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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Determine the better deal.
6 candy bars for $7.55 7 candy bars for $8.33 9 candy bars for $10.45
Answer:
Step-by-step explanation:
$7.75/6= $1.29
$8.33/7= $1.19
$10.45/9= $1.16
The better deal in the 9 candy bars for $10.45 because its only $1.16 PER candy bar.
both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.?
At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.
(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:
f'(t) = 400 + 200cos(πt/12).
At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.
(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:
g'(t) = 200 - 200cos(πt/12).
At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.
the complete question is :
both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?
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The point A(2, 1) is a vertex of a square ABCD. M(5, 1) is the point of intersection of the
diagonals of the square. Find the coordinates of B, C and D. (Remember: The diagonals
of a square are equal in length and bisect each other at right angles.)
pls give serious answers!!
Answer:
Step-by-step explanation:
Since M is the point of intersection of the diagonals of the square, it is also the midpoint of both diagonals. This means that AM is equal to half the length of a side of the square and also bisects the angle formed by the two sides that it connects.
Let's call the length of a side of the square s. Then, the distance AM can be found using the Pythagorean theorem:
AM = sqrt((5 - 2)^2 + (1 - 1)^2) = sqrt(3^2 + 0^2) = sqrt(9) = 3
So, the length of a side of the square is 2 * AM = 2 * 3 = 6.
Next, we can use the length of a side and the coordinates of A to find the coordinates of B. Since AB is a side of the square and is 6 units long, we can find B by moving 6 units to the right of A:
B = (2 + 6, 1) = (8, 1)
We can also find the coordinates of C by moving 6 units up and 6 units to the left of A:
C = (2 - 6, 1 + 6) = (-4, 7)
Finally, we can find the coordinates of D by moving 6 units down and 6 units to the right of A:
D = (2 + 6, 1 - 6) = (8, -5)
So, the coordinates of the other vertices of the square are B = (8, 1), C = (-4, 7), and D = (8, -5).
This year, Clean Machine used 4,508.8 gallons of soap. That is 16.5% less than last year, How many gallons of soap did the company use last year? (round your answer to the nearest tenth)
The soap used by the machine last year is 5399.76 gallons.
What are percentages?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."
Let the soap used last year = x.
Then, according to the given condition:
4,508.8 = x (1 - 16.5%)
4,508.8 = x (83.5/100)
x = 4,508.8(100) / 83.5
x = 5399.76
Hence, the soap used by the machine last year is 5399.76 gallons.
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please help with q26 and show working
Answer:
13 square units
Step-by-step explanation:
The composite figure can be decomposed into
2 semicircles each of diameter 3
1 rectangle of height 1 and length 5
1 square of side 1
Radius of each semicircle = 3/2 = 1.5 units
Area of a semicircle of radius r = 1/2 area of circle of radius r = 1/2 x π x r²
Two semicircles make a circle
So area of the two semicircles = 2 x (1/2 x π x r²) = πr² = π x 1.5²
= 2.25π = 7.07
= 7 square units rounded to nearest whole number
Area of the rectangle = width x length = 1 x 5 = 5 square units
Area of square of side 1 = 1 x 1 = 1 square unit
Total area of shaded area = 7 + 5 + 1 = 13 square units
of the following is the correct label to show volume?
O inches
O ft²
O m³
O square centimeters
Answer:
О m³ (cubic meters)
Step-by-step explanation:
The volume formula is length * width * height
Example:
volume = 3m * 5m * 4m
volume = 60m³
The solution is, О m³ (cubic meters), is the correct label to show volume.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
to find the correct label to show volume.
now, we know that,
The volume formula is length * width * height
as we know that,
the standard unit for length is meter (m).
now, we have,
length has unit m
width (= length) has unit m
and, height (=length) has unit m
so, we get,
Volume = length * width * height
= m * m* m (as unit)
= m³
Example:
volume = 3m * 5m * 4m
volume = 60m³
Hence, The solution is, О m³ (cubic meters), is the correct label to show volume.
