Answer:
We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.
First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
Step-by-step explanation:
Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.
Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
12. Vreni took part in a charity walk.
She walked a distance of 20 kilometres.
a) She raised money at a rate of $12.50 for each kilometre.
i. How much money did she raise by walking the 20 kilometres?
(1 mark)
ii. The money she raised in part (a)(i) was 5
52
of the total money raised.
Work out the total money raised.
(2 marks)
iii. In the previous year the total money raised was $2450.
Calculate the percentage increase on the previous year’s total.
(2 marks)
11b) Part of the 20 kilometres was on a road and the rest was on a footpath.
The ratio road distance : footpath distance was 3 : 2.
i. Work out the road distance.
(2 marks)
ii. Vreni walked along the road at 3km/h and along the footpath at 2.5km/h.
How long, in hours and minutes, did Vreni take to walk the 20 kilometres?
(2 marks)
iii. Work out Vreni’s average speed.
(1 mark)
iv. Vreni started at 08 55. At what time did she finish?
(1 mark)
12
c) On a map, the distance of 20 kilometres was represented by a length of 80 centimetres.
The scale of the map was 1 ∶ .
Calculate the value of .
12. i) By walking the 20 kilometers in the charity walk, Vreni raised $250 at a unit rate of $12.50 per kilometer.
12. ii) The total money raised by all participants in the charity walk was $3,100, using proportions.
12. iii) The percentage increase on the previous year's total is 26.53%.
Part B:
11. i) Based on a ratio of 3:2 of road and footpath distance, the road distance covered 12 kilometers.
11. ii) Using the distance, time, and speed formula, Vreni took 7 hours and 12 minutes to walk the 20 kilometers.
11. iii) Vreni's average speed is 2.78 km/h.
11. iv) Vreni finished the charity walk at 16:07.
Part C: The scale of the map to the total distance covered by Vreni was 1: 4 or a scale factor of 25%.
What is the ratio?The ratio is the quotient of a value compared to another.
Ratios are proportionate values, which are equated to each other.
The average speed and scale factor show the ratios of one value and the whole.
12) Charity Walk and Vreni:
The total distance walked = 20 kilometers
The unit rate of raising money per kilometer = $12.50
i) The total amount raised = $250 ($12.50 x 20)
Money raised in 12. 1 = 5/52 of the total money raised
ii) The total money raised in the charity walk = $3,100 ($250 ÷ 5/52)
iii) The total amount raised in the previous year = $2,450
The total amount raised in the current year = $3,100
Difference between current and previous year = $650 ($3,100 - $2,450)
Percentage increase on the previous year's total = 26.53% ($650/$2,450 x 100)
11b) Ratio of road and footpath walk = 3:2
The sum of ratios = 5
Road distance = 3/5 x 20 = 12 kilometers
Footpath distance = 2/5 x 20 = 8 kilometers
Vreni's walking speed along the road = 3 km/h
Road distance = 12 kilometers
Time to walk the road = 4 hours (12/3)
Vreni's walking speed along the footpath = 2.5 km/h
Footpath distance = 8 kilometers
Time to walk the footpath = 3.2 hours or 3 hours and 12 minutes (8/2.5) or 192 minutes (8/2.5 x 60)
Total time spent by Vreni = 7 hours and 12 minutes (4 hr + 3 hr + 12 min)
Vreni's average speed = Distance/Time
= 20 km/7.2 hrs
= 2.78 km/h
Starting time = 08:55
Total hours = 7 hours and 12 minutes
Finishing time = 16:07 (08:55 + 7 hrs + 12 min)
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let f be the function with derivative given by f'(x)=x^2-2/x. On which of the following intervals is f decreasing ?
A. (- [infinity], -1] only
B. (- [infinity], 0)
C. [- 1,0) only D. (0, ∛2]
E. (∛2, [infinity])
Therefore, the function f is decreasing on the interval (- [infinity], -1].
A. (- [infinity], -1] only
We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.
For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.
We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.
Therefore, the function f is decreasing on the interval (- [infinity], -1].
