The accurate comparison of diameters of the given planets is 7, under the given condition that Neptune is 5 x 10⁴ kilometers in diameter. Mars is 7 x 10³ kilometers in diameter.
Therefore the correct answer for the given question is Option A
The diameter of Neptune is approximately counted to be 50,000km while the diameter of Mars is approximately counted to be 7,000 km.
The ratio of the diameters of Neptune and Mars is given as:
diameter of Neptune / diameter of Mars
= 50,000km / 7,000km
= 7.14
≈ 7 times
The Neptune diameter is 7 times greater Mars diameter.
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The complete question is
Neptune is approximately 5 x 10⁴ kilometers in diameter. Mars is approximately 7 x 10³ kilometers in diameter. Which is an accurate comparison of the diameters of these two planets?
A. The diameter of Neptune is more than 7 times greater than the diameter of Mars.
B. The diameter of Mars is more than 7 times greater than the diameter of Neptune.
C. The diameter of Neptune is about 1.4 times greater than the diameter of Mars.
D. The diameter of Mars is about 1.4 times greater than the diameter of Neptune.
How many more cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth
To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:
1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.
Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.
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Rewrite the polynomial 2x^2+x^3+-7x+1 in standard form. Show your steps
So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.
What is the polynomial?To rewrite the polynomial 2x² + x³ - 7x + 1 in standard form, we need to write the terms in descending order of degree.
So we start with the highest degree term:
x³
Then we add the next highest degree term: 2x²
Followed by the next highest degree term: -7x
Finally, we add the constant term: +1
Putting all the terms together, we get:
x³ + 2x² - 7x + 1
So the polynomial 2x² + x³ - 7x + 1 in standard form is x³ + 2x² - 7x + 1.
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Farmer jones raises only pigs and geese. he wants to raise at most 16 animals. he wants no more
than 12 geese. he spends $5 to raise a pig and $2 to raise a goose and has 550 available to spend. if he
makes a profit of s4 per pig and s8 per goose, how many of each does he need to raise in order to
maximize his profits?
write the objective function. let a represent the number of pigs and y represent the number of geese.
The profit per pig is $4 and the profit per goose is $8.
How can the farmer raise at most 16 animals in order to maximize his profits?Let's start by defining the variables:
a = number of pigs Farmer Jones raises
y = number of geese Farmer Jones raises
The problem tells us that he wants to raise at most 16 animals, so we can write:
a + y ≤ 16
It also tells us that he wants no more than 12 geese, so we can write:
y ≤ 12
We know that it costs $5 to raise a pig and $2 to raise a goose, and he has $550 available to spend. So the cost of raising the animals can be expressed as:
5a + 2y ≤ 550
Finally, we want to maximize his profits. The profit per pig is $4 and the profit per goose is $8. So the objective function for Farmer Jones' profits is:
Profit = 4a + 8y
To summarize, the linear programming model for this problem is:
Maximize: Profit = 4a + 8y
Subject to:
a + y ≤ 16
y ≤ 12
5a + 2y ≤ 550
where a and y are non-negative integers.
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Create trig ratios for sin, cos, and tan:
You can look the image.
It is very clear.
Answer:
[tex]\sin (Z)=\sf\dfrac{9}{15}[/tex] [tex]\cos (Z)=\sf\dfrac{12}{15}[/tex] [tex]\tan(Z)=\sf \dfrac{9}{12}[/tex]
Step-by-step explanation:
To create trigonometric ratios for angle Z in the given right triangle XYZ, we can use the trigonometric ratios.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the right triangle XYZ:
θ = ZO = XY = 9A = YZ = 12H = XZ = 15Substitute these values into the three ratios to create the trigonometric ratios for angle Z:
[tex]\sin (Z)=\sf \dfrac{O}{H}=\dfrac{9}{15}[/tex]
[tex]\cos (Z)=\sf \dfrac{A}{H}=\dfrac{12}{15}[/tex]
[tex]\tan(Z)=\sf \dfrac{O}{A}=\dfrac{9}{12}[/tex]
pyramid A and pyramid B are similar. find the surface area of pyramid B to the nearest hundredth.
