Median: 212
Mode: 212
The median and mode of the data set are 273 and 212 respectively.
What is the median?The median is the value that splits the mathematical numbers or expressions in half. The median value is the middle number of data points. To find the median first arrange the data points in ascending order.
To find the median, we need to arrange the numbers in order from least to greatest:
3, 4, 5, 212, 212, 334, 414, 823
There are 8 numbers in total, so the median is the average of the two middle numbers, which are 212 and 334.
Median = (212 + 334)/2 = 273
To find the mode, we need to identify the number(s) that occur most frequently. In this case, 212 appears twice, so it is the mode.
Mode = 212
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Part 2: Identify key features and graph a circle from general form.
I
Answer the following questions to determine the key features of the circle whose equation is shown and
then graph it.
x+y+12x-2y-12=0
a) Write the equation of the circle in standard form. (3 points)
b) What is the center of the circle? (1 point)
The equation of the circle is (x + 6)² + (y - 1)² = 7² and it's center is (-6, 1)
What is equation circleThe standard equation of a circle is given by:
(x - h)² + (y - k)² = r²
Where (h,k) is the coordinates of center of the circle and r is the radius.
In the given problem, the equation is;
x² + y² + 12x - 2y - 12 = 0
This can be rewritten as;
(x + 6)² + (y - 1)² = 7²
The center of the circle is (-6, 1) from the coordinates (h, k) of the equation of the circle.
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10. Mr. Brown bought a car for commuting to
work and completing errands. He found
that he traveled an average 1,100 miles per
month, with a standard of 100 miles. About 95% of the data lies in which interval
To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.
Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:
- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.
Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.
Therefore, the interval within which about 95% of the data lies is:
1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles
So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).
d = 5t + 20
your answer is there so i'll be on my way, Have a nice day!!
Select the correct answer. Which equation represents a circle with center Z (-3,5) and a radius of 4 units? A. (x − 3)2 + (y + 5)2 = 4 B. (x − 3)2 + (y + 5)2 = 16 C. (x + 3)2 + (y − 5)2 = 4 D. (x + 3)2 + (y − 5)2 = 16
The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x + 3)² + (y - 5)² = 16
We have to given that;
In a circle,
Center = (- 3, 5)
Radius = 4
Since, The standard form of equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) = center
And, r is radius
Here, Center = (- 3, 5)
Radius = 4
Hence, The correct equation which represents a circle with center Z (-3,5) and a radius of 4 units is,
⇒ (x - (- 3))² + (y - 5)² = 4²
⇒ (x + 3)² + (y - 5)² = 16
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COVID Vaccines As of March 2022, in the United States, 127 million people aged 12 years and older have been vaccinated for COVID (the first full sequence plus one booster) and 38 million have not (Source: How to Compare COVID Deaths for Vaccinated and Unvaccinated People - Scientific American). For those vaccinated, there have been an average of 261 deaths per week and for those who have not, there have been an average of 383 deaths per week. Assume that those data are correct for the past week (so the proportion of vaccinated deaths is 261/127,000,000 and unvaccinated is 383/38,000,000).
1. Which group can be considered the placebo group? Why is it important to have a placebo group? What other factors are important in designing a study like this?
2. What are the conditions that must be met to perform a hypothesis test comparing the vaccinated to the placebo group? Were they met?
3. Regardless of your answer in Part 2, test the hypothesis that the vaccine was effective in reducing the number of deaths from COVID. Use = 0.01 and make sure you state your null and alternative hypotheses and write a sentence stating your conclusion
This question involves statistical analysis and hypothesis testing, and the provided information does not contain all the necessary information to answer the questions fully and accurately. However, I can provide some general guidance on hypothesis testing and the factors to consider when designing a study.
It is not appropriate to refer to the vaccinated group as the placebo group. A placebo group is a group that receives a treatment that is inactive or does not contain the active ingredient being tested, while the treatment group receives the active treatment. In the case of the COVID vaccine, the treatment group is the group that received the vaccine, while the control group would be the group that did not receive the vaccine. In this scenario, it is important to have a control group to compare the effectiveness of the vaccine to the effectiveness of no intervention.
Other important factors to consider when designing a study include sample size, randomization, blinding, and the choice of outcome measures. These factors help to reduce bias and ensure that the results are generalizable to the target population.
To perform a hypothesis test comparing the vaccinated group to the control group, the following conditions must typically be met: the samples are independent, the samples are randomly selected from their respective populations, and the samples are normally distributed (or the sample size is large enough, typically n > 30). Additionally, the variances of the two populations should be assumed to be equal unless there is strong evidence to the contrary.