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a newly constructed fish pond contains 2000 liters of water. unfortunately the pond has been contaminated with 5 kg of a toxic chemical during the construction process. the pond's filtering system removes water from the pond at a rate of 200 liters/minute, removes 50% of the chemical, and returns the same volume of (the now somewhat less contaminated) water to the pond. write a differential equation for the time (measured in minutes) evolution of:
The differential equation for the time evolution of the toxic chemical in the pond is dy/dt = -200y + (100/2000)x
where y represents the amount (in kg) of the contaminant in the pond and x represents the amount of contaminant added to the pond per minute (5 kg/minute in this case). The negative sign in the equation indicates that the amount of contaminant is decreasing in the pond, while the positive term (100/2000)x indicates that the contaminant is being added to the pond at the rate of 5 kg/minute.
To solve for y, we can integrate the equation with respect to time. We start by multiplying both sides by dt, giving us the integral form of the equation: dy = -200y dt + (100/2000)x dt. Integrating both sides gives us the solution y = -200y(t) + (100/2000)x(t) + C, where C is an integration constant. Since we know the initial amount of contaminant in the pond is 5 kg, we can set y(0) = 5 and solve for C, giving us C = 5. Therefore, the solution to the differential equation is y(t) = -200y(t) + (100/2000)x(t) + 5.
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help with this question
Answer:
distance from beginning is 225 and the change is -65 per hour
Step-by-step explanation:
What is the slope of the line that contains the points (2, -8) and (-4, 4)?
2
1/2
-1/2
-2
Option D) The slope of the line that contains the points (2, -8) and (-4, 4) is -2
What is a slope ?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.
Slope is give by 2 points on a line is [tex]\frac{y\x_{2}- y\x_{1} }{x_{2}-x_{1}}[/tex]
so the slope is
[tex]\frac{4 - (-8)}{-4 - 2} = \frac{12}{-6} = -2[/tex]
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Help :
(1 + 2 + 3 .... + 5) - 4 = ?
(1 + 2 + 3 .... + 4) - 1 = ?
(1 + 2 + 3) - 2 = ?
Interpret the answer with some logic
Answer:
whats ..... representating
is it a continuous series?
jessie worked 22 hours last week at the auto shop and earned 242 dollars. if she continues at the same hourly pay, how many more hours must she work to earn an additional 154 dollars
On solving the provided question, we can say that by unitary method 14 more hours must she work to earn an additional 154 dollars
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
jessie worked = 22 hours last week at the auto shop
shop and earned = 242 dollars
1 hour = 242/22
154 dollars = 22/242*154 = 0.0909090909 * 154 = 13.9999999986 = 14 hours
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i dont know the answer to this question Mark wants to eat one last cookie from the cookie jar. In the jar there are 5 chocolate chip cookies, 6 peanut butter cookies, and 9 oatmeal cookies. He will randomly select one cookie from the jar. What is the probability that Mark will NOT pick a peanut butter cookie?
so the sample space will be simply all the cookies in the jar, namely 5 + 6 + 9 = 20.
the probability that Mark will NOT pick a Peanut Butter one hmm, that means that Mark will pick either a Chocolate Chip or an Oatmeal one, now this is an OR case so that means sum. so what are the chances Mark will pick either one? P(Chocolate) + P(Oatmeal)
[tex]\stackrel{P(Chocolate)}{\cfrac{5 }{20}}~~ + ~~\stackrel{P(Oatmeal)}{\cfrac{9}{20}}\implies \cfrac{5+9}{20}\implies \cfrac{14}{20}\implies \cfrac{7}{10}\implies 0.7~\hfill \text{\LARGE 70\%}[/tex]
Parallelogram AB'C'D' was obtained by dilating parallelogram ABCD using the center if dilation.
A. What was the scale factor of the dilation?
B. How many congruent copies of ABCD can fit inside of AB’C’D’?
C. If the original area was 12 square units, what is the dilated area of AB’C’D’?
Answer:
A) 2, B) 4, C) 48--------------------------------
Part AThe scale factor is 2, since each side is twice the initial length.
Part BThere are 4 congruent copies, as we can see on the picture.
Part CThe dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.
Is dividing by 1 2 the same as dividing in half?
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately). No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively. For example, if we have the number 10, dividing by 1/2 would give us 5 (10/2), while dividing by 1 and 2 would give us 5 and 5 (10/1 = 10 and 10/2 = 5).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing by one and two (separately).
No, dividing by 1/2 means dividing by one half, while dividing by 1 and 2 means dividing the number into two separate parts and then dividing each part by 1 and 2 respectively.
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(03.05 MC)
A moon's elliptical orbit around a planet is modeled by the equation 225x2 +576y2 = 176,400, where distance is measured in megameters
(Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon?
As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.
What is an elliptical orbit?
