The equation will be y = kx²z², where k is the proportionality constant.
Given that y varies jointly as the square of x, the square of z,
And when x = 3 and z = 4, then y = 72,
So, we can write,
y ∝ x²z²
or,
y = kx²z² [k = proportionality constant]
Now, given x = 3 and z = 4, then y = 72,
Therefore,
72 = 3²·4²·k
72 = 9·16 k
k = 72 / 144
k = 0.5
Therefore, the value of proportionality constant k is 0.5.
Hence the equation will be y = kx²z², where k is the proportionality constant.
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Solve for w.
-3/8 w = 12
Simplify your answer as much as possible.
Answer:
w=-4.5
Step-by-step explanation:
12÷3/8=4.5
-w= 4.5
w= -4.5
To solve the equation -3/8 w = 12 for w, you need to isolate w. You do this by dividing both sides by -3/8 which is equivalent to multiplying by -8/3 (the reciprocal). This gives w = -32.
Explanation:To solve the given equation -3/8 w = 12 for w, we need to isolate w on one side of the equation. To do this, you can divide both sides of the equation by -3/8. In mathematics, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of -3/8 is -8/3. So, when you multiply both sides of the equation by -8/3 you get:
w = 12 * (-8/3)
Simplify this further to get: w = -32
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w^(3)-w(w^(2)+2w-1)+2w
A rectangle has a length of 7 millimeters and an area of 203 square millimeters. What is the width? What is the perimeter?
Required width is 29 millimeters and perimeter is 72 millimeters.
What is width of rectangle?Given, Length of rectangle (L) = 7 millimeters
Area of the rectangle = 203 square millimeters
We know that, area of rectangle = Length × Width = L × W
According to the problem,
[tex]\sf L\times W = 203[/tex]
[tex]\sf \Rightarrow 7\times W=203[/tex]
[tex]\sf \Rightarrow W = \dfrac{203}{7}[/tex]
[tex]\sf \Rightarrow W = 29[/tex]
So, Width of rectangle = 29 millimeters
What is perimeter of rectangle?Perimeter of rectangle = 2 × (Length + Width)
[tex]\sf = 2\times(L+W)[/tex]
[tex]\sf = 2\times(7+29)[/tex]
[tex]\sf = 2\times36[/tex]
[tex]\sf = 72 \ millimeters[/tex]
So, perimeter of rectangle = 72 millimeters
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URGENT! Pleasee help me for brainliest :)
A line of best fit was drawn for 6 data points. What is the maximum number of these data points that may not actually be on the line?
A. 6
B. 3
C.5
D. 4
The maximum number of points that may not be on the line is given as follows:
A. 6.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
When we insert the points on a calculator, we get a linear function that is obtained using the mean and sum of squares of coefficients. This means that the line has on average the least distance to the points, but it can happen that none of the points is exactly on the line.
Hence option A is the correct option in the context of this problem.
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Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 3.3 Determine the measurement of FD. FD = 1.1 FD = 1.39 FD = 2.28 FD = 2.37
Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11,.The length of fd is 2.28.
we can use the property that corresponding sides of similar triangles are proportional to find the length of side fd. let's set up the proportion:
ab/de = bc/ef = ac/df
plugging in the given values, we get:
11/3.3 = 7.9/ef = 7.6/fd
simplifying, we get:
fd = (7.6 x 3.3) / 11fd = 2.28 answer choice c. 2.28 is the correct answer.
Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled
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1.
The owner of a deli recorded the number of customers who
ordered each of four sandwiches available.
Sandwich
Ham
Cheese
Turkey
Veggie
Number of Customers
160
100
180
60
Based on the data collected,
a. What is the probability that the next customer that comes
to the deli will order a ham sandwich? Write as a fraction
and decimal
b. What is the probability that the next customer that orders
from the deli will NOT order a cheese sandwich? Write as
fraction and decimal
the probability that the next customer that comes to the deli will order a ham sandwich is, 0.32
And, the probability that the next customer that orders from the deli will NOT order a cheese sandwich is, 0.8
Given that;
The owner of a deli recorded the number of customers who ordered each of four sandwiches available.