Assuming the conditions for performing a hypothesis test are met, the null hypothesis (H0) is that there is no difference in the number of deaths from COVID between the vaccinated group and the unvaccinated group, while the alternative hypothesis (Ha) is that the vaccine is effective in reducing the number of deaths from COVID. A two-sample t-test can be used to test whether the means of the two groups are significantly different. If the p-value is less than the significance level (alpha) of 0.01, the null hypothesis can be rejected in favor of the alternative hypothesis, and it can be concluded that the vaccine is effective in reducing the number of deaths from COVID.
Once again, please note that the information provided may not be sufficient to provide an accurate analysis of this question, and further information may be necessary to perform an appropriate hypothesis test and draw meaningful conclusions.
Mario buys a shirt for $28.95 and a pair of socks for $4.29. He gives the clerk at the store two 20 bills. How much change should Mario receive?
Building A is 165 feet tall and Building B is 210 feet tall. If the angle of depression from the top of Building B to the top of Building A is 52°, how far apart are the buildings?
help please
Help please (elementary statistics)
The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.
To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.
(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.
[tex]x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%[/tex]
Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.
(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:
[tex]CI = x \pm z*(S/sqrtn)[/tex]
where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).
From the z-table, the z-score for a 90% confidence level is 1.645.
Plugging in the values, we get:
CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)
Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.
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Identify the domain and range for the graph:
0
O Domain: (-∞, ∞)
O Domain: (-∞, ∞)
O Domain: (∞, -∞)
Domain: (∞, -∞)
Range: (-4, ∞)
Range: (∞, - 4)
Range: (-4, ∞)
Range: (∞, - 4)
The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:
Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:
Domain: Not specified
Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:
Range: Not specified
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What is the definition of withholding?
how many dozen is he left with?
Answer:
1.75
Step-by-step explanation:
convert to fraction
a train of length 180 m approaches a tunnel of length 620 m. how long will it take the train to pass completely through the tunnel at a speed of 54 km per hour?
It will take the train 53.33 seconds to pass completely through the tunnel.
We have,
First, let's convert the speed from km/h to m/s:
54 km/h = 54000 m/3600 s = 15 m/s
We need to find the total distance the train travels, which is the sum of its length and the tunnel's length:
So,
distance = 180 m + 620 m = 800 m
Now we can use the formula:
time = distance/speed
time = 800 m / 15 m/s
time = 53.33 seconds
Therefore,
It will take the train 53.33 seconds to pass completely through the tunnel.
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Marcela's grocery bills for three months were
$75, $87, and $25. To add the bills mentally,
Marcela thought:
"75 + 87 + 25 = 75 + 25 + 87"
What property did Marcela use?
Answer:
Marcela used the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:
For any three numbers a, b, and c, (a + b) + c = a + (b + c)
For example: (2 + 3) + 4 = 2 + (3 + 4) = 9
So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.
For the right triangle below, find sec exact (not decimal approximations):
p.s. No calculator allowed. IGNORE what I wrote.
The exact value of sec(θ) is 8√(39)/39.
Given information:
In a right triangle,
Perpendicular side = 5, Hypotenuse side = 8.
Then to find exact secθ:
We can use the definition of secant, which is the reciprocal of cosine:
sec(θ) = 1/cos(θ)
In a right triangle, the cosine of an angle is equal to the adjacent side length divided by the hypotenuse length. Therefore, we first need to find the length of the adjacent side of the angle θ.
Let's label the sides of the right triangle as follows:
the hypotenuse side is H, with a length of 8
the perpendicular side is P, with a length of 5
the base side (adjacent to the angle theta) is B
Using the Pythagorean theorem, we can find the length of the base side B:
B² + P² = H²
B² + 5² = 8²
B² + 25 = 64
B² = 64 - 25
B² = 39
B = √(39)
Now we can use the cosine function to find cos(theta):
cos(θ) = B/H
cos(θ) = √(39)/8
Finally, we can find sec(θ) by taking the reciprocal of cos(θ):
sec(θ) = 1/cos(θ)
sec(θ) = 8/√(39) x √(39)/√(39)
sec(θ) = 8√(39)/39
Therefore, the exact value of sec(θ) is 8√(39)/39. This is the simplified form of the expression and cannot be further reduced because the square root of 39 is not a perfect square.
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Use the internet to identify a major league ballpark in which the distance from home plate to the center field fence and the height of the center field fence require that a ball hit 2 feet above the ground will necessitate an angle of elevation less than .86 degrees to just clear the center field fence. what is the name and location of the major league ballpark that you identified? what is the distance from home plate to the center field fence and what is the height of the center field fence in the ballpark? What is the angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground? Round to the nearest hundredth of a degree.