When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.
The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by
x²/a² + y²/b² = 1
Now,
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.
Since the equation of the path is the equation of an ellipse, we write it in standard form
As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is
x²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
So, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm
How to find the maximum distance between the planet and its moon?
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.Since the equation of the path is the equation of an ellipse, we write it in standard form.Equation of ellipse in standard formThe standard form of the equation of an ellipse wth center at the origin (0,0) and x - axis major axis is given byx²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
o, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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A rectangular plot of land is divided into 4 parcels
with integer dimensions (see the diagram, which is not to
scale). Parcels A and D are square plots with a combined
area of 898 ft.². Parcel B has an area of 351 ft.². How
wide is the rectangular plot of land?
A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a 0. If x + 20 = 0, then x must be -20.
What is quadratic equation?A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a 0. Length + breadth equals the area of a rectangle. The length is 8 feet greater than the breadth in this instance since we are aware that it is 8 feet longer than its width. We may therefore write the length as x+8 if the width is x.
We may now express length and width as x•(x+8). We get x2 + 8x after multiplying.
We know that the area is 240 square feet but also that it is equal to x2 + 8x. So, x2 + 8x = 240. To get the equation, take 240 away from both sides.
x2 + 8x - 240 = 0.
The equation must now be solved. This can be accomplished by factoring, by applying the quadratic formula, or by solving the square. By factoring, I will demonstrate:
The formula for factoring x2 + 8x - 240 is (x + __)(x + ). The integers must be multiplied by -240 and added to equal 8.
Following are some number pairs that add up to -240:
-4 and 60-24 and 10-12 and 20Because they both sum up to 8, the numbers -12 and 20 are the ones we seek. -12•20 = -240, and -12 + 20 = 8.
We can factor x2 + 8x - 240 as (x - 12)(x + 20) as a result. Set each component to 0 in order to solve.
If x - 12 = 0, then x must equal 12.
If x + 20 = 0, then x must be -20.
The answers to the problem are 12 and -20, but neither of them makes sense. The solution -20 does not work since a rectangle's width cannot be negative. The width being 12 is the only answer that makes sense in this situation.
Consider what kind of form "width" is when choosing the units for width. 'Width' is a line. You use basic units, not squared or cubed units, for lines. The width measurement is therefore in feet.
The complete question is.
A regular plot of land has an area of 240 square feet and is 8 feet longer than its width....
a) Write a quadratic equation in the form ax2 + bx + c = , whose solution gives the width of the rectangular plot of land.
The equation for the width is blank (Type an equation. Type your answer in standard form)
b) Solve the equation.
The solution(s) to the quadratic equation found in part a is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed)
The width of the plot is blank (ft3, ft2, or ft?
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Approximately 10% of all people are left-handed ("11 little-known facts," 2013). consider a grouping of fifteen people. a.) state the random variable. x = ____________________________ b.) show that this is a binomial. find the probability that c.) none are left-handed. d.) seven are left-handed. e.) at least two are left-handed. f.) at most three are left-handed. g.) at least seven are left-handed. h.) find the mean of x. i.) find the variance of x. j.) find the standard deviation of x.
a) The random variable in this problem is the number of left-handed people in a grouping of 15 people.
x = number of left-handed people in a group of 15 people
Show that this is a binomial?b) This is a binomial experiment because it meets the following criteria:
The experiment consists of a fixed number of trials (15 people in this case)
Each trial has two possible outcomes (left-handed or not left-handed)
The probability of success (left-handed) is constant for each trial (10% or 0.1)
c) To find the probability that none are left-handed, we use the binomial probability formula:
P(x = 0) = (15 choose 0)(0.1)^0(0.9)^15 = 0.3429
d) To find the probability that seven are left-handed, we use the binomial probability formula:
P(x = 7) = (15 choose 7)(0.1)^7(0.9)^8 = 0.1540
e) To find the probability that at least two are left-handed, we need to find the probability of getting 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≥ 2) = P(x = 2) + P(x = 3) + P(x = 4) + ... + P(x = 15)
f) To find the probability that at most three are left-handed, we need to find the probability of getting 0, 1, 2, and 3 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
g) To find the probability that at least seven are left-handed, we need to find the probability of getting 7, 8, 9, 10, 11, 12, 13, 14, and 15 left-handed people, and add them up. We can use the binomial probability formula to find the probability of getting each of these values of x, and add them up to find the total probability:
P(x ≥ 7) = P(x = 7) + P(x = 8) + P(x = 9) + ... + P(x = 15)
h) The mean of x is given by:
E(x) = 15(0.1) = 1.5
i) The variance of x is given by:
Var(x) = 15(0.1)(0.9) = 1.35
j) The standard deviation of x is given by:
SD(x) = √1.35 = 1.16
So, the mean of x is 1.5 and the standard deviation is 1.16. The probability of getting at least 2 left-handed people is 0.717, the probability of getting at most 3 left-handed people is 0.547 and the probability of getting at least 7 left-handed people is 0.0256.
