A and B share the cost in a ratio of 3:2. A pays £125 how much does b pay?
To solve this problem, we can set up proportion, which is two equivalent ratios. In this case, we are using the ratio of A to B to figure out the amount that B pays using our value for A. We are allowing x to represent the unknown value for the B payment. This is modeled below:
3/2 = £125/x
To simplify, we can perform cross-multiplication. This means multiplying the numerator of one fraction by the denominator of the other and setting it equal to the product of the other numerator and denominator. This is modeled below:
(125)(2) = (3)(x)
Next, we can simplify the equation by performing the multiplication on both sides of the equation.
250 = 3x
Finally, we should divide both sides by 3 to get our unknown variable x alone on the right side of the equation.
x = 83.33
Therefore, B costs £83.33.
Hope this helps!
A twelve inch candle and an 18 inch candle are lit at 6pm. The 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Let h represent the number of hours.
Answer:
At 10 PM both candles will be same height.
Step-by-step explanation:
Let h represent the number of hours.
We have twelve inch candle and an 18 inch candle are lit at 6pm and the 12-in. candle burns 0.5 inches every hour. The 18 inch candle burns 2 inch every hour.
Height 18 inch candle after h hours, = 18 - 2h
Height 12 inch candle after h hours, = 12 - 0.5h
At same height we have
18 - 2h = 12 - 0.5h
1.5 h = 18 - 12
h = 4 hours.
Time = 6 PM + 4 hours = 10 PM
At 10 PM both candles will be same height.
Answer:
At 10 PM, both the candles will be of same height.
Step-by-step explanation:
Two candles are lit at 6 PM.
The length of candles is 12 inch and 18 inch.
The rate of burning of 12 inch candle is 0.5 inch per hour.
The rate of burning of 18 inch candle is 2 inch per hour.
Let [tex]h[/tex] represents the number of hours of burning.
In [tex]h[/tex] hours, the remaining length of the 12 inch candle will be,
[tex]l_1=12-0.5\times h[/tex]
In [tex]h[/tex] hours, the remaining length of the 18 inch candle will be,
[tex]l_2=18-2\times h[/tex]
Now, it is required to find the time at which the length of both the candles will be same.
So, the time [tex]h[/tex] in hours will be,
[tex]l_1=l_2\\12-0.5h=18-2h\\1.5h=6\\h=4\rm hour[/tex]
So, after 4 hours, both the candles will be of same length.
Therefore, the time will be [tex]6+4=10[/tex] PM. At 10 PM, both the candles will be of same height.
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C) the function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold, and f(x) is the amount of profit. part
a.determine the vertex. what does this calculation mean in the context of the problem? part
b.determine the x-intercepts. what do these values mean in the context of the problem?
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
A. 2
B. 12
C. 13
D. 1
m 2 = 40°, m 4 = 150°, m 3 =
The answer is 110° Hope this helps!
The coordinate grid shows the plot of four equations. A coordinate plane is shown with four lines graphed. Line A crosses the x axis at negative 3.2 and has a slope of 4. Line B crosses the x axis at 3 and the y axis at 6. Line C crosses the x axis at 1.5 and the y axis at negative 6. Line D crosses the x axis at negative 3 and the y axis at 3. Which set of equations has (2, 2) as its solution? A and D B and D A and C B and C
To convert a distance of 1.25 miles to feet, which ratio could you multiply by? Remember that 1 mile = 5280 feet.
The negative sign can be read as "the opposite of." true or false
Answer:
true
Step-by-step explanation:
which function is a quadratic function?
Answer:
y = -2x² - x is quadratic function.
Step-by-step explanation:
Given : Function .
To find : Which function is a quadratic function.
Solution : We have given that functions .
Quadratic function: A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers.
We can see from given options
y = -2x² - x in form of f(x) = ax² + bx + c,
Where, a = -2 , b = -1 c = 0
Therefore, y = -2x² - x is quadratic function.