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I need Help i Have a C in my class
Answer:B
Step-by-step explanation:
R^2=Q^2-P^2
R^2=2025
R=45
Answer:
b) 45cm
Step-by-step explanation:
by pythagoras theorem:
R² = P² - Q²
R² = 53² - 28² = 2809 - 784
R² = 2025
R = √2025
R = 45cm
Hope this helps!
Chose the expression that is equivalent to the expression below 3(2x-1)
Answer: 6x - 3
Step-by-step explanation:
I believe this question is asking you to expand the equation
Distribute the 3 to both terms on the inside to get: 3(2x -1) = 6x-3
Answer:
Step-by-step explanation:
i believe its 5x?
sorry if im wrong but i times 3 x 2 then 6 -1 or you can do 3 x 2 then 3 x -1 to get 6x and -3
Linda wants new carpeting for her bedroom her bedroom is a 75m by 50m rectangle if carpeting cost AED 12 per square meters how much will it cost to lay carpet for her entire bedroom?
(please answer as soon as possible i need this answer) thank you
If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.
Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:
Area = length x width = 75 meters x 50 meters = 3750 square meters
Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:
Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter
Multiplying the area by the cost per square meter gives us:
Total cost = AED 45,000
Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
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Can someone help me with this
Answer: 4(9a-4) and x = 18
Step-by-step explanation:
36a - 16 a common factor in this is 4 so if we factor out 4 we would get
4(9a-4)
1/2x - 7 = 1/3(x-12) we would distribute out the 1/3 so 1/3x and 1/3 x - 12 which would simply into 4
1/2x - 7 = 1/3x - 4 get the x's into one side so subtract 1/3x and add 7 on both sides
1/2x - 1/3x = 3 --- multiply 1/2x with 3/3 and 1/3x with 2/2
3/6x - 2/6x = 3
1/6x = 3 --- isolate x by multiplying 6 on both sides
x = 18
f(x) = -2x
g(x) = 8x² - 5x+7
Find (f g)(x).
O-16x³5x+7
O 16x4 + 10x³ - 14x²
O-16x² + 10x - 14x
O-16x³ + 10x² - 14x
Answer:
-16x² + 10x - 14.
Step-by-step explanation:
To find the composition of two functions, (f g)(x), we first evaluate g(x) and then substitute the result into f(x).
So, let's first evaluate g(x):
g(x) = 8x² - 5x + 7
Next, substitute g(x) into f(x):
(f g)(x) = f(g(x)) = f(8x² - 5x + 7) = -2(8x² - 5x + 7) = -16x² + 10x - 14
Therefore, (f g)(x) = -16x² + 10x - 14.
A beaker contains 1/14 pints of a chemical. A scientist pours the chemical out of the beaker until only 3 fluid ounces remain. How many fluid ounces of the chemical did the scientist pour out of the beaker?
The scientist poured 17 ounces of chemical out of the beaker, calculated from the total and remaining amount of chemical.
We are aware of the conversion unit that 1 pint is equal to 16 fluid ounces. So, total amount of chemical in the beaker is -
Chemical in beaker in points = 5/4
Chemical in beaker in ounces = 16×1/14
Chemical in beaker = 20 ounces
Now, the expression to calculate poured amount of chemical will be -
Total amount = poured chemical + remaining chemical
20 = poured chemical + 3
Poured chemical = 20 - 3
Performing subtraction on Right Hand Side of the equation
Poured chemical = 17 ounces
Therefore, 17 ounces of chemical was poured.
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The correct question is -
A beaker contains 1 1/4 pints of a chemical. A scientist pours the chemical out of the beaker until only 3 fluid ounces remain. How many fluid ounces of the chemical did the scientist pour out of the beaker?
Find the number that makes the ratio equivalent to 63:9.