We can actually deduce here that the major league ballpark that I identified is T-Mobile Park in Seattle, Washington.
How to find the angle of elevation?The distance from home plate to the center field fence is 409 feet and the height of the center field fence is 8 feet.
Thus, to solve for the angle of elevation, we can use the following equation:
tan θ = (y - h) / d
Where:
θ is the angle of elevation
y is the height of the fence
h is the height of the ball
d is the distance to the fence.
tan θ = (8 - 2) / 409
tan θ = 0.602
θ = [tex]tan^{-1}[/tex] (0.602)
θ = 0.85°
The angle of elevation that is required for a hit ball to just clear the center field fence when it is hit 2 ft above the ground is 0.85°.
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can someone help me with this question please?
The value of the missing angle x is: 38°
How to find the angle of the parallelogram?We know that the sum of angles in a triangle is 180 degrees and as such:
∠DAE = 180 - (82 + 68)
∠DAE = 30°
Now, we know that alternate angles are congruent. Thus:
∠DAE ≅ ∠ADC = 30°
Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).
Thus:
∠BAE = ∠BDE = 82 + 30
= 112°
Thus:
∠ABC = ∠ACB = 68°
Thus:
∠BAC = 180 - 2(68)
∠BAC = 44°
Thus:
x = 112 - (44 + 30)
x = 112 - 74
x = 38°
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-3*10^2t=-28 Solve the equation for
t
Express the solution as a logarithm in base-
10
The solution for t is t = log(28/3) / 2, the Logarithm in base-10.
The equation -3 * 10^(2t) = -28 for t, the exponential term and then take the logarithm of both sides. Let's go through the steps:
Step 1: Divide both sides of the equation by -3:
(10^(2t)) = -28 / -3
Step 2: Simplify the right-hand side:
(10^(2t)) = 28/3
Step 3: Take the logarithm of both sides using base-10 logarithm (log):
log(10^(2t)) = log(28/3)
Step 4: Apply the power rule of logarithms to bring down the exponent:
2t * log(10) = log(28/3)
Step 5: Since log(10) = 1, we have:
2t = log(28/3)
Step 6: Divide both sides of the equation by 2:
t = log(28/3) / 2
Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.
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What is the standard form of the line that passes through the points (-4, 6) and (0, -7)?
Ax+4y= -7
B
4x+y=-7
13x + 4y = -28
D-4x+y=-28
30960995
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]
Josiah ties together two strings. One string is 3 3/4 feet long. The other string is 1 1/2 yards long. The knot he makes to tie the strings subtracts 2 1/2 inches from the total length. Mark the length, in inches, of the two tied strings on the number line.
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
The length of the two tied strings on the number line would be between 96 and 97.
We first need to convert both the lengths of the strings to inches, since the knot's length is given in inches.
The first string is 3 3/4 feet long, which is equivalent to 45 inches (since 1 foot = 12 inches, and 3 3/4 feet = 45 inches).
The second string is 1 1/2 yards long, which is equivalent to 54 inches (since 1 yard = 36 inches, and 1 1/2 yards = 54 inches).
The total length of the two strings before the knot is tied is 45 inches + 54 inches = 99 inches.
Subtracting the length of the knot (2 1/2 inches) from the total length of the two strings gives us:
99 inches - 2 1/2 inches = 96 1/2 inches
Therefore, the length of the two tied strings on the number line would be between 96 and 97.
Since we know that the length is closer to 97 inches than 96 inches, we can mark the length at point 97 on the number line
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Use the distributive property to remove the parentheses.
-5(- 6w + 2u -5)
The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Expression is,
⇒ - 5 (- 6w + 2u - 5)
Now, By using distributive property we get;
⇒ - 5 (- 6w + 2u - 5)
⇒ - 5 × - 6w - 5 × 2u - 5 × - 5
⇒ 30w - 10u + 25
Thus, The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
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Pls help me I will mark the brainliest
The most specific correct name for this figure is a trapezoid.
A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.
An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.
A parallelogram has opposite sides parallel. >>> This figure is not a parallelogram.
A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.
The revenue generated by a company manufacturing lawn mowers is R= -0.5x^2+91x, where x represents the number of mowers produced. The cost to produce the mowers is C= 38x+300,where x is the number of mowers produced.
Find the profit polynomial (Hint: Profit = Revenue - Cost) that describes the total profit generated by the company manufacturing lawn mowers based on the number of mowers produced.
--------------------------
Give the profit earned if 53 mowers are sold. ------------
add work please
The profit earned if 53 mowers are sold is $1104.50.