Jack has a collection of new nickels and quarters. He has a total of 50 coins worth $10.30. How many of each coin does he have?
The ratio of gold charms to silver charms is 1:3. Which statement does not describe the relationship?
Answer: A
Step-by-step explanation:
Danielle built a ramp with a stopping block at the bottom for her scout troop’s pinewood derby. She wants to paint the top and sides of the ramp. Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Did Danielle calculate the area correctly? If not, what was her mistake?
A. Yes, Danielle calculated the area correctly.
B. No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
C. No, Danielle needs to add 1 triangle to the ramp and remove 1 rectangle from the block.
D. No, Danielle needs to remove 1 triangle from the ramp and add 1 rectangle to the block.
Answer:
Actually its b).
Step-by-step explanation:
She only wants to paint the top and sides of the ramp therefore you will have to take off the bottom parts of the ramps aka b).
No, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area. The space inside the perimeter or limit of a closed shape is referred to as the "area".
Danielle calculated the area by adding the areas of 2 triangular faces and 3 rectangular faces from the ramp and 6 rectangular faces from the block.
Danielle calculated some extra Areas.
As, per the discussion Danielle do not need to calculate the part ramp and block that coincides.
Thus, Danielle needs to remove 1 rectangle from the ramp and 1 rectangle from the block.
Learn more about Area here:
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please help with this vertical asymptote of rational functions problem
A. x= -5
B. x=0
C. x= -2
D. x= 5
Divide 420 in the ratio of 2:1
Why are jobs at food stands and restaurants good for college students?
Answer:
The reason a university student is looking for work is that he needs an extra salary income.
Step-by-step explanation:
It is a way to get a salary without overloading tasks.
In addition to that many times, they are given the time to study and work because there are very flexible schedules.
The university student gets used to the need to work for a fixed salary.
In addition, many university students need income to be able to pay the value of the semester or any project necessary for the university.
ANY HELP WOULD BE REALLY APPRECIATED
Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by h(t) = −16t^2 + 79t + 6, where h is in feet and t is in seconds. The height of Andre's baseball is given by the graph below (it's the attached image). Brett claims that his baseball went higher than Andre's, and Andre says that his baseball went higher.
1. Who is right? Fill out the table below to justify your answer. Approximate
when necessary (table is second attached image).
1. Brett was right because her baseball reached a maximum height of 103.52 feet.
2. A table that justifies Brett's claim is shown below.
In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the maximum value of Brett's quadratic function can be determined by finding the axis of symmetry;
Axis of symmetry, x = -b/2a
[tex]h(t) = -16t^2 + 79t + 6[/tex]
where:
a = -16, b = 79, and c = 6.
By substituting the values of a and b into the formula, we have;
Axis of symmetry, x = -79/2(-16)
Axis of symmetry, x = 79/32 = 2.46875.
Now, we can determine the maximum value (vertex) as follows;
[tex]h(t) = -16t^2 + 79t + 6\\\\h(2.46875) = -16(2.46875)^2 + 79(2.46875) + 6[/tex]
h(2.46875) = 103.52 feet.
Based on the graph, we can logically deduce that the maximum height attained by Andre's baseball was below 80 feet. Hence, Brett was right.
Lastly, we would complete the table as follows;
t Brett Andre
0 6 6
1 69 58
2 100 78
3 99 67
4 66 6
5 0
In conlusion, we can logically deduce that Brett was right because her baseball reach a maximum height of 103.52 feet, which was greater than Andre's.
A rectangular room has an area of 315 square feet. the length is 6 feet more than the width. find the dimensions of the room.
The room's width is calculated to be 15 feet, and the length, which is 6 feet more than the width, comes to 21 feet. These dimensions satisfy the given area of 315 square feet for the rectangular room.