Here, Total number of sandwiches = 160 + 100 + 180 + 60
= 500
Hence, the probability that the next customer that comes to the deli will order a ham sandwich is.,
⇒ 160 / 500
⇒ 16/50
⇒ 8/25
⇒ 0.32
And, the probability that the next customer that orders from the deli will NOT order a cheese sandwich is,
⇒ 1 - 100/500
⇒ 1 - 1/5
⇒ 4/5
⇒ 0.8
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for the next 21 days that sasha travels to work, what is the probability that sasha will experience a delay due to traffic on at least 3 of the days?
The probability of experiencing exactly k delays in n days is given by:
P(X = k) = (nCk) * p^k * (1 - p)^(n - k)
To calculate the probability that Sasha will experience a delay due to traffic on at least 3 of the next 21 days, we need to consider the probability of experiencing a delay on each individual day and then use the binomial distribution.
Let's assume that the probability of experiencing a delay on any given day is p. The probability of not experiencing a delay on a single day is 1 - p.
Using the binomial distribution formula,
In this case, we want to find the probability of experiencing at least 3 delays, which means we need to calculate the probabilities for k = 3, 4, 5, ..., 21 and sum them up.
P(at least 3 delays) = P(X = 3) + P(X = 4) + P(X = 5) + ... + P(X = 21)
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Given the circle below with secant EFG and IHJ find the length of EF round to the nearest 10th if necessary
Answer:
EF ≈ 23.3
Step-by-step explanation:
given 2 secants drawn from an external point to the circle.
then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is
GF × GE = GH × GI
8 × GE = 10 × (10 + 15) = 10 × 25 = 250 ( divide both sides by 8 )
GE = 31.25
then
EF = GE - GF = 31.25 - 8 = 23.25 ≈ 23.3 ( to the nearest tenth )
For the system shown, what is the value of x+2y?
x+1/3y=0
6x-2y=6
Answer:
Let x = 6-2y/6
substitute into equation 2
6(6-2y/6)-2y = 6
6-4y = 6
-4y= -12
y = 3
From equation 2
6x-2y =6
substitute y=3
6x-2(3)= 6
6x = 12
x= 2
substitute both into the given equation
x+2y
2+2(3)= 8
Therefore x+ 2y= 8
My kitchen is working properly but was showing 10: 06, which is the wrong time, when I left to walk to my friend's house for coffee. My friend's clock, which was correct, was showing 10:28 when I arrived and 11:55 when I left. I walked home at the same speed as when I went, and when I arrived home my clock was showing 11:55. I then adjusted my clock to show the correct time. How many minutes back did I have to move my clock?
According to the given information, the friend's clock showed that 1 hour and 27 minutes had passed between the time we left and the time we arrived. The kitchen clock needs to be adjusted 1 hour and 5 minutes back, which is equal to 65 minutes.
When we left the house, the kitchen clock was showing 10:06, but according to the friend's clock, the correct time was 10:28.
Therefore, we left the house 22 minutes before the correct time. When we arrived at the friend's house, their clock showed 11:55, which means that 1 hour and 27 minutes had passed since we left our house.
However, the kitchen clock was only showing 10:28 + 22 minutes = 10:50, which means that the kitchen clock was slow by 1 hour and 5 minutes.
To adjust the kitchen clock to the correct time, we need to move it back by 1 hour and 5 minutes, which is equal to 65 minutes. Therefore, the correct time on the kitchen clock should be 10:06 - 1 hour and 5 minutes = 9:01. By adjusting the clock back by 65 minutes, it will now show the correct time of 11:55 when we return home.
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Tom needs to paint a fence that is made of 5 panels. He has red, yellow, green, blue, and white paint. In how many ways can Tom paint the fence if no two neighboring panels can be painted the same color?
Answer: In how many ways can Tom paint the fence if no two neighboring panels can be painted the same color?
Step-by-step explanation:
There are a total of 120 ways to paint the fence with no two neighboring panels painted the same color.
To see why, consider the first panel. Tom can paint it any of the 5 colors. Without loss of generality, assume that he paints it red.
For the second panel, he can choose any of the 4 remaining colors (since he cannot use red again). Without loss of generality, assume that he paints it yellow.
For the third panel, he can choose any of the 3 remaining colors (since he cannot use red or yellow again). Without loss of generality, assume that he paints it green.
For the fourth panel, he can choose any of the 2 remaining colors (since he cannot use red, yellow, or green again). Without loss of generality, assume that he paints it blue.