7:
Pls help thank you will mark the Brainliest
the first choice is the right answer
please check my working for guidance
5. To ship a package, UPS charges $4 for the first pound and $0.50 for each additional
pound. FedEx charges $6 for the first pound and $0.40 for each additional pound. How
many pounds will it take for UPS and FedEx to charge the same?
It will take 20 pounds for both charges to be the same.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
To ship a package,
UPS charges $4 for the first pound and $0.50 for each additional pound.
FedEx charges $6 for the first pound and $0.40 for each additional pound.
These can be written in the linear equation form as,
Let p be the pound charges by both UPS and FedEx,
then, 4+0.50p-------(1)
6+0.40p-----(2)
When the charges are same, (1)=(2)
4+0.50p = 6+0.40p
⇒0.10p=2
⇒p=20
Hence, this means that, it will take 20 pounds for both charges to be the same.
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Find the distance between P(6,3) and (8,7)
Answer:[tex]\sqrt{6}[/tex]
Step-by-step explanation:
The distance between 2 points is given by:
[tex]\sqrt{(x2-x1)+(y2-y1)}[/tex]
Let (6,3) be (x1, y1) and (8,7) (x2,y2).
=[tex]\sqrt{(8-6)+(7-3)}[/tex]
=[tex]\sqrt{2+4}[/tex]
=[tex]\sqrt{6}[/tex]
Hope this helps :)
[tex]\sqrt{p^1^2-16p^6+80}[/tex]
A pic down below is given:
Use the net to find the surface area of the prism.
5 in.
12 in.
13 in.
8 in.
Step-by-step explanation:
Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.
The surface area of the solid is the sum of all of the areas of its faces.
The area of a right triangle is a well-known formula. You should already know this.
I have 2 questions. 1.If the Percent of Discount is 80% and the Sale Price is $90 then what is the Original Price? 2. If the Percent of Discount is 15% and the Sale Price is $146.54 then what is the Original Price? HELP ME PLEASE!!???
The requried solutions are as follows,
(1) the original price is $450. (2) the original price is $172.40.
Sale price is defined as the price of a product marked including of various price cut such as discounts.
Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)
Sale price = Original price - Discount
$90 = x - 0.8x
Simplifying the right-hand side:
$90 = 0.2x
x = $450
Therefore, the original price is $450.
If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:
Sale price = Original price - Discount
$146.54 = x - 0.15x
Simplifying the right-hand side:
$146.54 = 0.85x
x = $172.40
Therefore, the original price is $172.40.
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Determine the period.
10
Check the picture below.
Jennifer's dining room is 10 feet wide and 23 feet long. Jennifer wants to install wooden trim around the top of the room. The trim costs $0.85 per foot. How much will it cost Jennifer to buy enough trim?
Answer:
Step-by-step explanation:
Given room looks like a rectangular room.Let w be the wide and l be long of the rectangular room respectively.Given,w=10 feet and l=24 feet.
we know area of the rectangular room= l*w
So,area=10*23
area=230 sq.feet
Given,cost of trim=$0.85 per foot
So,total cost =230* 0.85
=195.5
So,Jennifer charges $195.5 to buy enough
surface area of a rectangular prism with sides of 5,4,3,3.7
Surface area of a rectangular prism is 444 square unit.
A rectangular prism is a three-dimensional shape with six faces (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular. As an outcome, there really are three sets of exactly equal faces here. A rectangular prism is also recognized as a cuboid due to its shape.
The sides of a rectangular prism is 5, 4, 3, 3.7.
This can be calculated by multiplying each of the side lengths together and then multiplying that result by two.
Surface area of a rectangular prism = 2 × (5 × 4 × 3 × 3.7)
Surface area of a rectangular prism = 2 × 222
Surface area of a rectangular prism = 444 square unit
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Volume of right circular cylinder if radius is 7 and hight is 1. 5
The volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.
The volume of a right circular cylinder can be calculated using the formula:
V = π * r² * h
Where r is the radius and h is the height of the cylinder.