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Please help explain with how you got the answer step by step
Answer:
B
Step-by-step explanation:
You solve all until you get the exact expression being found.
(x-7)(x+2) Step.1 ) Distribute Multipliciation
=X^2 +2x -7x -14. Step 2.) Add like terms
=X^2 -5x -14. Step 3.) Solve
Final Answer: B
Using f(x) = 3x - 3 and g(x) = -x, find g(f(0)).
0
1
3
-3
Answer: 3
Step-by-step explanation:
[tex]f(0)=3(0)-3=-3\\\\\implies g(f(0))=g(-3)=-(-3)=3[/tex]
Now you're going to imagine that you invested $1,000 in a company one year ago, and you want to see how well your investment would be doing today.
To begin, choose a company that you're familiar with and that seems as if it might be a good investment - that is, a company that you think will have rising stock prices. Think about companies that you use or know are popular Remember, not all companies are public companies. You'll need to check the New York Stock Exchange to find out if you can actually buy shares in this company Once you've settled on a company, find its stock price from one year ago and for today Write a journal entry about your imagined investment Answer the following questions as you write
1.) What stock did you buy?
2.) Why did you think buying this stock would be a good idea?
3.) How much would you have made or lost on an investment of $1,000?
(Hint First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today Compare that to your initial investment of $1,000)
4.) Could you have made more money by selling sooner?
Answer:
Step-by-step explanation:
1. What stock did you buy?
Apple Inc.
2. Why did you think buying this stock would be a good idea?
Apple products are becoming more and more popular every day. The company is always introducing new and exciting devices. I knew it would be a safe choice to invest in.
3. How much would you have made or lost on an investment of $1,000?
I would have made $105.
Hint: First find out how many shares you could've bought one year ago by dividing $1,000 by the price of the stock one year ago today. You may have to estimate the stock price from the graph. Round the number of shares to the nearest whole number. Then, find out the current value of your shares by multiplying the number of shares you bought by the price of the stock today. Compare that to your initial investment of $1,000.
4. Could you have made more money by selling sooner?
Yes, on October 3, 2018 it was at its peak for the year.
your investment would be doing great today. you would make $115 from the given investment.
What are Stocks?A stock usually referred to as equity, is a type of investment that denotes ownership in a portion of the issuing company. Shares, also known as units of stock, entitle their owners to a share of the company's assets and income in proportion to the number of shares they possess.
Given, you're going to imagine that you invested $1,000 in a company one year ago
I will buy the stocks of amazon.The popularity of Amazon products is rising daily. The business frequently introduces cutting-edge technology. I was confident that it would be a secure investment.I would have made $115.Hint: To start, divide $1,000 by the stock's current price, one year ago, to see how many shares you might have purchased. It can be necessary to infer the stock price from the graph. The number of shares should be rounded up to the next whole number. Then, multiply the number of shares you purchased by the stock's current price to determine the share's current worth. Contrast that with your $1,000 original investment.on September 5, 2022, it was at its peak for the year.Therefore, Today, your investment would be flourishing. Your return on the stated investment would be $1,115.
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What are the 4 parts of a system?
It can include things like answers to equations, solutions to problems, and visualizations of data.
1. Input: The data and instructions a system receives.
2. Process: The manipulation of data and instructions to produce an output.
3. Output: The result of the system's processing of the data and instructions.
4. Feedback: Information from the output that is used to improve the system's performance.
1. Input: The first part of a system in mathematics is the input. This is the data and instructions that the system receives. It can include things like numbers, equations, formulas, and instructions for how to process the data.
2. Process: The second part of a system in mathematics is the process. This is where the data and instructions are manipulated to produce an output. This can include things like calculations, algorithms, and other mathematical operations.
3. Output: The third part of a system in mathematics is the output. This is the result of the system's processing of the data and instructions. It can include things like answers to equations, solutions to problems, and visualizations of data.