The surface area of pyramid B to the nearest hundredth is 58.67 cm²
What are similar figures?Similar figures are two figures having the same shape. The ratio of the corresponding sides of similar shapes are equal.
The scale ratio of the height of the pyramid A to B is
9/6 = 3/2
Area factor = (3/2)² = 9/4
9/4 = 132/x
9x = 132×4
9x = 528
divide both sides by 9
x = 528/9
x = 58.67cm²
Therefore the surface area of pyramid B is 58.67cm².
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Write an appropriate and interesting word for 15000 and 3000.solve it
An appropriate and interesting word for 15,000 is "fifteen thousand," while for 3,000, it is "three thousand."
To solve this question, we need to write the numbers 15,000 and 3,000 as words. To do this, first, we look at the place values of each digit. In 15,000, the "15" is in the thousands place, so we write it as "fifteen thousand." Similarly, in 3,000, the "3" is in the thousands place, so we write it as "three thousand."
By doing this, we have expressed the numbers using their word forms, which helps in understanding and communicating numerical values more effectively, especially in written or spoken contexts. Remember, when writing large numbers as words, we use the place values to guide us in expressing them accurately and understandably.
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Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Investment: $100
Annual % Rate: ?
Amount of time it takes to double: ?
Amount after 10 years: $1405
Answer:
Annual % Rate: 26.43%
Amount of time it takes to double: 2.62yr
Step-by-step explanation:
Solving for r(Annual%Rate)
A=P⋅e^(r⋅t)
1405=100⋅^(r⋅10)
1405=100⋅e(^10r)
1405/100=100/100⋅e^(10r)
14.05 = e^(10r)
log(14.05) = log(e^10r)
1.1476 = 10r⋅log(e)
1.1476/log(e) = 10r
1.1476/10⋅log(e) = r
r = 0.26426
=26.43%
Now we have r=26.43%. We can use this information to solve for t, the time period to double the initial investment:
2P = Pe^(rt)
2 = e^(0.2643t)
ln(2) = 0.2643t
t = ln(2)/0.2643
t = 2.62yr
4 (2) This question is about the series n2 + 4n +3 n=1 (a) Show that this series converges, using the integral test. (Hint: Partial fraction decomposition.) (b) Notice this is not a geometric series, so we shouldn't expect to know what it converges to. But use the decomposition 4 into the difference n2 4n of two sums. (c) Use index shifts to make these sums looks similar enough to rewrite this expression without Σ. 4 (d) Take the limit as B+ 0 to find n2 + 4n +3 B from part (a) to break m2 + An + 3 n=1 n=1 (2) 10
(a) Given: f(x) = x^2 + 4x + 3.
The partial fraction decomposition of f(x) is:
f(x) = (x+1)(x+3)
Now, we need to find the integral of this function from 1 to infinity:
∫[1,∞] (x+1)(x+3) dx
Since the integral converges, we can conclude that the series also converges.
(b) This series is not geometric, so we don't know what it converges to. However, we can decompose the given series as the difference of two sums:
Σ(n^2 + 4n + 3) = Σ(n^2) - Σ(4n)
(c) We can use index shifts to make these sums look similar enough to rewrite the expression without Σ:
Σ(n^2) - Σ(4n) = Σ(n^2 - 4n)
(d) To find the limit as B approaches 0, we can evaluate the limit of the expression n^2 + 4n + 3:
lim(B→0) (n^2 + 4n + 3) = n^2 + 4n + 3
So, the limit of the series is n^2 + 4n + 3.
Marcos harvests a lot of cherry tomatoes in his garden this year. each day, he keeps one-third and brings the rest into the office to give away. by the time the tomatoes start to get a little mushy, marcos has less than
one eighty first of the original harvest left. how many days after marcos harvested the tomatoes do they start to get a little mushy?
