The margin of error would have been much smaller if Dr. Si Sanchez had increased his sample size to 1,000.
A margin of error quantifies the amount of random sampling error in survey results. The smaller the margin of error, the larger the sample size. This is due to the fact that a larger sample size reduces the amount of random variation in the data, allowing the estimate to be more precise.
Dr. Sanchez's margin of error decreases as he increases his sample size from 500 to 1000, because sample size is proportional to margin of error.
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The circle graph represents the jobs at a digital animation company with 1600 employees. How many more character designers are there than interns? Intern 5%, Set Shading 10%, Character shading 10%, Story artist 20%, Character design 25%, Animator 30%.
At the Digital animation studio, character designers outnumber interns by 320.
Let's break down the information given in the circle graph and find out how many more character designers there are than interns.
1. Determine the number of employees for each job type by multiplying the percentage by the total number of employees (1600):
- Interns: 5% * 1600 = 80 employees
- Set Shading: 10% * 1600 = 160 employees
- Character Shading: 10% * 1600 = 160 employees
- Story Artist: 20% * 1600 = 320 employees
- Character Design: 25% * 1600 = 400 employees
- Animator: 30% * 1600 = 480 employees
2. To find how many more character designers there are than interns, subtract the number of interns from the number of character designers:
- Character Design - Interns = 400 - 80 = 320 employees
In conclusion, there are 320 more character designers than interns at the digital animation company.
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the monthly payment on a mortgage with a principal of p dollars is m dollars. the mortgage is taken out for y years. express the interest I as a function of p, m, and y.
Answer:
I = 12my -p
Step-by-step explanation:
You want to express the interest I on a mortgage of principal p that has a monthly payment of m for y years.
Total of paymentsThe number of monthly payments in y years is 12y.
The value of those monthly payments is (12y)(m).
InterestThe interest paid is the difference between the value of payments and the principal amount of the loan:
I = 12my -p
What's the surface area?
The given surface is the pyramid and the area of the pyramid is [tex]301.98978[/tex].
What is the area of the pyramid?The formula to calculate the total surface area of a triangular pyramid is[tex]\frac{1}{2} (a*b)+\frac{3}{2}(b*s)[/tex]
Calculate the area of each triangular face. This can be done using the formula for the area of a triangle: [tex]\frac{1}{2} bh[/tex], where b is the base of the triangle and h is the height of the triangle.
In this case, the base is one of the sides of the base triangle, and the height is the slant height of the pyramid.
Add up the areas of all the triangular faces and the area of the base to get the total surface area of the pyramid.
Add the area of the square.
Therefore the given surface is the pyramid and the area of the pyramid is [tex]301.98978[/tex].
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please help me!!!!
PLease hurry!!!!
The absolute value equation is |x - 11| = 6.
Howe to write the absolute value equation?Givent he values 5 and 17 on the numberr line, we want to write an absolute value equation in the form |x - c| = d.
Now, given two numbers a and b, we have that
c = (a + b)/2 and d = (b - a)/2So, given that
a = 5 and b = 17,we have that
c = (a + b)/2
= (5 + 17)/2
= 22/2
= 11
Also, given that
a = 5 and b = 17,we have that
d = (b - a)/2
= (17 - 5)/2
= 12/2
= 6
So, to write the absoiute value equation, we substitute the values of the variables into the equation
|x - c| = d.
So, substituting the values of the variables into the equation, we have that
|x - c| = d.
|x - 11| = 6.
So, the absolute value equation is |x - 11| = 6.
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5^2 over 53^3 in simplest form
After converting 5²/53³ in simplest form we get 25/148,877 as the correct answer.
To simplify the expression 5²/53³, we first evaluate the exponents of 5 and 53.
5² means 5 multiplied by itself, or 5 × 5, which equals 25.
53³ means 53 multiplied by itself three times, or 53 × 53 × 53. This can be calculated using a calculator or by multiplying the numbers out by hand. The result is 148,877.
So, we can rewrite the expression 5²/53³ as: 25/148,877
This expression cannot be simplified any further because 25 and 148,877 have no common factors other than 1.
Therefore, the expression in its simplest form is 25/148,877.
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PLEASE HELP AND HURRY
To solve the system of linear equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations 3 x minus 2 y = 4 and 9 x minus 6 y = 12 with his graphing calculator, but he could only see one line. Why is this?
because the system of equations actually has only one solution
because the system of equations actually has no solution
because the graphs of the two equations overlap each other
because the graph of one of the equations does not exist
Answer:
the answer is that the lines overlap each other
Step-by-step explanation:
If you put both linear questions into desmos both linear equation have the same slope and x intercept so they would be shown to overlap on the graphing calculator.