To find the dimensions of a rectangular room with a known area where one dimension is dependent on the other, we can use algebraic methods to determine the length and width. In this case, the area of the room is given as 315 square feet and it is known that the length is 6 feet more than the width. Let's denote the width of the room as 'w' feet. Therefore, the length will be 'w + 6' feet. The area of a rectangle is calculated by multiplying the length by the width, so we have the following equation:
w imes (w + 6) = 315
Expanding the left side of the equation gives us:
w²+ 6w = 315
To find the value of w, let's move all terms to one side to form a quadratic equation:
w²+6w - 315 = 0
Now we can solve this quadratic equation either by factoring, completing the square, or using the quadratic formula. For this case, factoring is applicable. We look for two numbers that multiply to -315 and add up to 6. The numbers 21 and -15 satisfy this condition. Therefore, we can write the equation as:
(w + 21)(w - 15) = 0
The possible solutions for w are -21 or 15; since a width cannot be negative, we take the positive solution:
w = 15 feet
Having obtained the width, we can now find the length:
Length = w + 6 = 15 feet + 6 feet = 21 feet
Therefore, the dimensions of the room are 15 feet in width and 21 feet in length.
The equation sin(40o) =b/20 can be used to determine the length of line segment AC. What is the length of AC? Round to the nearest tenth.
Convert \dfrac{23}{50} 50 23 start fraction, 23, divided by, 50, end fraction to a percent.
Please help! Vectors and angles
A ship is sailing through the water in the English Channel with a velocity of 22 knots along a bearing of 157° (knots being a unit used to measure the speed of aircrafts and boats). The current has a velocity of 5 knots along a bearing of 213°. Find the resultant velocity and direction of the ship. (Remember that bearing is measured clockwise from the north axis).
1) 25 knots at 166.5 degree
2) 27 knots at 350 degree
3) 166.5 knots at 25 degree
4) 350 knots at 27 degree
Suppose that a jar contains 4 pens: 2 black, 1 blue, and 1 red. three people select a pen at random from the jar, sign a document, and replace the pen in the jar before the next person selects a pen. what is the probability that none of the people use the red pen to sign the document?
The velocity of sound in air is given by the equation
please only answer if you're gonna show work
Find the margin of error for each sample. Then find an interval likely to contain the true population proportion.
a. 15% of 457 teachers
b. 56% of 87 musicians
Full answers please
Keisha is investing her money in an IRA. Initially she will be putting in $775. Using C as the additional amount invested each month, translate this problem into an algebraic expression that will show how much Keisha invested for the entire year.
BRAINLIEST!!PLEASE HELP MEE
The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.
Which number line illustrates the capacity of the Nichols minivan as an inequality?
If using the method of completing the square to solve the quadratic equation x^2+13x-35=0x 2 +13x−35=0, which number would have to be added to "complete the square"?
Answer:
42.25 or 169/4 on delta math
Step-by-step explanation:
If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square
Answer: Yes, the 3 foot 3 foot square opening in your ceiling is big enough to insert a 4x8 piece of plywood.
In a 3x3 foot square, we can form two right triangles with same diagonal side or hypotenuse. .
Using the Pythagorean theorem/formula, we can find the length of the hypotenuse or the longest side of the triangle ( c) given the two sides a and b
Substitute values a=3 and b=3 to formula
a^2^+b^2^=C^2^=
3^2^+3^2^=C^2^=
9+9= C^2^
C= square root of 18
C=4.24
A 4x8 piece of plywood can be inserted in a 4.24 opening diagonally.
The steepness, or grade, of a highway or railroad is expressed as a percent. In the photo of the cog railway at Pike’s Peak, in Colorado, the grade is 18%. Thus, for every 100 ft of horizontal run, the train rises 18 ft. Find the angle of the inclination of the railway.
If (x + 1)(x - 3) = 12, then which of the following statements is true?
A system of equations is shown below:
x + y = 3
2x – y = 6
The x-coordinate of the solution to this system of equations is _____.