For the fifth panel, he can choose the only remaining color (since he cannot use red, yellow, green, or blue again). Without loss of generality, assume that he paints it white.
Therefore, there are 5 × 4 × 3 × 2 × 1 = 120 ways to paint the fence with no two neighboring panels painted the same color.
{Hope This Helps! :)}
Factorise: (x-y/xy)^3
The factorized form of the expression[tex](x - y/xy)^3[/tex] is:
[tex]x^3 - 3x + 3/x - 1/x^3[/tex]
To factorize the expression [tex](x - y/xy)^3,[/tex] we can start by simplifying the expression inside the parentheses.
The term y/xy can be simplified to 1/x, so the expression becomes:
[tex](x - 1/x)^3[/tex]
Now, let's apply the cube of a binomial formula, which states that
[tex](a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.[/tex]
Using this formula, we have:
[tex](x - 1/x)^3 = x^3 - 3x^2(1/x) + 3x(1/x)^2 - (1/x)^3[/tex]
Simplifying further, we get:
[tex](x - 1/x)^3 = x^3 - 3x + 3/x - 1/x^3[/tex]
Therefore, the factorized form of the expression[tex](x - y/xy)^3[/tex] is:
[tex]x^3 - 3x + 3/x - 1/x^3[/tex]
Please note that in this factorization, we simplified the term y/xy to 1/x based on the assumption that y is not equal to zero.
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Beetles may be the most varied order of animals. New beetle species are authenticated, completely unpredictably, at a typical rate of one every 7.0months. A supplement to a guide is planned to be published after 20 new species have been discovered.
a)What are the expected value and standard deviation of the number of months (treated as a continuous measure of time) until the supplement is published?
b)What is the probability that the supplement will be published within 10 years (120.0 months)?c)Recalculate the answer to b) using normal approximation and compare (that was certainly easier, was it not?).
a) The standard deviation of T is the square root of the variance, which is SD(T) = sqrt(980) ≈ 31.3 months.
The rate of discovery of new beetle species can be modeled by a Poisson process with rate parameter λ = 1/7.0 new species per month. Let T be the time (in months) until 20 new species are discovered. Then T follows a gamma distribution with shape parameter k = 20 and rate parameter λ. The expected value of T is E(T) = k/λ = 20/(1/7.0) = 140 months. The variance of T is Var(T) = k/λ^2 = 20/(1/7.0)^2 = 980 months^2.
b) The probability that the supplement will be published within 10 years (120 months) is equal to the probability that T ≤ 120. Using the cumulative distribution function (CDF) of the gamma distribution, we can compute this probability as follows:
P(T ≤ 120) = F(120) = ∫[0,120] f(t) dt
where f(t) is the probability density function (PDF) of the gamma distribution, given by:
f(t) = λ^k * t^(k-1) * e^(-λt) / Gamma(k)
where Gamma(k) is the gamma function. Substituting the values of k, λ, and t, we get:
f(t) = (1/7.0)^20 * t^19 * e^(-t/7.0) / Gamma(20)
Using numerical integration or a software program, we can compute the integral:
P(T ≤ 120) ≈ 0.981
Therefore, the probability that the supplement will be published within 10 years is approximately 0.981, or 98.1%.
c) Alternatively, we can approximate the gamma distribution by a normal distribution using the central limit theorem, since the sample size (k = 20) is relatively large. The mean and standard deviation of the normal approximation are given by:
μ = E(T) = 140 months
σ = SD(T) = sqrt(980) ≈ 31.3 months
Using the standard normal distribution, we can standardize the random variable Z = (T - μ) / σ and compute the probability as follows:
P(T ≤ 120) = P(Z ≤ (120 - μ) / σ) ≈ P(Z ≤ (120 - 140) / 31.3) ≈ P(Z ≤ -0.64)
Using a standard normal table or a software program, we can find that the probability of Z being less than or equal to -0.64 is approximately 0.261. Therefore, the probability that the supplement will be published within 10 years using the normal approximation is approximately 0.261, which is lower than the exact probability obtained in part b). This is because the gamma distribution is not exactly symmetric and has a longer tail than the normal distribution, which makes the normal approximation less accurate in the tails of the distribution.
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Write the quadratic equation given the points (-1,0), (-4, 0), and (1, 10).