Answer:c. They Overlap
Step-by-step explanation: This is because when we change both terms from standard to slope intercept, they are both y=-3/2x -2, causing them to have the same solution, which means they overlap, or they have infinite solutions
the two adjacent angles formed when two lines meet or intersect.
so is it vertical liner or complementary angles
Adjacent angles are a pair of angles that have a similar vertex and side and add up to 180 degrees. Contrarily, complementary angles are two angles that together measure 90 degrees and have a number of mathematical uses.
There are numerous angles created when two lines intersect. When two of these angles are referred to as neighbouring, it signifies that they have a similar vertex and side. A linear pair of angles is any two angles that are next to one another on one side of the intersection.
The sum of two linear angles is 180 degrees. As a result, it is simple to determine the measure of another angle if you know the size of one. Geometry relies on linear pairings of angles to solve problems involving angles and lines, hence they are crucial.
Complementary angles, on the other hand, are two angles that sum up to 90 degrees. Although they are not need to be, they can be adjacent angles. When two angles are parallel to one another, the sum of their respective measures is 90 degrees.
Trigonometry and geometry are two areas of mathematics where complementary angles are helpful. In issues involving right triangles, where one of the angles is always 90 degrees, they are frequently used.
In conclusion, neighbouring angles are a pair of parallel angles that have the same vertex and side and add up to 180 degrees. Contrarily, complementary angles are two angles that together measure 90 degrees and have a number of mathematical uses.
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28. The height of a cylinder whose radius is 7 cm
and the total surface area is 968 cm2 is.............
(A) 15 cm
(C) 19 cm
(B) 17 cm
(D) 21 cm
[tex]\huge\bold{Solution }[/tex]
[tex]\large\mathfrak{given}[/tex]
TSA = 968cm²Radius = 7 cmHeight = ?[tex] \large \: \mathfrak{ {formula}}[/tex]
2πr(r + h)Let height be : x
[tex]\sf\Rightarrow{ \: 968 = 2\pi \: r(r \: + h) } \: [/tex]
[tex]\sf\Rightarrow{968 = 2 \times \frac{22}{7} \times 7 \times (7 + x) }[/tex]
[tex]\sf\Rightarrow{ 968 = 2 \times 22 \times(7 + x)}[/tex]
[tex]\sf\Rightarrow{ 968 = 44(7 + x)}[/tex]
[tex]\sf\Rightarrow{ \frac{968}{44} = 7 + x}[/tex]
[tex]\sf\Rightarrow{22 = 7 + x }[/tex]
[tex]\sf\Rightarrow{22 - 7 = x }[/tex]
[tex]\sf\Rightarrow{x = 15 }[/tex]
[tex]\bf\Rightarrow{ x = 15}[/tex]
[tex]\sf\Rightarrow{ \underline{{ height \: = 15}}} \\ \\ \sf \: option \: A is \: correct \: [/tex]
[tex] {\underline{ \rule {200pt}{6pt}}}[/tex]
Use the graph to identify the value of k for the function f(x)=log0.5 x+k
The value of k for the logarithmic function f(x)=log0.5 x+k is k = log2 (1/2x).
Here we need to understand that the logarithmic function f(x)=log0.5 x+k can be written in the form f(x)=log0.5 x + log0.5 b.
The given logarithmic function is of the form f(x) = log0.5 x + k.
We want to express this function in terms of a logarithm with base 0.5 and a constant b.
Using the property of logarithms that states that the logarithm of a product is the sum of the logarithms of the factors, we can write:
f(x) = log0.5 x + log0.5 b
where b is a constant that we need to determine.
We want to find a value of b such that the expression above is equivalent to the original function f(x) = log0.5 x + k. We can do this by setting the two expressions equal to each other:
log0.5 x + log0.5 b = log0.5 x + k
b = [tex]0.5^k[/tex]
Substituting this value of b into the expression we obtained earlier gives:
f(x) = log0.5 x + log0.5 (0.5^k)
f(x) = log0.5 (x([tex]0.5^k[/tex]))
Using the property of logarithms that states that the logarithm of a power is the product of the exponent and the logarithm of the base, we can simplify this expression:
f(x) = log2 x - k
We are now given that the function f(x) T z the x-axis, which means that f(x) = 0.
