Andreas, Isla and Paulo share some money in the ratios 3:2:5 The total amount of money that Isla and Paulo receive is £76 more than the amount of money that Andreas receives, Andreas buys a video game for £48. 50 with some of his share of the money. Work out how much money Andreas has left from his share of the money when he has bought the video game
The money Andreas has left from his share of the money when he has bought the video game is £179.50.
Let the amount of money that they share be represented by the variable x.
Given that they share the money in the ratio 3:2:5, we can express their share of the money as:
Andreas' share = 3x/10
Isla's share = 2x/10
= x/5
Paulo's share = 5x/10
= x/2Also, given that the total amount of money that Isla and Paulo receive is £76 more than the amount of money that Andreas receives, we can form an equation:
x/5 + x/2 = 3x/10 + £76
Multiplying both sides by 10 to get rid of the fractions, we get: 2x + 5x = 3x + £760x = £760
Therefore, the total amount of money shared is £760.
Now that we know the total amount of money shared, we can determine how much Andreas has left after buying the video game.
We are told that Andreas buys a video game for £48.50 with some of his share of the money.
Therefore, he has £48.50 less than his share of the money left, which is:3x/10 - £48.50.
This simplifies to:(3/10)(£760) - £48.50= £228 - £48.50= £179.50
Therefore, Andreas has £179.50 left from his share of the money after buying the video game.
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What is the solution to the equation v/4
+ 2 = 8
V=2
V=-4
V = 40
V = 24
Answer:
4,16,32,320,240
Step-by-step explanation:
Answer:
he got it super wrong itś v/4,v/16,v/32,v/320,v/240
Step-by-step explanation:
Need help on this explain if you can if you can’t it’s okay!
Answer:
25 ft
Step-by-step explanation:
based on the graph on the width of the porch with the greatest area is 25
what's the difference between the arithmetic and geometric average return (conceptually, not mathematically), and when is it best to use each?
Conceptually, the arithmetic and geometric average returns are different measures used to describe the performance of an investment or an asset over a specific period.
The arithmetic average return, also known as the mean return, is calculated by adding up all the individual returns and dividing by the number of periods. It represents the average return for each period independently.
On the other hand, the geometric average return, also called the compound annual growth rate (CAGR), considers the compounding effect of returns over time. It is calculated by taking the nth root of the total cumulative return, where n is the number of periods.
When to use each measure depends on the context and purpose of the analysis:
1. Arithmetic Average Return: This measure is typically used when you want to evaluate the average return for each individual period in isolation. It is useful for analyzing short-term returns, such as monthly or quarterly returns. The arithmetic average return provides a simple and straightforward way to assess the periodic performance of an investment.
2. Geometric Average Return: This measure is more suitable when you want to understand the compounded growth of an investment over an extended period. It is commonly used for long-term investment horizons, such as annual returns over multiple years.
The geometric average return provides a more accurate representation of the overall growth rate, accounting for the compounding effect and reinvestment of returns.
In summary, the arithmetic average return is suitable for analyzing short-term performance, while the geometric average return is preferred evaluating long-term growth and the compounding effect of returns.
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Write a sine and cosine function that models the data in the table. I need steps to both the sine and cosine functions for a, b, c, and d. I need a good explantion. Thank you!