To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:
Profit = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = (-0.5x^2 + 91x) - (38x + 300)
P(x) = -0.5x^2 + 53x - 300
So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.
To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:
P(53) = -0.5(53)^2 + 53(53) - 300
P(53) = -0.5(2809) + 2809 - 300
P(53) = -1404.5 + 2509
P(53) = 1104.5
Therefore, the profit earned if 53 mowers are sold is $1104.50.
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who contributed proof of complex functions to geometry
We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.
What is complex function?A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.
Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.
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Twenty-two people have hair 2.5 inches long and twenty-eight people have hair 5.7 inches long. What is the average hair length of all the people detailed? A. 4.29 B. 5.10 C. 4.92 D. 4.57
Answer:
A. 4.29
Step-by-step explanation:
The average of a set of numbers is the sum of the numbers divided by the total numbers present.
Sum of numbers: Instead of having to write out 2.5 twenty-two times and 5.7 twenty-eight times, we can remember that adding 2.5 twenty-two times is the same as multiplying 2.5 and 22 while adding 5.7 twenty-eight times is the same as multiplying 5.7 and 28. Thus, our numerator for the average is (2.5 * 22) + (5.7 * 28)
Total number of people: We know that there are 50 people in all since 22 + 28 = 50. Thus, our denominator for the average is 50
Average: We divide our numerator by our denominator and simplify to find our average:
Average = ((2.5 * 22 + (5.7 * 28)) / 50
Average = (55 + 159.6) / 50
Average = 214.6 / 50
Average = 4.292
Average = 4.29
Thus, the average and our answer is A. 4.29
Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 3 units right and 4 units up
B. shifted 3 units right and 2 units up
C. shifted 2 units right and 3 units up
D. shifted 2 units right and 4 units up
PLS HELP I WILL MARK AS BRAINLIST IF SHOW WORK
4 Mr. Qureshi writes 4s = 56 and {13, 14, 15) on the board. Tell if each value in the
set is a solution of the equation. Show your work
The solution is: the value of s is:
s = 8
Explanation:
The initial equation is:
4s - 28 = 4
So, to solve for s, we can add 28 to both sides:
4s - 28 + 28 = 4 + 28
4s = 32
Finally, we can divide both sides by 4:
4s/4 = 32/4
s = 8
So, the value of s is 8
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complete question:
What is the value of s for the equation 4s-28=4
A fisherman catches three different fish. The first fish weighs 2.02 pounds, the second weighs 2.20 pounds, the third weighs 2.2 pounds.
Do all three fish weigh the same? Explain.
Answer:
No
Step-by-step explanation:
2.20 and 2.2 are the same
but 2.02 is not the same as the others
find the value of x such that line L and M are parrle
Answer:
3x+10+5x+18=180
8x+28=180
8x= 152
x=19
Suppose a star has a luminosity of 8.0×1026 watts
and an apparent brightness of 1.5×10−12 watt/m2
. How far away is it? Give your answer in both kilometers and light-years.
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
We have,
We can use the inverse square law to find the distance to the star:
Luminosity / (4π(distance)²) = Apparent brightness
Rearranging this formula to solve for the distance, we get:
distance = √(Luminosity / (4π (Apparent brightness)))
Plugging in the given values, we get:
distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))
Simplifying this expression, we get:
distance = 3.04 × 10^{20} meters
Converting this distance to kilometers, we get:
distance = 3.04 × 10^{17} kilometers
To convert this distance to light-years, we divide by the speed of light in kilometers per year:
distance = (3.04 × 10^{17}) / (9.46 × 10^{12})
Simplifying this expression, we get:
distance = 32.2 light-years
Therefore,
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
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Help pls! ( Don’t mind this text)
The value of the expression 10 ÷ 40 using the long division method will be 0.25.
The expression is given below.
10 ÷ 40
Division means the separation of something into different parts, sharing of something among different people, places, etc.
The division is given below by the long division method. Then
40 ) 100 ( 0.25
- 80
200
- 200
0
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find the area (exact)
The area of the figure is 24.28 cm²
What are composite shapes?Any figure that we can break and form more than one basic shape from is called a composite figure.
The composite figure can be broken into a right triangle, a rectangle and a semi circle.
area of triangle = 1/2 bh
= 1/2 × 4 × 3
= 2 × 3
= 6 cm²
area of the rectangle = l × w
= 3 × 4
= 12 cm²
area of the semi circle = 1/2 πr²
= 1/2 × 3.14 × 2²
= 3.14 × 2
= 6.28cm²
Therefore the area of the composite figure =
6 + 12 +6.28
= 24.28 cm
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