 15 days. Otherwise, the full amount is due within 30 days.
The customer makes a partial payment of P1,000, which means that they still owe P5,000. However, since the discount is only given upon full payment, the customer is not eligible for any discounts at this point.
Assuming that the customer pays the balance on May 12, they will have taken 11 days to make the payment. Since this is within the 15-day discount period, they are entitled to a 1% discount.
The calculation of the discount is as follows: P5,000 x 1% = P50. Therefore, the customer will only need to pay is calculated as,
=> P5,000 - P50 = P4,950
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Complete Question:
On May 1, RVQ Company sold goods for P6,000 on terms of 2/10, 1/15, n/30. Customer made a partial payment of P1,000 discounts are given only upon full payment of an account. The customer pays the balance on May 12, RVQ will receive on May 12 the amount of
Write an inequality to represent the tablespoons of ground cofee, g, mrs. Smith might use at this event
Approximately one full tablespoon of coffee powder is required for each 200 ml cup of coffee. We advise using seven teaspoons of ground coffee to produce a full litre of filter coffee at once.
To create coffee, coffee beans must first be roasted. Coffee is a dark-colored, bitter, and slightly acidic beverage that stimulates individuals due to its high caffeine content. In terms of sales, hot beverages have the largest market worldwide. The roasted beans are ground into tiny particles, frequently steeped in hot water, and then filtered to create a cup of coffee. Despite the fact that coffee is typically served hot, it is frequently served cold or iced. Unroasted green coffee beans are made by separating the seeds from the fruits of the Coffea plant. To produce a cup of coffee, the roasted beans are ground into tiny particles, regularly soaked in hot water, and then filtered. Coffee is commonly served cold or iced even though it is traditionally served hot.
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A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answers are below ----v
Step-by-step explanation:
1. Clockwise
2. 3
3. (y, -x)
4. (3x,3y)
Match each pair of equivalent values.
1.
square root of 16
2. square of 8
3. 42
4. 12
5. √4
6. √144
k
16
1
4
2
64
12
Answer:
1 -
12 - ?
4 - square root of 16
64 -
16 -
2.828 - square root of 8
Step-by-step explanation:"
I need more terms to match them.
solve the equations y=2x+56 and y=9x
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The equations are given below.
y = 2x + 56 ....1
y = 9x ....2
From equations 1 and 2, then we have
9x = 2x + 56
7x = 56
x = 8
Then the value of the variable 'y' is given as,
y = 9(8)
y = 72
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
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to decide which thing of coffee is better value-for-money calculate the price per gram of a 250 g of coffee for 2949 stands and a 750 grams of coffee for $69.99
The second option has the better value-for-money.
Which coffe has the better value-for-money?To find the price per gram, you need to take the quotient between the cost and the mass for each case.
The first brand costs $29.49 for 250 grams, then the cost is:
c = $29.49/250g = $0.12 per gram.
The other brand costs $69.99 for 750 grams, then the cost per gram is:
C = $69.99/750g = $0.09 per gram
We can see that the second option has the better vale-for-money.
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SOLVING EQUATIONS Solve the equation. Check your solution.
49. b+7+12=30
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle OPQ = (9x-19)^{\circ}m∠OPQ=(9x−19) ∘ , \text{m}\angle PNO = (2x+5)^{\circ}m∠PNO=(2x+5) ∘ , and \text{m}\angle NOP = (3x+16)^{\circ}m∠NOP=(3x+16) ∘. Find \text{m}\angle NOP. M∠NOP
The measure of angle NOP is found by solving an equation that is obtained by using the fact that the sum of the angles in a triangle is 180 degrees. The solution is m∠NOP to obtain the answer of 53.13 degrees.
In the problem, we are given a triangle NOP, where \overline{NP} is extended through point P to point Q. We are given the measures of three angles: m∠OPQ, m∠PNO, and m∠NOP.
We are asked to find the measure of angle NOP.To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we add up the measures of the three angles we know:
m∠OPQ + m∠PNO + m∠NOP = 180
We are given the measures of m∠OPQ, m∠PNO, and m∠NOP in terms of x. We substitute these values and get an equation in terms of x:
(9x-19) + (2x+5) + (3x+16) = 180
Simplifying the left side of the equation, we combine like terms:
14x + 2 = 180
We can then isolate x by subtracting 2 from both sides of the equation:
14x = 178
And then we can solve for x by dividing both sides of the equation by 14:
x = 12.71
Now that we know x, we can use it to find the measure of angle NOP, which is what we were asked to do. We substitute x = 12.71 into the equation for m∠NOP:
m∠NOP = 3x + 16 = 3(12.71) + 16 = 53.13
Therefore, the measure of angle NOP is 53.13 degrees.
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16.0 meters Question 9(Multiple Choice Worth 2 points) (09.06 MC) 01.6 meters Sara's Kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How much higher was Tayjen's kite
Tayjen's kite flew 5,860 centimeters in the air then Tayjen's kite flew 10.6 meters higher than Sara's kite.
What is BODMAS?