4. Feedback: The fourth part of a system in mathematics is the feedback. This is information from the output that is used to improve the system's performance. This can include things like error messages, suggested changes, and suggestions for optimization.
The four parts of a system in mathematics are input, process, output, and feedback. Input is the data and instructions a system receives. Process is the manipulation of data and instructions to produce an output. Output is the result of the system's processing of the data and instructions. Feedback is information from the output that is used to improve the system's performance.
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In a sale, the price of a TV is reduced from £250 to £180 what is the decreased percentage?
Answer:
Step-by-step explanation: 80
Answer: THE ANSWER IS 28%
worked it out on the calculator in the end
Step-by-step explanation:
Why is absolute value always positive or zero?
The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.
The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.
Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }
if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.
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What topics are introduced in Algebra 2?
Answer:
Algebra 2 typically builds on the concepts covered in Algebra 1 and introduces more advanced topics such as:
Quadratic equations and functions
Complex numbers
Polynomial functions and their operations
Rational functions and their operations
Conic sections
Exponential and logarithmic functions
Sequences and series
Trigonometry
Matrices and determinants
Permutations and combinations
Probability
Functions and relations
Limits and derivatives
Answer:
rrtgf thing for them code mine took also
3
Step-by-step explanation:
tutfd
Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adults
ticket and the price of a child's ticket.
The price of an adult ticket is $20
The price of a child's ticket is $19
How to calculate the price of an adult and child ticket ?Let x represent the price of a child ticket
Let y represent the price of an adult ticket
Three adults and four children must pay 136
3y + 4x= 136.........equation 1
Two adults and three children must pay $97
2y + 3x= 97.........equation 2
From equation13 1
3y+4x= 136
3y= 136-4x
y= 136-4x/3
Substitute 136-4x/3 for y in equation 2
2(136-4x) + 3x= 97
272-8x/3 + 3x/1= 97
272-8x+9x/3= 97
cross multiply
272-8x+9x=291
collect the like terms
-8x+9x= 291-272
x= 19
Substitute 19 for x in equation 1
3y+4x= 136
3y + 4(19)= 136
3y+ 76= 136
3y= 136-76
3y=60
y= 60/3
y= 20
Hence children tickets cost $19 and adult tickets cost $20
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What is the domain and range for this function?
if x+3/3=y+2/2 then x/3=
a. y+1
b. y/3
c. y/2
d. y-1
The fraction is :
[tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex] then :[tex]\frac{x}{3} = \frac{y}{2}[/tex]
The correct option is (c).
Now, According to the question:
The given fraction is :
[tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex]
To solve the above fraction and find x/3 =?
We can solve this by cross-multiplying.
Since [tex]\frac{x+3}{3} =\frac{y+2}{2}[/tex] ,we can cross-multiply both sides of the equation to remove the denominators.
Multiple the right side by 2 and the left side by 3 to get 2(x+3)=3(y+2).
Distribute to get the x on one side. 2x+6=3y+6.
The 6s on both sides cancel out so we are left with
2x=3y.
Divide both sides by 2 to get x on one side, so x= 3y/2
The question asks for x/3,
so we can divide both sides of the equation to get:
[tex]\frac{x}{3} = \frac{3y}{6}[/tex]
Simplify, We get:
[tex]\frac{x}{3} = \frac{y}{2}[/tex]
Hence, (c) is the correct answer.
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find the area of the shaded triangle
Answer:
20cmStep-by-step explanation:
4x10 40 divided by 2a museum room, circular in shape, has 5 equally spaced sensors on its walls. there are no dead or overlapping spots along the perimeter of the room. each sensor has the same angle of detection. what is the detection angle of each sensor?
According to the given information the detection angle is 72.
How would you define an angle?An angle is formed anytime two straight lines and rays meet at a single terminal. The intersection of two points at such an angle is known as the vertex. The word "angle" comes from the Latin word "angulus," which meaning "corner."
What is the math behind angles?Degrees are a measure representing circularity or rotation and are used to express angles. You would turn 360° in order to face back in the exact direction after completing a full revolution. As a result, a quarter-circle, or straight angle, is 90°, and a half-circle is 180°. The sum of any two or maybe more angles on the a straight line is 180°.