Setting this equal to the expression we obtained above, we get:
log2 x - k = 0
log2 x = k
Solving for k gives:
k = log2 x
Substituting this expression for k back into the original function f(x) = log0.5 x + k, we get:
f(x) = log0.5 x + log0.5 ([tex]0.5^{(log2 x)[/tex])
f(x) = log0.5 (x ( [tex]0.5^{(log2 x)[/tex]))
f(x) = log0.5 (x ( [tex](1/2)^{log2[/tex]))
f(x) = log0.5 (x ( (1/2)))
f(x) = log0.5 (x/2)
Therefore, the value of k for the function f(x) = log0.5 x + k is k = log2 x, and the equivalent expression for the function is f(x) = log0.5 (x/2).
The value of k for the function f(x) = log0.5 x + k is k = log2 (1/2x).
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URGENT! Will give brainliest :)
What is the first quartile of the data set represented by the box plot shown below?
A. 30
B. 18
C. 25
D. 45
Answer:
C. 25
Step-by-step explanation:
You want to know the first quartile as shown in the given box plot.
Box plotA box plot has vertical lines at (left to right) ...
minimumfirst quartilemedian (2nd quartile)third quartilemaximumThe left end of the "box" is the first quartile.
The first quartile of the dataset represented by this box plot is 25.
an auto liability coverage has a policy limit of 100. claim sizes observed are 20, 45, 50, 80, 100, where the claim at 100 was for exactly 100. in addition, there are 2 claims above the limit. the data are fitted to an exponential distribution using maximum likelihood. determine the mean of the fitted distribution
The mean of the fitted exponential distribution is 66.67.
To find the mean of the fitted exponential distribution, we first need to estimate the parameter lambda using maximum likelihood estimation.
The probability density function of the exponential distribution is given by
f(x; lambda) = lambda * exp(-lambda * x)
where x is the claim size and lambda is the parameter to be estimated.
The likelihood function for the observed data is the product of the individual probabilities of each claim
L(lambda) = lambda^n * exp(-lambda * sum(x_i))
where n is the number of observed claims and x_i is the i-th claim size.
The log-likelihood function is given by:
ln L(lambda) = n * ln(lambda) - lambda * sum(x_i)
To estimate the parameter lambda, we need to maximize the log-likelihood function with respect to lambda:
d/d(lambda) ln L(lambda) = n/lambda - sum(x_i) = 0
Solving for lambda, we get
lambda = n / sum(x_i)
Substituting the observed values, we get
lambda = 6 / (20 + 45 + 50 + 80 + 100 + 2*100) = 0.015
Therefore, the estimated parameter of the fitted exponential distribution is lambda = 0.015.
The mean of the exponential distribution is given by
E(X) = 1/lambda
Substituting the estimated value of lambda, we get
E(X) = 1/0.015 = 66.67
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The point ( 2, √—
5 ) lies on the circle centered at the
origin with radius 3.
To check whether the point (2, √5) lies on the circle centered at the origin with radius 3, we can use the distance formula for a point (x, y) on the circle:
d = √((x - 0)^2 + (y - 0)^2)
Since the center of the circle is at the origin, the x-coordinate is 0 and the y-coordinate is 0. The radius is given as 3. So, substituting these values in the above formula, we get:
3 = √((2 - 0)^2 + (√5 - 0)^2)
Simplifying the right side of the equation:
3 = √(4 + 5)
3 = √9
3 = 3
Since both sides of the equation are equal, the point (2, √5) lies on the circle centered at the origin with radius 3.
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
In this case, the IQR should be used because the data in both Sunny Town and Desert Landing is not normally distributed and has different shapes.
What is outliers ?
Outliers are pieces of information that dramatically deviate from the rest of the information in a dataset. These could be values that are atypically high or low or values which vary significantly from the data's central trend. Outliers can appear for a number of causes, including measurement or record errors, inherent data variability, or unusual events. It is frequently required to recognize and effectively handle outliers because of their potential to significantly affect statistical analyses.
given,
IQR, as it can provide a better measurement of the variability of the middle 50% of the data and is less impacted by outliers.
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a circular tablecloth has a diameter of 3 feet. which measurement is closest to the area of the tablecloth in feet?
Answer:
[tex]≈7.07 \: {ft}^{2} [/tex]
Step-by-step explanation:
Given:
d = 3 ft
Find: A (area) - ?
First, we can find the length of the radius, since we know the diameter:
r = 0,5× d
r = 0,5 × 3 = 1,5 ft
[tex]a = \pi {r}^{2} = \pi \times( {1.5})^{2} = 2.25\pi ≈7.07 \: {ft}^{2} [/tex]
The area of the circular tablecloth is approximately 7 square feet.