The tomatoes start to get mushy after more than 6 days.
Note: The calculation assumes that the number of tomatoes harvested is large enough for the continuous division process to approach zero.
Let's assume that Marcos initially harvested X cherry tomatoes.
According to the given information, each day Marcos keeps one-third of the tomatoes and brings the remaining amount into the office. This means that after the first day, Marcos would have 2/3 (or 2/3X) of the original harvest left.
On the second day, he would keep one-third of the remaining tomatoes and bring 2/3 × 1/3 (or 2/9) of the original harvest into the office. This would leave him with 2/3 × 2/3 (or 4/9) of the original harvest.
In general, after N days, the amount of tomatoes left can be calculated using the following formula:
Amount of tomatoes left = (2/3)^N × X
The question states that Marcos has less than one eighty-first of the original harvest left when the tomatoes start to get mushy. In other words, when the amount of tomatoes left is less than 1/81 of the original harvest, we can write the following inequality:
[tex](2/3)^N × X < 1/81[/tex]
To find the number of days (N) when the tomatoes start to get mushy, we need to solve for N in the inequality above.
Taking the logarithm (base 2/3) of both sides of the inequality:
[tex]N > log2/3(1/81) / log2/3(2/3)[/tex]
N > 4 / (2/3)
N > 4 × 3/2
N > 12/2
N > 6
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Debra has these snacks from a birthday party in a bag.
4 bags of chips
5 fruit snacks
6 chocolate bars
3 pieces of bubble gum
Debra will randomly choose one snack from the bag. Then she will put it back and randomly choose another snack. What is the probability that she will choose a chocolate bar and then a piece of gum?
A. 1/2
B. 1/3
C. 1/9
D. 1/18
Your answer is D. 1/18 is the probability that she will choose a chocolate bar and then a piece of gum
First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks
Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.
Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.
Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18
So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.
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Miles is buying a new rain barrel to help with his watering problem. the rain barrel is shaped like a right circular cylinder. what is the volume of the rain barrel if it is 27 inches tall and has a diameter of 22 inches. use 3.14 for pi.
The volume of the rain barrel is approximately 10,256.58 cubic inches.
To get the volume of the rain barrel, which is shaped like a right circular cylinder, you need to use the formula for the volume of a cylinder: V = πr²h. Here, V represents the volume, r is the radius, and h is the height of the cylinder.
The given diameter of the rain barrel is 22 inches. To find the radius (r), you need to divide the diameter by 2:
r = 22 / 2 = 11 inches.
The height (h) of the rain barrel is given as 27 inches.
Now, you can plug these values into the formula and use 3.14 for pi (π):
V = πr²h
V = 3.14 * (11²) * 27
V = 3.14 * (121) * 27
V = 3.14 * 3267
V ≈ 10,256.58 cubic inches
So, the volume of the rain barrel is approximately 10,256.58 cubic inches.
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if loga 3=p and log 5=q then loga 45 is equivalent to which of the following:
QP^2, Q+2P, 5Q+3P, 3(Q+P), or 3(Q+2P)
the answer to log 45 will be Q + 2P.
What is Logarithmic functions?
A logarithmic function is a type of function that can be expressed in the form: f(x) = a log(bx + c) + d where a, b, c, and d are constants and x is the independent variable. The base of the logarithm is usually assumed to be 10, but can be any other positive number.
Logarithmic functions are used in a variety of applications, including finance, physics, and engineering. In finance, logarithmic functions are used to calculate compound interest. In physics, logarithmic functions are used to describe exponential decay and growth. In engineering, logarithmic functions are used to model the behavior of electrical circuits and other systems.
log a (45) = log a (9) + log a (5)
Next, we can use the fact that log a (x^n) = n log a (x) to simplify the first term:
log a (9) = log a (3²) = 2 log a (3) = 2p
Finally, we can substitute the given values for p and q and simplify the expression:
log a (45) = 2p + q = 2 log a (3) + log a (5) = log a (3²) + log a (5) = log a (3² * 5)
Therefore, we have:
log a (45) = log a (3² * 5)
Now, using the property that log a (x * y) = log a (x) + log a (y), we can simplify this expression even further:
log a (45) = log a (3²) + log a (5) = 2 log a (3) + log a (5) = Q + 2P
Therefore, log a (45) is equivalent to Q + 2P.