Answer(s):
\(\displaystyle y = -29sin\:(\frac{\pi}{6}x + \frac{\pi}{2}) + 44\frac{1}{2} \\ y = -29cos\:\frac{\pi}{6}x + 44\frac{1}{2}\)
Step-by-step explanation:
\(\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 44\frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-3} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{6}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{12} \hookrightarrow \frac{2}{\frac{\pi}{6}}\pi \\ Amplitude \hookrightarrow 29\)
OR
\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 44\frac{1}{2} \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{12} \hookrightarrow \frac{2}{\frac{\pi}{6}}\pi \\ Amplitude \hookrightarrow 29\)
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of \(\displaystyle y = -29sin\:\frac{\pi}{6}x + 44\frac{1}{2},\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [centre photograph] is shifted \(\displaystyle 3\:units\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle 3\:units,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{3} = \frac{-\frac{\pi}{2}}{\frac{\pi}{6}}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = -29sin\:(\frac{\pi}{6}x + \frac{\pi}{2}) + 44\frac{1}{2}.\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit \(\displaystyle [12, 15\frac{1}{2}],\)from there to the y-intercept of \(\displaystyle [0, 15\frac{1}{2}],\)they are obviously \(\displaystyle 12\:units\)apart, telling you that the period of the graph is \(\displaystyle 12.\)Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 44\frac{1}{2},\)in which each crest is extended twenty-nine units beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the cosine graph in the photograph farthest to the right is the OPPOCITE of the cosine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
The cube of the sum of six and a number express in a mathematical expression and is it linear or non linear ?
EXPLANATION:
The cube of the sum of 6 is equal to 18 and any number can form any mathematical expression, but that does not mean that it is a line, because both the value of 18 and that other number must maintain a constant pattern that allows obtaining a straight line.
Something linear is means a trend or pattern that is involved with that other value in a process.
Analyze: 5r+ 3 when r=3
5r+3
5(3)+3
15+3
Answer is 18
Answer:
You plug 3 in for R
So the answer is 18
Work
5(3)+3
5(3) = 15
15 + 3 = 18
Help........Betty wants to bake the perfect cookie. She wants to determine the ideal temperature at which to bake the cookies. She has enough batter to make 60 cookies. She decides to randomly assign 15 cookies to be baked at 300°, 15 at 325°, 15 at 350°, and 15 at 375°. The baking time for each batch is 12 minutes. Which statement about the randomization for the completely randomized design is correct? Betty should place the first 15 balls of cookie dough that she scoops from the batter on a tray, and those will be baked at 300°. The next 15 will be placed onto a second tray to be baked at 325°. She should continue in this manner until all 60 cookies have been placed on trays. Betty should scoop a ball of cookie dough from the batter, and then roll a die. Numbers 1–4 would indicate at which temperature the cookies will be baked, and 5–6 would indicate that she should roll again. She should repeat this process until all 60 cookies have been allocated. Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated. Betty should place the first cookie on a tray to be baked at 300°. The second cookie will go on a tray to be baked at 325°, the third will go on a tray to be baked at 350°, and the fourth will go on a tray to be baked at 375°. She will continue placing the cookies in this pattern until all 60 cookies are on trays to be baked.
Answer: Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.
Step-by-step explanation: I just got it correct on Edge :)
The true option about the randomized design is (c) Betty should prepare all 60 cookies. Each cookie will receive a number. The numbers will be written on slips of paper, put into a hat, and shuffled well. The first 15 numbers drawn will indicate the cookies to be baked at 300°, the next 15 will indicate the cookies to be baked at 325°, and so on until all 60 cookies are allocated.
The given parameters are:
\(\mathbf{n = 60}\)
\(\mathbf{Batches = 4}\)
\(\mathbf{Cookies= 15}\) ---- the number of cookies in each batch
\(\mathbf{Temperature= 300,325,350,375}\)
To randomly assign the cookies to the given temperatures, all cookies have to be subjected to the same conditions (except the difference in the temperature).
This means that, she can bake all the cookies at once at different temperatures, while noting down the cookies with a given number.
Hence, the true option is (c)
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Last year a community had 32 incidents of vandalism.
This year they only had 23 incidents of vandalism.
Answer: 22%
Step-by-step explanation:
Which equation represents a line which is parallel to the line 7y-4x=-141. y= 7/4x+22. y = 4/7x-13. y = -7/4x+64. y = -4/7x-3
The general equation of a line is y = mx+b, m being the slope and b the intercept on the y-axis.