BODMAS is an acronym used to remember the order of operations in arithmetic. The acronym stands for:
B - Brackets (or Parentheses)
O - Orders (exponents and roots)
DM - Division and Multiplication (performed left to right)
AS - Addition and Subtraction (performed left to right)
BODMAS provides a set of rules that dictate the order in which mathematical operations should be performed in an expression that contains multiple operations. It is important to follow the order of operations to ensure that the expression is evaluated correctly and consistently. For example, in the expression 5 + 3 x 2, if we follow the BODMAS rule, we first perform the multiplication (3 x 2) and then the addition (5 + 6), giving us the answer of 11. If we were to perform the addition first, we would get a different answer (5 + 3 = 8, and 8 x 2 = 16), which would be incorrect.
To compare the height of Sara's kite, which is measured in meters, with the height of Tayjen's kite, which is measured in centimeters, we need to convert Tayjen's kite's height to meters.
To do that, we divide the height of Tayjen's kite by 100, since there are 100 centimeters in a meter:
5,860 centimeters ÷ 100 = 58.6 meters
Now we can compare the heights of the two kites:
58.6 meters - 48 meters = 10.6 meters
Therefore, Tayjen's kite flew 10.6 meters higher than Sara's kite.
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what is the value of y?
Answer:
y = 43
Step-by-step explanation:
47° , y and 90° lie on the straight line AB and sum to 180° , that is
47 + y + 90 = 180
y + 137 = 180 ( subtract 137 from both sides )
y = 43
(SAT Prep) Find the value of x.
A kangaroo hopped 3,5203,5203, comma, 520 yards to the lake with her baby in her pouch. She hopped the remaining 5,2805,2805, comma, 280 yards without her baby in her pouch.
How many miles did the kangaroo hop to the lake?
Answer:
so im a little confused 3,5203,5203, is not a proper number and there is not enought yards to make a full mile could you reword it?
Step-by-step explanation:
-Identity the measures of the reference angle for 521°.
-Identify the measure of the largest negative angle co-terminal with 521°
The reference angle would be 155 degrees.
What is reference angle?An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.
The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.
The reference angle is acute angle, it must be < 90°.
The terminal side lies in Quadrant II.
The positive measure is:
=180-25
=155°.
And the negative measure is:
= 155-360
= -205°.
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Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns.Is the value a parameter or a​ statistic?
A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.
In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.
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Complete Question
Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?
I need help. Please :(
Answer:
x-8
Step-by-step explanation:
the answer is x-8 correct answer x-8
In ΔLMN, m = 450 inches, � m∠M=74° and � m∠N=41°. Find the length of l, to the nearest 10th of an inch
In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )
In triangle LMN,
Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.
Measure of side m = 450 inches
Measure of ∠M = 74°
Measure of ∠N = 41°
Sum of all the angles in a triangle is equal to 180°
m ∠M + m ∠N + m ∠L = 180°
⇒ 74° + 41° + m ∠L = 180°
⇒ m ∠L = 180° - 115°
⇒ m ∠L = 65°
Using sine law of triangle we have,
sin L / l = sin M / m = sin N / n
⇒sin L / l = sin M / m
Substitute the value we get,
⇒ sin 65° / l = sin 74° / 450
⇒ l = sin 65° × ( 450 / sin 74°)
⇒ l = 0.9063 × ( 450 / 0.9613 )
⇒ l = 42.43 inches
⇒ l = 42.4 inches ( nearest tenth )
Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).
The above question is incomplete, the complete question is:
In ΔLMN, m = 450 inches, m ∠M=74° and m ∠N=41°. Find the length of l, to the nearest 10th of an inch.
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Answer: 424.3
Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and
m∠N=41°. Find the length of l, to the nearest 10th of an inch.
A.A.S.→Law of Sines
Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3
l=
sin74
450sin65
≈424.2742≈424.3
10x^2-x-2=0 solve by factoring
1. The sum of two rational numbers is 5
6
. If one of the numbers is 7
36
,
find the other number.
Answer:
So, the rational number is [tex]\frac{52}{12}[/tex] .
Step-by-step explanation:
Let x be the other number.
We know ,
[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]
To find x, we need to convert both to have a common denominator.
So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex] ,
[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]
After multiplication the fraction [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex] .
[tex]\frac{70}{360}[/tex]+ x = [tex]\frac{56}{10}[/tex]
Now we have common denominator of 360in both fraction,
Now,
we can simplify the equation ,
[tex]\frac{70}{360}[/tex] + x = [tex]\frac{56}{10}[/tex]
70 + 360x = 56 × 36
2520 + 360x = 2016
504 + 360x = 2016
360x = 1512
x = [tex]\frac{1512}{360}[/tex]
=[tex]\frac{52}{12}[/tex]
So, the rational number is [tex]\frac{52}{12}[/tex] .
John and Mary are building towers out of lego bricks. John used fewer than 18 bricks for his
tower. Mary used twice as many bricks as John. What is the greatest number of bricks Mary
could have used?
Answer:
34 bricks is the greatest amount Mary could have used
Step-by-step explanation:
Suppose your home is located at (0, 0) on a coordinate plane. The school is located 5 miles west of your home. The playground is 3 miles south of the school. What is the shortest distance, in miles, between your home and the playground? Round your answer to the nearest tenth
The shortest distance is 5.83 miles as we calculate this by distance formula.
A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:
PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
The school is located 5 miles west of your home the co ordinate is (-5,0)
The playground is 3 miles south of the school so co - ordinate is (0,-3)
shortest distance = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
√([tex]5^{2} +3^{2}[/tex]) = √34
=5.830 miles
And this Question also can be do by right angle triangle method
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