Therefore, the answer is Q + 2P.
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Miles driven to see a space shuttle launch 19 27 14 28 30 51 28
For the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.
To analyze this data, let's find the mean (average), median, and mode.
1. Mean (average): Add all the miles together and divide by the total number of data points.
(19 + 27 + 14 + 28 + 30 + 51 + 28) / 7 = 197 / 7 = 28.14
The mean miles driven to see a space shuttle launch is 28.14.
2. Median: Arrange the data points in ascending order and find the middle value.
14, 19, 27, 28, 28, 30, 51
Since there are 7 data points, the median is the 4th value, which is 28.
The median miles driven to see a space shuttle launch is 28.
3. Mode: Identify the most frequently occurring value in the data set.
14, 19, 27, 28, 28, 30, 51
The number 28 appears twice, which is more than any other value.
The mode for miles driven to see a space shuttle launch is 28.
In summary, for the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.
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Of 100 random students surveyed, 42 own a dog, 34 own a cat, 15 own a dog and a cat, and 9 own neither a dog nor a cat. Based upon the results, how many of the next 20 students surveyed would you expect to own a dog and a cat?
In the next 20 students surveyed, you would expect 5 to own a dog and a cat
How many of the next 20 students surveyed would you expect to own a dog and a cat?From the question, we have the following parameters that can be used in our computation:
Dog = 42
Cat = 34
Dog and cat = 15
Neither = 9
This means that
P(Dog and cat) = 15/100
When evaluated, we have
P(Dog and cat) = 5/20
So, when the next 20 students surveyed, we have
Dog and cat = 5/20 * 20
Evaluate
Dog and cat = 5
Hence, the number of dogs and cats is 5
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what fraction is less greater than 1/2 and less than 4/5
A fraction that is greater than 1/2 and less than 4/5, we need to consider fractions between these two values. A fraction that is greater than 1/2 and less than 4/5 is 6/10.
Compare the two given fractions by finding a common denominator.
The lowest common denominator for 1/2 and 4/5 is 10.
Convert both fractions to equivalent fractions with a denominator of 10.
1/2 = 5/10
4/5 = 8/10
Identify a fraction between 5/10 and 8/10.
One possible fraction between these two is 6/10.
A fraction that is greater than 1/2 and less than 4/5 is 6/10.
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a car drives 10.5 miles in 1/6 hour. what is its speed in miles per hour
Answer:
(Credit to guy/girl above) 63 miles 10 1/2 x 6 is 63.
Step-by-step explanation:
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Sam has a box shaped like a rectangular prism. It measures 1/6 inches in height, 1/3 in. Wide and 1/2 in. Long. What is the volume of the box? Leave your answer as an improper fraction
A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. The volume of a rectangular prism can be found by multiplying the length, width, and height of the prism.
In this case, Sam's box has a height of 1/6 inches, a width of 1/3 inches, and a length of 1/2 inches. To find the volume, we need to multiply these three dimensions:
(1/6) x (1/3) x (1/2) = 1/36 cubic inches.
Therefore, the volume of Sam's box is 1/36 cubic inches, which is an improper fraction because the numerator is greater than the denominator.
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Gabby had 578 yards of fabric. she used 3215 yards of fabric. estimate the amount of fabric gabby has left. 1 yard 2 yards 3 yards 4 yards
Gabby does not have any fabric left, as she used more fabric than she had to start with.
How much fabric does Gabby have left after using 3215 yards, and what is the estimate?