We are given the line 7y-4x=-14, let's organize the equation like the general form:
\(\begin{gathered} 7y-4x=-14 \\ 7y=4x-14 \\ y=\frac{4}{7}x-2 \end{gathered}\)In order to be parallel to your line, a line has to have the same slope as your line. So the slope has to be 4/7.
Thus any line parallel to the line y=4/7x-2 has an equation of the form y=4/7x+b, where b is any number.
By looking at the answer options, we can select the second option y= 4/7x-1
a rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. the equation (x 5)x
The length and width of the rectangle are: 10 inches and 5 inches.
What is a rectangle?Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Given:
Area of the rectangle = 104 sq. inchesLength of the rectangle is 5 inches more than the width.To find: the length and width of the rectangle.
Finding:
Let the width of the rectangle be 'x'
Then the length of the rectangle = x + 5
Now, area of the rectangle = width (length)
=> 104 = x ( x + 5)
=> x² + 5x - 104 = 0
=> x² + 13x - 5x - 104 = 0
=> (x + 13) (x - 5) = 0
Since the lengths can't be negative, x = 5, i.e., the width of the rectangle = 5 inches
=> Length = 5 + 5 = 10 inches
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Which of the following shows the correct first step to solve x^2-18x=-45
A x^2 - 18x + 18= -45 + 18
B. x^2 - 18x + 9 = -45 + 18
C. x^2 -18x + 81 = -45
D. X^2 -18 + 81 = -45 + 81
Answer:
D, X^2 -18 + 81 = -45 + 81
Step-by-step explanation:
it is complating squer method that used for solving x in a quadratic equetion . in this step you will add
(y/2)^2 if y is the cofitient of x .
Solve 75 = 6 · w.
The solution is w =
.
Answer:
75=6w?/w=25/2
Step-by-step explanation:
What component does an axiomatic system begins? Is it Undefined Terms or Axiom?
In an axiomatic system, the component that typically comes first is the set of Undefined Terms.
The Undefined Terms are the fundamental concepts or entities that are not explicitly defined within the system. These terms serve as the basic building blocks of the system and are left undefined to avoid circular reasoning. Examples of Undefined Terms in mathematics include points, lines, and sets.
On the other hand, Axioms are statements or principles that are assumed to be true within the system. They provide the foundational rules or properties that govern the behavior of the Undefined Terms. Axioms are derived from intuitive or self-evident truths, and they form the starting point for deductive reasoning within the axiomatic system.
Therefore, the correct answer is that an axiomatic system begins with Undefined Terms. The Axioms come next and are used to establish the properties and relationships among the Undefined Terms.
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determin the open intervals of the domain for the the function shown in the graph below
Given: Graph of the function.
Required: Open interval of the domain for which the function is
(a) increasing
(b) decreasing
(c) constant
Explanation:
Firstly, if we see from left hand side, function is coming downwards that is it is decreasing.
Then at a point, it stops decreasing and become constant.
Then after a point it starts going upwards, that it starts to increase.
Now,
(a) increasing
The function starts increasing at x = 2, and it keeps on increasing after that (as the arrow suggests)
So the open interval in which the function is increasing is
\((2,\infty)\)(b) decreasing
The function is decreasing in the beginning, and it decreases till x = -2
So the open interval in which the function is decreasing is
\((-\infty,-2)\)(c) constant
The function remains constant in the open interval
\((-2,2)\)Final answer:
The function is
(a) increasing in
\((2,\infty)\)(b) decreasing in
\((-\infty,-2)\)(c) constant in
\((-2,2)\)an italian sausage is 8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch?
12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.
Define division.Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch.
Divide 8 by 2/3
8÷ 2/3
8× 3/2
12
12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.
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Jimmy wants to draw a 50° angle. Fill in the missing step to make sure his drawing is completed in the correct order: (3 points)
Step 1: He draws a ray.