Plugging in the values for r and h, we get:
V = π * 7² * 1.5
V = π * 49 * 1.5
V = 73.5 * 1.5
Therefore, V = 110.25
So the volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.
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Mr. Titus travels from Charlotte to New York City and back 12 times each year. The total distance for each round trip is 623 miles. What is the total number of miles Mr. Titus travels from Charlotte to New York City and back each year? Enter your answer in the box.
Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.
The total distance will be calculated as:-
Distance = 12 x 623
Distance = 7476 miles
Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.
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Complete the following proof.
Answer:
See proof below
Step-by-step explanation:
We will use the SAS condition for congruency of two triangles
SAS (Side-Angle-Side)
If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.
In the two triangles ΔHIK and ΔJIK we have
m∠4 = m∠3 (given)
HK ≅ KJ
IK is the common side
So the two sides HK and IK are equal and the included angles ∠4 and ∠3 are also equal
So by SAS, the two triangles are equal
So m∠2 = m∠1
which means IK bisects ∠HIK
What quantity must be added to 3-7x+4 to obtain - +4x-2?
A-4x2+3x+2
B.-412 + 11x + 2
C.-4x² + 11x-6
D. 2x²-3x+2
E. 2x²-3x+6
Answer:
Step-by-step explanation: (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient
Hope it helps =}
Answer:
b
Step-by-step explanation:
A student has completed 3 tests in biology class. How many points above her present test average must she
score on the fourth test in order to raise her test average 4 points?
OA. 7
OB. 9
OC. 12
O D. 16
OE. 20
The student must she score on the fourth test in order to raise her test average 4 points is 4 points.
What is average?An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,
Let the required point be x,
According to question,
x+4×3 / (3+1) = 4
x+12 = 16
x = 4
Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.
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The red triangle is a dilation of the blue triangle, with scale factor, k =
1.5.
Use the hotspots to fill in the missing measurements and similarity
statement.
R
20 cm
44°
S
Vide
26 cm
scale factor, k =
15
N
ARSTA
ange
1.5
57 cm
side
44°
121°
L
M
1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.
What is transformation?Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.
Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.
As a result, the red triangle is a dilation of the blue triangle.
When triangle is dilated the angles remain the same. Thus,
1. 121 degree.
2. 15 degree.
The side of the dilated triangle increases by scale factor. Here, 1.5, thus:
3. LM = (20)(1.5) = 30
4. MN = 26(1.5) = 39
5. RT = 57/1.5 = 38
6. Triangle RST is congruent to triangle LMN.
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$200 invested at 5% compounded quarterly after a period of 3 years
Given:-
[tex] \rm{Principal= \bold{200}}[/tex][tex] \rm{Time = \bold 3}[/tex][tex] \rm{Intrest \: Rate = \bold 5}[/tex]By using formula:-
[tex]\boxed { \color{green}\rm{Simple \: interest= \frac{Principal×Time×Rate}{100}}}[/tex]Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{2\cancel{00}×3×5}{1\cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI=2×3×5}[/tex][tex] \: [/tex]
[tex] \boxed { \rm \red{ SI = 30}}[/tex][tex] \: [/tex]
hope it helps! :)
Help me asap it is due soon pls
The solution of the system of equation y - 10 = 2x and 1/2 y = x + 5 is
A. (0, 10)How to solve the simultaneous equationThe simultaneous equation is solved by substitution method as follows
y - 10 = 2x and
1/2 y = x + 5
Isolate y in the first equation to get
y = 2x + 10
substitute y in 1/2 y = x + 5
1/2 (2x + 10) = x + 5
x + 5 = x + 5
x = 0
substitute x = 0 into y = 2x + 10
y = 2(0) + 10
y = 10
hence the solution is (0, 10)
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There are 50 teachers in a school. 40% of them are women and the rest are men. If 70% of the women and 80% of the men are married, find the number of unmarried teachers in the school.