Based on the information given, Gabby started with 578 yards of fabric and used 3215 yards of fabric. To estimate the amount of fabric Gabby has left, we need to subtract the amount of fabric used from the starting amount of fabric:
578 yards - 3215 yards = -2637 yards
Since the result is a negative number, it doesn't make sense in this context. It's possible that there was a mistake in the numbers given, or Gabby used more fabric than she had to start with.
Without further information or clarification, we cannot estimate the amount of fabric Gabby has left.
To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount of fabric she had initially.
So, to find the estimate for the amount of fabric Gabby has left, we can perform the following calculation:
Estimate for the amount of fabric Gabby has left = 578 yards (initial amount) - 3215 yards (amount used)
Estimate for the amount of fabric Gabby has left = -2637 yards
However, the result is negative, which means that Gabby doesn't have any fabric left, and she needs to purchase an additional 2637 yards to make up for the shortfall.
Therefore, the estimate for the amount of fabric Gabby has left is 0 yards (she needs to purchase more fabric to continue her work).
Evaluate the following indefinite ∫x tan^2 x dx
To evaluate the indefinite integral ∫x tan^2 x dx, we can use integration by parts.
Let u = x and dv = tan^2 x dx. Then, du/dx = 1 and v = ∫tan^2 x dx = tan x - x.
Using the formula for integration by parts, we have:
∫x tan^2 x dx = uv - ∫v du/dx dx
= x(tan x - x) - ∫(tan x - x) dx
= x(tan x - x) + ln|cos x| + C
Therefore, the indefinite integral of x tan^2 x dx is x(tan x - x) + ln|cos x| + C, where C is the constant of integration.
To evaluate the indefinite integral ∫x tan^2(x) dx, we can use integration by parts, which is defined as ∫udv = uv - ∫vdu.
First, let's choose our u and dv:
u = x, so du = dx
dv = tan^2(x) dx
To find v, we need to integrate dv. Since tan^2(x) = sec^2(x) - 1, we get:
v = ∫(sec^2(x) - 1) dx = tan(x) - x
Now, using integration by parts:
∫x tan^2(x) dx = x(tan(x) - x) - ∫(tan(x) - x) dx
Let's evaluate the remaining integral:
∫(tan(x) - x) dx = ∫tan(x) dx - ∫x dx
= ln|sec(x)| - (1/2)x^2 + C
So, the final answer is:
∫x tan^2(x) dx = x(tan(x) - x) - [ln|sec(x)| - (1/2)x^2] + C
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Find the average rate of change of g (x) = 2x² - 7x from x = 1 to x = 6.
Simplify your answer as much as possible.
The average rate of change of g(x) from x = 1 to x = 6 is 7
Finding the average rate of change of g(x)The average rate of change of a function over an interval is given by the difference in the values of the function at the endpoints of the interval, divided by the length of the interval.
In this case, we want to find the average rate of change of g(x) = 2x² - 7x from x = 1 to x = 6.
The value of g(x) at x = 1 is:
g(1) = 2(1)² - 7(1) = -5
The value of g(x) at x = 6 is:
g(6) = 2(6)² - 7(6) = 30
So the difference in the values of g(x) is:
g(6) - g(1) = 30 - (-5) = 35
The length of the interval is:
6 - 1 = 5
Therefore, the average rate of change of g(x) from x = 1 to x = 6 is:
Rate = 35/5
Evaluate
Rate = 7
So, the rate is 7
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The average rate of change is 7.
We know that,
The average rate of change = (final value - initial value)/change in the value of x.
Now,
The given function is,
g(x)=2x²-7x
The initial value of x is 1 (given)
∴ The initial value of the function g(x), at x=1,
g(1)=2(1)²-7(1)=2-7
or, g(1)= -5
Now, the final value of x is 6,
∴ Finding the final value of the function g(x) at x=6,
i.e, g(6)=2(6)²-7(6)
or, g(6)=72-42 = 30
∴ The change in the value of function g(x), from x= to x=6,
= g(6)-g(1)
= 30-(-5)
= 35
Now, change in the value of x = 6-1=5
∴ The average rate of change = 35/5 = 7
Hence the average rate of change is 7.