[tex]\begin{aligned}5\theta & =360^{\circ} \\\theta & =\frac{360^{\circ}}{6} \\& =72^{\circ}\end{aligned}[/tex]
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what is the difference between using the unit rate to find how many feet are in a given number of inches and using the unit rate to find how many inches are in a given number of feet
For feet we will divide the given no. of inches by 12 and for inches we will multiply the given number of feet by 12.
What is feet and inches?Since 1 foot is equal to 12 inches, the given value (in feet) is converted to inches by multiplying by 12. To compare lengths given in different units or to perform arithmetic operations on them, it is crucial to learn how to convert feet to inches (ft to in).
We know that 1 feet = 12 inches.
And to find how many feet are in a given number of inches
We will divide the given no. of inches by 12.
And
To find how many inches are given in a number of feet
We will multiply the given number of feet by 12.
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A rectangle has an area that can be represented by the
expression 16x4 +48x³ 82. Which of the
expressions could represent one of the dimensions of the
rectangle? Select ALL that apply.
Please Help!!
Answer: A rectangle has two dimensions: length and width. The area of a rectangle is given by the formula A = L * W, where L is the length and W is the width.
Given the area can be represented by the expression 16x^4 + 48x^3 + 82, we can see that it's a polynomial of 4 degree.
So, one of the dimensions (L or W) must be represented by a polynomial of degree 4 and the other dimension by a polynomial of degree 3.
So the expressions that could represent one of the dimensions of the rectangle are:
L = 16x^4
W = 48x^3 + 82
It's important to note that this is just one of the possible representations of the dimensions of the rectangle, depending on the values of x.
Step-by-step explanation:
suppose we select every fifth invoice in a file. what type of sampling is this?
Select one:
a. Random
b. stratified
c. cluster
d. systematic
We select every fifth invoice in a file is systematic sampling.
'What is systemic sampling?'
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).
This method will provide you with a representative sample that can be utilized to make inferences about your community of interest if the population order is random or random-looking (for example, alphabetical).
Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out. Similar to basic random sampling, systematic sampling can be used using a list of every member of the population. Contrary to simple random sampling, however, you can also utilize this strategy if you don't have access to a list of your population in advance.
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[tex]\frac{x+5}{x+9}+\frac{x+7}{x^{2}-9}÷\frac{x^{2}-9}{x+3}[/tex]
The result for the division of the fractions in this problem is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
How to divide two fractions?The division of two fractions is given by the multiplication of the first fraction by the inverse of the second fraction.
The first fraction in this problem is composed by the sum of two fractions, as follows:
[tex]\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}[/tex]
Applying the subtraction of perfect squares, we have that:
x² - 9 = (x - 3)(x + 3).
The second fraction is given as follows:
(x² - 9)/(x + 3).
Considering the factoring of x² - 9, the second fraction is given as follows:
x - 3.
Hence the inverse is of:
1/(x - 3).
Then the entire quotient is given as follows:
[tex]\left(\frac{x + 5}{x + 9} + \frac{x + 7}{x^2 - 9}\right) \times \frac{1}{x - 3}[/tex]
The addition of the two fractions is given as follows:
[tex]\frac{(x + 5)(x^2 - 9) + (x + 7)(x + 9)}{(x + 9)(x^2 - 9)} = \frac{x^3 + 6x^2 + 7x + 18}{(x + 9)(x^2 - 9)}[/tex]
Applying the multiplication by x - 3 in the denominator, the quotient is given as follows:
[tex]\frac{x^3 + 6x^2 + 7x + 18}{(x - 3)(x + 9)(x^2 - 9)}[/tex]
Missing InformationThe problem asks for the quotient between the two fractions.
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There are four typical measures of the central tendency of a frequency distribution. Which of the following is NOT ameasure of central tendency?a. meanb. medianC moded. method of least squares
method of least squares is not a measure of central tendency which is not involved in the typical measures.
The central tendency of the dataset are defined as three important measures namely mean, median and mode. The mean shows the average value of the dataset. which can be calculated as the sum of all the values in the dataset which are divided by the number of values. and it is considered as the arithmetic mean. Some of the other measures of mean which is used to find the central tendency are as mentioned as:
Geometric Mean , Harmonic Mean ,Weighted Mean.
Median is the middle value of the dataset in which the it is arranged in the ascending order or in descending order. When the dataset which contains an even number of values, then the median value of the dataset can be calculated by taking the mean of the middle two values.
The mode shows the frequently occurring value in the dataset. Sometimes the dataset are arranged and which contain multiple modes and in some situations , it does not contain any mode at all.
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