Step 2: He lines up his protractor with the baseline on the ray and the origin of the protractor on the vertex.
Step 3: ________
Step 4: He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.
Step 5: He draws arrows on both ends to make them rays.
a
He lines up his ruler with the ray and the zero on the ruler.
b
He finds 50° on the protractor and draws a mark on the paper.
c
He lines up his protractor with a straight line and draws a mark on the paper.
d
He draws parallel lines.
The step that is missing for Jimmy to draw a 50° angle is "He finds 50° on the protractor and draws a mark on the paper" (option B).
What is the next step Jimmy needs to complete?According to the process described, Jimmy has already draw the first ray that is going to work as the baseline for him to draw the angle he requires. After this, he will need to line up his protactor with this ray (step 1).
Then the next step would be to use a pencil or similar material to make a mark in the 50°, this is an important step as it guarantees the angle is correct before he draw the line.
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a rectangular prism is filled exactly with 248 cubes. the edge length of each cube is 12 cm. what is the volume of the rectangular prism?
The volume of the rectangular prism is 428,544 cubic cm.
To find the volume of the rectangular prism, we can start by determining the dimensions of the prism.
Let's assume the length, width, and height of the prism are L, W, and H, respectively.
Given that the rectangular prism is filled exactly with 248 cubes, we can express the total number of cubes as the product of the length, width, and height of the rectangular prism:
\(L \times W \times H = 248\)
Since each cube has an edge length of 12 cm, the volume of one cube can be calculated as follows:
Volume of one cube \(= (12 cm) \times (12 cm) \times(12 cm)\)
Volume of one cube \(= 1728 cm^3\)
Now, we can set up the equation based on the given information:
\(L \times W \times H = 248 \times Volume of one cube\)
\(L \times W \times H = 248 \times 1728 cm^3\)
To find the volume of the rectangular prism, we need to calculate the right side of the equation:
\(248 \times1728 = 428,544 cm^3\)
Therefore, the volume of the rectangular prism is \(428,544 cm^3\).
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Will give brainliest answer plz help
Answer:
The missing value for the cats is 15
Step-by-step explanation:
10+5=15
Answer:
Missing value for dogs is 2. The missing value for cats is 80
Step-by-step explanation:
In the chart it goes from 10 cats to 5 cats. To turn 10 into 5 you have to divide 10 by 2. So to find how many dogs would go with 5 cats, you have to divide the amount of dogs by 2 as well. 4 divided by 2 is 2. So the missing value for dogs is 2.
Now, in the dog row, it goes from 2 to 32. We have to find 2 times _____ is 32.
2 times 16 is 32 so we multiply the 5 dogs by 16 as well. 5 times 16 is 80. So the missing value for cats is 80.
I hope that made sense.
There are 250 cars in a car park.165 of them are Toyota. What is the probability that the first car to leave the car park is: a)a Toyota b)not a Toyota?
Answer:
Toyota
Step-by-step explanation:
im not sure im a 5th grder that just guessed
Answer:
a) 33/50 b) 17/50
Step-by-step explanation:
total cars = 250
toyotas = 165
The probablity of the first car to leave being a toyota is
165/250
Simplify it to 33/50
The probability of the first car to leave not being a toyota is
(250 - 165)/250
= 85/250
= 17/50
a. 320 km in 5 hours is a rate of ______ per hour.
b. 48 books bought for $360 is at the rate of _______ per book.
c. If 900 litres of water flows through a tap in 2 hours, it is the rate of _____ per minute.
d. Richard works for 10 hours and is paid $145. His rate of pay is _____ per hour.
e. 5kg of peas cost $12.58, which equals _____ per kg.
Answer:
a. 64
b. 7.5
c. 7 min 5 sec
d. 14.5
e. 2.52
The rate per hour is known as the average speed.
Average speed = total distance / time
320 / 5 = 64 km / hr
The rate per book is the cost of one book.