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Which figure is a dilation of figure A?
The line passes through the same point on figure A and D.
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point A must pass through the same point on the shape
From the figure, the line passes through the same point on figure A and D.
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PLEASE HELPPP
MEEE LAST QUESTION FOR THE DAY!
Answer:
There are 16 unit squares on the geoboard. Each unit square represents 5 meters, so the total area is 16*5 = 80 square meters.
Here is a diagram of the geoboard with the unit squares labeled:
[Image of a geoboard with 16 unit squares labeled]
I hope this helps! Let me know if you have any other questions.
ANSWER THIS PLS BRAINLIEST IF CORRECT!!!!!!!!
x^5√x^9
Answer:
x^9√x
Step-by-step explanation:
2 Tom Milk his cow and got 2 litres of Milk He gave Kevin 350 ml and Sold 500m to Bob. How much milk is left?
The amount of milk left is given by A = 1.150 Liters of milk = 1150 mL
Given data ,
Let the total amount of milk be = 2 Liters = 2000 mL
Now , Tom gave Kevin 350 ml and Sold 500mL to Bob
So , the remaining amount of milk is given by A
where A = total amount of milk - 350mL - 500mL
On simplifying the equation , we get
A = 2000 - 350 - 500
A = 1150 mL
Hence , the amount of milk left is 1150 mL
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400 people attended a concert 10% of the people came from Scotland 25% of the people came form Wales How many more pepole came from Wales than Scotland
If 400 people attended a concert 10 percent of the people came from Scotland 25 percent of the people came form Wales, there were 60 more people from Wales than from Scotland.
To find out how many more people came from Wales than Scotland at a concert with 400 attendees, we'll first calculate the number of people from each region.
1. Determine the number of people from Scotland:
Since 10% of the people came from Scotland, we'll multiply the total attendees (400) by 10% (0.10).
400 * 0.10 = 40 people from Scotland.
2. Determine the number of people from Wales:
Since 25% of the people came from Wales, we'll multiply the total attendees (400) by 25% (0.25).
400 * 0.25 = 100 people from Wales.
3. Calculate the difference between the number of attendees from Wales and Scotland:
Subtract the number of people from Scotland (40) from the number of people from Wales (100).
100 - 40 = 60 more people from Wales than Scotland.
In conclusion, at the concert with 400 attendees, there were 60 more people from Wales than from Scotland.
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The table shows the number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p.
Pound Cakes, p 3 6 9 14
Cups of Flour, f 8. 25 16. 5 24. 75 ?
Part A
Which equation relates the number of cups of flour to the number of pound cakes that the bakery makes?
f = 2. 75p
f = 0. 343p
f = 2. 75p + 8. 25
f = 0. 343p + 16. 5
Part B
How many cups of flour are needed for 14 cakes?
4. 802
21. 302
38. 5
46. 75
A) The equation relates the number of cups of flour to the number of pound cakes that the bakery makes is f = 2.75p
B) Cups of flour are needed for 14 cakes is 38.5
A) The number of cups of flour, f, that a bakery needs for the number of pound cakes that they make, p is directly proportional to each other which can be written in form ,
f/p = 8.25/3
f = (8.25/3)×p
f = 2.75 p
The equation forms is f = 2.75p
B) Cups of flour are needed for 14 cakes
Here p = 14
by putting the value in the equation we get ,
f = 2.75(14)
f = 38.5
hence , cups of flour are needed for 14 cakes is 38.5
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The regular polygon has the following measures.
a = 2√3 yd
s = 4 yd
Segment a is drawn from the center of the polygon
perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
The vocabulary for the segment a is the apothem
The area of the polygon is about 41.6 yd²
What is the area of a regular figure?The area of a regular figure is the extent of the planer space the figure occupies.