O g(x) = x² + 5x +4
Og(x)=x²-5x +4
O g(x)=x²-5x - 4
O g(x)
g(x) = x² + 4x + 4
The quadratic equation from the points is g(x) = x² + 5x + 4
Writing the quadratic equation from the pointsFrom the question, we have the following parameters that can be used in our computation:
(-1,0), (-4, 0), and (1, 10).
A quadratic function is represented as
g(x) = a(x - x₁)(x - x₂)
Using the given points, we have
g(x) = a(x + 4)(x + 1)
Next, we have
a(1 + 4)(1 + 1) = 10
This gives
a = 1
So, we have
g(x) = (x + 4)(x + 1)
Expand
g(x) = x² + 5x + 4
Hence, the quadratic equation from the points is g(x) = x² + 5x + 4
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There are 240 students in the 6th grade with 12 teachers. How many students per 1 teacher?
A. 13
B. 24
C. 20
D. 30
Answer:
24
Step-by-step explanation:
Answer:
C. 20
Step-by-step explanation:
To find out how many students per teacher, we can divide the total number of students by the total number of teachers:
240 students / 12 teachers = 20 students per teacher.
Therefore, the answer is C. 20.
a six-sided die is thrown 50 times. the numbers of occurrences of each face are shown below. can you conclude that the die is not fair?
To determine if the die is fair or not, we can perform a chi-square goodness-of-fit test. The null hypothesis for this test is that the observed frequencies match the expected frequencies, assuming the die is fair.
We can set the expected frequency for each face to be 50/6 = 8.33 (since there are six faces on the die and 50 total throws).
Next, we calculate the chi-square test statistic by comparing the observed frequencies to the expected frequencies. Using the formula:
χ² = ∑((O - E)² / E), where O is the observed frequency and E is the expected frequency.
Once we have the test statistic, we compare it to the critical value from the chi-square distribution with (number of categories - 1) degrees of freedom (in this case, 6 - 1 = 5) at a chosen significance level (e.g., 0.05). If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that the die is not fair.
It's not possible to perform the chi-square test without the observed frequencies for each face of the die. Please provide the observed frequencies for each face, and I can help you analyze the data to determine if the die is fair or not.
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beyond struggling pls help
FIND THE FOLLOWING MEASUREMENTS
Check the picture below.
well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}[/tex]
Answer:
angle CED 90°. CE = 21. EB = 8.
Step-by-step explanation:
angle CED = 90° (right angle).
the radius (centre to edge) is the same right around the circle.
so that means that distance CD = 29.
draw a line from C to D. notice how that has just become an hypotenuse?
we know that DE = 20.
we have a right-angled triangle.
CE² = hypot² - DE²
= 29² - 20²
= 841 - 400
= 441
CE = √441 = 21.
EB must be radius subtract CE. that is, 29 - 21 = 8.
What is the relationship between the two radios 10/24 and 5/12
Answer: These two ratios, 10/24 and 5/12 share a proportional relationship.
Step-by-step explanation:
Because when you divide the denominator and the numerator (10/24) by two they’ll equal the other ratio.
Madeline has $680 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $318.67.
She buys 2 bicycle reflectors for $12.89 each and a pair of bike gloves for $30.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $78.20 each.
Write and solve an inequality which can be used to determine x, the number of outfits Madeline can purchase while staying within her budget.
The inequality is x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680. The value of 'x' is $226.78.
Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Let 'x' be the remaining amount. Then the inequality is calculated as,
x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680
Simplify the inequality, then we have
x + $318.67 + $12.89 + $30.57 + $78.20 ≤ $680
x + $453.22 ≤ $680
x ≤ $226.78
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Tim brought $40. 50 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Tim had $2. 00 left over after buying these items. What was the cost of each item?
The cost of the burger was approximately $2.19, the cost of the souvenir was approximately $8.
let's first assign variables to the cost of each item. let b be the cost of the burger, s be the cost of the souvenir, and p be the cost of the pass.
from the problem, we know that:
b + s + p = 40.50 (total cost of all three items)b = (1/4)s (the burger cost one-fourth the price of the souvenir)
s = (2/3)p (the souvenir cost two-thirds the price of the pass)b + s + p + 2.00 = 40.50 (tim had $2.00 left over)
we can use substitution to solve for the unknown variables.