Cost of one book = total cost of the book / number of books bought
$360 / 48 = $7.50
The rate per minute = total litres / total minutes
900 / (2 x 60)
900 / 180 = 5 litres per minute
Rate pay per hour = total amount earned / total hours worked
$145 / 10 = $14.50 per hour
Cost per kg = total cost of the peas / total weight of the peas
$12.58 / 5 = $2.52 per kg
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The formula for the speed of a tsunami in deep water is v = √gh, where g is acceleration due to gravity, 9.8 m/s2, and h is the depth of the ocean in meters.Use this formula to estimate the speed at which the tsunami that started with an earthquake in Sumatra struck Sri Lanka about 1550 km away.The Bay of Bengal is 4 km (4000 m) deep.Enter your answer, rounded to the nearest whole number, in the box.v = m/s
Explanation
We are required to determine the speed at which the tsunami that started with an earthquake in Sumatra struck Sri Lanka about 1550 km away.
The formula given is:
\(\begin{gathered} v=\sqrt{gh} \\ where \\ g=acceleration\text{ due to gravity} \\ h=depth\text{ of the ocean } \end{gathered}\)Therefore, we have:
\(\begin{gathered} v=\sqrt{gh} \\ where \\ g=9.8\text{ m/s}^2 \\ h=4000m \\ \\ \therefore v=\sqrt{9.8\times4000} \\ v\approx198\text{ m/s} \end{gathered}\)Hence, the answer is:
\(v\approx198\text{ m/s}\)what's 2 plus 2 i need help please:(
Answer:
i think its 4......i dont know......probably 5
Step-by-step explanation:
it is 4
4) Select one of your desserts.
Desserte ice cream Price: 3.00
This dessert hasn't been selling well so.
you have decided to decrease the price
by $0.50. What is the percent of
change?
Answer:
Step-by-step explanation:
see calculate bro 3 = 100%
1.5 is 50%
0.50 is then 25%
Which is a factor of the polynomial f(x) = 6x4 – 21x3 – 4x2 24x – 35? 2x – 7 2x 7 3x – 7 3x 7
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the polynomial:
f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35
The polynomial can be further simplified to:
f(x) = (2x - 7)(3x³ - 2x + 5)
A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7
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Answer:
2x-7
Step-by-step explanation:
TLDR verified answer, correct on edge 2023
the mean number of words per minute (wpm) read by sixth graders is 89 with a standard deviation of 16 wpm. if 66 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 5.09 wpm? round your answer to four decimal places.
Answer:
High
Step-by-step explanation:
The probability is high because those 66 students could have 10 really fast readers that change that wpm. Or they could have 15 slow readers that could change the wpm and make it go down.
There are many possibilities.
Which of the following decimals is equivalent to 6%? A. 600 B. 6 C. 0.6 D. 0.06
Answer:
D
Step-by-step explanation:
For the hiking portion of your trip, you and your friends carry the same amount of
equipment, which works out to 35 pounds of equipment each. For extra money, you can
hire an assistant, who will carry 50 pounds of equipment. Each assistant charges a flat
fee of $50 and an additional $22 for each mile. The total amount you would have to pay
1 assistant is $512. How many miles will your group be hiking?
Answer:
28 miles
Step-by-step explanation:
subtract the pay to the additional pay
The triangle shown below is a right triangle with the right angle marked.
Which equation correctly expresses the Pythagorean Theorem for this triangle?
A)p²+q²=r²
B)r²+q²=p²
C)(p+q)²=r²
D)p²+r²=q²
Answer:
The Correct answer is A
Step-by-step explanation:
b) because r²=q²+p²,p²=r²-q² not
r²+q²
c) (p+q)²=r²
is not correct because
(p+q)²=(p+q)(p+q)
d) p²+r²=q² wrong
because
q²=r²-p²
hello please help its my birthday !!
Answer:
1,000
Step-by-step explanation:
Answer:
I think it's 1,000