The length of each side of the regular polygon, s = 4 yd
The length of the segment a = 2·√3
The vocabulary term for the segment a drawn from from the center of the polygon and perpendicular to one of its sides is the apothem
Therefore, the vocabulary term for segment a is the apothem
The polygon is a hexagon.
The area of a hexagon is; A = ((3·√3)/2) × s²
Therefore, the area of the polygon is; A = ((3·√3)/2) × (4)² = 24·√3 ≈ 41.6
The area of the polygon is about 41.6 yd²
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Lorena es una estudiante que utiliza una red social cada 8 días. Su amigo Luis accede cada 6 días y su hermana Alexa ingresa cada 10 días. Si ellos coincidieron en su visita a esta red social el día 24 de julio
The next time they will coincide is on November 21. when Lorena uses a social network every 8 days, Luis logs in every 6 days, and his sister and Alexa log in every 10 days.
To find the time when all three coincided, we need to find the least common multiple (LCM) of 6, 8, and 10. The LCM of 6, 8, and 10 is given as,
6 8 10 | 2
3 4 5 | 3
1 4 5 | 4
1 1 5 | 5
1 1 1
LCM = 2 × 3 × 4 × 5 = 120
if they coincided on July 24, To find the time when all three coincided we need to add 120 days to July 24 to find the next time they will coincide. if we add 120 days to July 24 we will get the result as November 21.
Therefore, The next time they will coincide is on November 21.
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The question is,
Lorena is a student who uses a social network every 8 days. His friend Luis logs in every 6 days and his sister Alexa logs in every 10 days. If they coincided with their visit to this social network on July 24 when will they coincide next time?
A survey of North middle school staff included staff members ages the ages were complied and displayed in a histogram which of the following statements best describes the data
The number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
From the given histogram,
A. Between the age 20-29 there are 10 members.
B. Under the age of 40 = 10+18
= 28
40 and older = 12+7+2+1
= 22
C) Total staff members = 28+22=50
D) Number of staff members are 50 years or older
= 7+2+1
= 10
Therefore, the number of staff members under the age of 40 are 28 and the number of staff members 40 and older are 22.
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geometry geometry geometry
We can solve this problem by using some properties of centroids of the triangle and the fact that the centroid divides each median in a 2:1 ratio.
What is a centroid of a triangle?The centroid of a triangle is the point intersection of the three medians of the triangle.
First find the value of MR. The centroid divides each median in a 2:1 ratio, so we have:
MR = 2/3 * R + 1/3 * M
R is the centroid, so R = (P + V + M)/3.
Substituting, we get: MR = 2/3 * [(P + V + M)/3] + 1/3 * M
= 2/9 * P + 2/9 * V + 5/9 * M
Now, substitute the given values of PV and M to find MR:
MR = 2/9 * (3w+7) + 2/9 * (12y-9) + 5/9 * (5x-9) = (2w/3 + 8y/9 + 25x/9) - 1
Simplifying the expression: MR = (2w + 24y + 25x - 27)/9
Next, let's find the value of RP using the centroid. Since R is the midpoint of PV:
RP = 2/3 * R + 1/3 * P
Substituting the values of R and P:
RP = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (3w+7)
= (2w/9 + 8y/9 + 5x/3 + 7/3) + (w+7)/3
= (5w/3 + 8y/9 + 5x/3 + 10)/3
Simplifying this:
RP = (5w + 8y + 5x + 30)/9
Next, find the value of RV using the centroid. R is the midpoint of PV:
So, RV = 2/3 * R + 1/3 * V
Substituting R and V values:
RV = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * (12y-9) = (2w/9 + 8y/9 + 5x/3 + 7/3) + 4y/3 - 3
Simplifying: RV = (5w + 20y + 5x - 18)/9
Find the value of RW using the centroid. R is the midpoint of VW, so: RW = 2/3 * R + 1/3 * W
Substituting the values of R and W:
RW = 2/3 * [(3w+7)/3 + (12y-9)/3 + (5x-9)/3] + 1/3 * 1.75x = (2w/9 + 8y
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