substituting b = (1/4)s and s = (2/3)p into the first equation, we get:
(1/4)s + s + (2/3)p = 40.50
multiplying both sides by 12 to eliminate the fractions, we get:
3s + 12s + 8p = 486
simplifying, we get:
15s + 8p = 486
substituting s = (3/2)p into the above equation, we get:
15(3/2)p + 8p = 486
simplifying further, we get:
37p = 486
solving for p, we get:
p = 486/37
p ≈ 13.14
now that we know the cost of the pass, we can use the second equation to find the cost of the souvenir:
s = (2/3)p = (2/3)(13.14) ≈ 8.76
finally, we can use the first equation to find the cost of the burger:
b = (1/4)s = (1/4)(8.76) ≈ 2.19 76, and the cost of the pass was approximately $13.14.
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what is 24.790000 to 2 significant figures ?
Answer:
25.
Step-by-step explanation:
The first thing we must note are thr rules of significant figures:
RULES FOR SIGNIFICANT FIGURES
1. All non-zero numbers ARE significant
2. Zeros between two non-zero digits ARE significant.
3. Leading zeros are NOT significant
4. Trailing zeros to the right of the decimal ARE significant
From this, we see the total amount of sig figs in 24.790000, which is every number, To round this to two sig figs, we just need to round to two places, which ends up being the tens and ones place to the left of the decimal. The answer would then be 25., with the decimal mark to denote that there are only two sig figs.
Why does a method to swap two array elements work correctly when a method to swap two integer values does not?
A method to swap two array elements works correctly because it is designed to swap the entire elements at two different indexes in an array.
The method receives two integer values representing the indexes of the elements to be swapped and then proceeds to swap the elements themselves.
On the other hand, a method to swap two integer values does not work correctly because integers are passed by value, which means that the method receives a copy of the integer values rather than the original values themselves. Thus, the method only swaps the copies and not the original values, and as a result, the original values remain unchanged.
To overcome this issue, one can use a workaround such as passing the integer values as references instead of values. This way, the method receives a reference to the original value, and any changes made to the reference will affect the original value as well. However, this approach can be more complex and less efficient than simply swapping array elements.
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it's a good deal bro take it
Answer:
3/4
Step-by-step explanation:
9/12
divide top and bottom by 3
3/4
Glenwood High School is constructing a new concrete basketball court that will need 60 cubic yards of concrete. When mixed, one bag of concrete will fill 0.5 cubic yards. The school ordered more than enough concrete to completely fill in the court.
Answer:To completely fill in the basketball court, Glenwood High School will need 60 cubic yards of concrete.
Since one bag of concrete fills 0.5 cubic yards, we can calculate the number of bags needed by dividing the total cubic yards by the cubic yards per bag:
Number of bags = 60 cubic yards / 0.5 cubic yards per bag
Number of bags = 120 bags
Therefore, Glenwood High School needs to order at least 120 bags of concrete to completely fill in the basketball court. Since the school ordered more than enough concrete to completely fill in the court, they likely ordered more than 120 bags of concrete.
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The options that have the same solution as the rewritten equation 2.3p - 10.1 = 6.49p - 4 are:
Option 2) 2.3p - 10.1 = 6.49p - 4
Option 5) 2.3p - 14.1 = 6.4p - 4
Both of these options are equivalent to the rewritten equation and have the same solution.
To rewrite the given equation, we can combine like terms and simplify:
2.3p - 10.1 = 6.5p - 4 - 0.01p
First, let's simplify the right side of the equation:
6.5p - 4 - 0.01p = 6.49p - 4
The equation becomes:
2.3p - 10.1 = 6.49p - 4
Now, we can compare the rewritten equation to the options provided:
2.3p - 10.1 = 6.4p - 42.3p - 10.1
= 6.49p - 4230p - 1010
= 650p - 400 - p23p - 101
= 65p - 40 - p2.3p - 14.1
= 6.4p - 4.
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the figure shown represents a plot of land and is drawn using a scale in which 1 cm equals 2 miles. one square mile is 640 acres. how large is the actual plot of land, in acres?
The area of the actual plot of land, in acres is given by 320000 acres.
Here given the figure is a Trapezium.
We know that the area of the Trapezium with parallel sides of length ' a ' and ' b ' and height between them is ' d ' is given by = (1/2)*(1 + b)*d
We know that, 1 cm = 2 miles.
So, 10 cm = 20 miles
15 cm = 15*2 = 30 miles
Here in given trapezium the length of parallel sides are 10 cm and 15 cm. that is 20 miles and 30 miles respectively.
Height between them is = 10 cm = 20 miles.
So the area of the land is = (1/2)*(20 + 30)*20 = 50*10 = 500 square miles.
we know that 1 square miles = 640 acres
So the area in acres = 500*640 = 320000 acres.
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The question is incomplete. The complete question will be -
"The figure shown represents a plot of land and is drawn using a scale in which 1 cm equals 2 miles. one square mile is 640 acres. how large is the actual plot of land, in acres?"
Ram Purchased a flat at ₹1. 1 lakh and Prem purchased aplot of land worth ₹ 1. 1 lakh. The respective annual rates at which the prices of the flat and the plot increases were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then who paid to whom by how much?
Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%.Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800. Ram's flat is more valuable than Prem's plot of land
After two years, the value of Ram's flat would be ₹1.1 lakh + (10% of ₹1.1 lakh × 2 years) = ₹1.43 lakh.
Similarly, the value of Prem's plot of land would be ₹1.1 lakh + (5% of ₹1.1 lakh × 2 years) = ₹1.21 lakh.
Therefore, the difference in value between Ram's flat and Prem's plot of land is ₹1.43 lakh - ₹1.21 lakh = ₹22,000.
Ram would have to pay ₹22,000 to Prem as Ram's flat is more valuable than Prem's plot of land.
Ram purchased a flat for ₹1.1 lakh and its price increased at an annual rate of 10%. After two years, the flat's value would be:
1.1 lakh * (1 + 0.1)^2 = 1.1 lakh * 1.21 = ₹1.331 lakh
Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%. After two years, the plot's value would be:
1.1 lakh * (1 + 0.05)^2 = 1.1 lakh * 1.1025 = ₹1.213 lakh
After exchanging their properties, the difference in value is:
₹1.331 lakh (flat) - ₹1.213 lakh (plot) = ₹0.118 lakh
Since Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800.
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Pls answer 40pts Drag the tiles to the correct boxes to complete the pairs.
Match each quadratic function to its graph.
f(x) = -2(x + 3)2 − 1
f(x) = -2(x + 3)2 + 1
f(x) = 2(x + 3)2 + 1
f(x) = 2(x − 3)2 + 1
Answer:
Step-by-step explanation:
f(x) = -2(x+3)^2 -1 would be the fourth graph because its translated 3 to the left, negative, and 1 down
f(x)=2(x+3)^2+1 would be the first graph since it's translated 3 to the left, positive, and shifted 1 up
f(x)=-2(x+3)^2+1 would be the second graph since it's translated 3 to the right, negative, and shifted 1 up
f(x)=2(x-3)^2+1 would be the third graph since it's translated 3 to the right, positive, and shifted 1 up
the quadrilateral is circumscribed about the circle. find the value of x. then find the perimeter of the quadrilateral.
The value of x is: x = 6, while the perimeter of the quadrilateral is calculated as: 52 units.
How to Find the Perimeter of the Quadrilateral?Based on the tangent theorem (two tangents meeting at the same point outside a circle have the length), we have:
x + 2 = 8
x + 2 - 2 = 8 - 2
x = 6
The value of x in the circumscribed quadrilateral is therefore, 6 units.
Using the same theorem the perimeter of the quadrilateral can be found by adding all sides of the quadrilateral as follows:
perimeter = 8 + 8 + 5 + 5 + 9 + 9 + 4 + 4
Perimeter = 52 units.
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copper has a face-centered cubic unit cell. how many atoms of cu are present in each unit cell?
The total number of copper (Cu) atoms in each face-centered cubic (FCC) unit cell is 7 atoms.
Here, we have,
In a face-centered cubic (FCC) unit cell, there are a total of 4 atoms.
Each corner of the unit cell contains 1/8th of an atom,
and since there are 8 corners in a cubic unit cell,
the total contribution from the corners is 8 * 1/8 = 1 atom.
Additionally, there is 1 atom located at the center of each face,
and since there are 6 faces in a cubic unit cell,
the contribution from the faces is 6 * 1 = 6 atoms.
Therefore, the total number of copper (Cu) atoms in each face-centered cubic (FCC) unit cell is 1 + 6 = 7 atoms.
Hence, 7 atoms of cu are present in each unit cell.
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