To find the area of a circle, you use the formula A = πr^2, where A is the area and r is the radius of the circle. The diameter of the tablecloth is 3 feet, so the radius is 1.5 feet. Plugging this into the formula, we get A = π(1.5)^2 ≈ 7.07 square feet. However, the question asks for the measurement closest to the area of the tablecloth in feet, so we can round the answer to 7 square feet.
Therefore, the area of the tablecloth is approximately 7 square feet.
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if the coefficient associated with an independent variable column is k, then how will you compute the angle of the associated regression line (model) in degrees?
The formula for calculating the angle of the related regression line in degrees is:
angle = (180/π) * arctan(k)
The angle of the related regression line (model) in degrees can be calculated using the coefficient involving a column of the independent variable (k) and the arctangent function.
Arctang of the coefficient (k) gives the angle in radians between the horizontal axis and the regression line. To convert this angle to degrees, we can multiply the angle in radians by 180/π.
Therefore, the formula for calculating the angle of the related regression line in degrees is:
angle = (180/π) * arctan(k)
where arctan(k) is the arc tangent of the coefficient associated with a column of the independent variable.
This formula gives the angle of the regression line to the horizontal axis.
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What are the domain and range of the function y=x^2-2x
-1 ?
Hello and regards 24kendalllove.
Therefore, the domain is the entire set of real numbers and the range is y ≥ -2.Being correct, alternative D.Step-by-step explanation:The given function is y = x^2 - 2x - 1.
Domain:The domain of a quadratic function, like this one, is the set of all values of x for which the function is defined. Since a quadratic function is defined for all real values of x, the domain of this function is all real numbers.
Range:To find the range of the quadratic function, we must first identify whether the parabola opens up or down. In this case, the coefficient of the x^2 term is positive (1), which means that the parabola opens up.
Since the parabola opens up, the vertex of the parabola will be the lowest point on the graph. To find the vertex, we use the formula x = -b / 2a, where a and b are the coefficients of the terms x^2 and x, respectively. In this case, a = 1 and b = -2, so x = -(-2) / (2 * 1) = 1. We then plug this value of x into the function to find the corresponding y value: y = (1)^2 - 2(1) - 1 = -2.
So, the vertex of the parabola is (1, -2). Since the parabola opens up, the range of the function will be all y-values greater than or equal to the y-value of the vertex. Therefore, the range of the function is y ≥ -2.
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Evaluate 3x +1 when x = 0
A. 0
B. 1
C. 3
Answer:
B
Step-by-step explanation:
you would fill in x for 0 and 3 times 0 is 0
then it would be zero plus 1 which would be !
Answer:
B. 1
Explanation:
3(0)+1
0+1=1
For the following problem write the simplest polynomial function with the given zeros: 2,
-1, and -8
Answer:
f(x) =x^2 - 3x^2 - 6x + 8.
Step-by-step explanation:
Question 25
A square piece of cloth has an area of 4y2-28y +49 square meters.
Find the length of each side.
What value of x is in the solution set of the inequality 9(2x + 1) < 9x – 18?
–4
–3
–2
–1
Answer:
9(2x + 1) < 9x - 18
9(2x + 1) < 9(x - 2)
2x + 1 < x - 2
x < -3
So -4 is in the solution set.
rosa has 15 quarters and 10 nickels. she buys juice from a store for herself and her friends. the juice costs 35 cents per can. she gives the cashier 2 3 of the quarters end 3 5 of the nickels. the cashier does not give her any change. how many cans of juice did she buy? cans
Rosa bought 8 cans of juice for herself and her friends.
To calculate how many cans of juice Rosa bought, we first need to calculate the total amount of money she gave the cashier:
2/3 of 15 quarters = (2/3) x 15 = 10 quarters (since each quarter is worth 25 cents,
10 quarters are worth 10 x 25 = 250 cents)
3/5 of 10 nickels = (3/5) x 10 = 6 nickels (since each nickel is worth 5 cents, 6 nickels are worth 6 x 5 = 30 cents)
Therefore, Rosa gave the cashier 250 + 30 = 280 cents.
Now, we need to find out how many cans of juice Rosa can buy with 280 cents:
1 can of juice costs 35 cents, so 280 cents can buy 280/35 = 8 cans of juice.
Therefore, Rosa bought 8 cans of juice for herself and her friends.
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if the area of a parallelogram is 23/42 inches to the power of 2, and the height is 1/6 in, write an equation that relates the height, base, and area of the parallelogram?
By answering the presented question, we may conclude that (1/7) × 23 parallelograms inches x (1/6) inches Equals 23/42 inches to the power of 2
What is parallelograms?In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of parallel sides. A parallelogram is a kind of quadrilateral in which both sets of opposite sides are parallel and equal. Parallelograms are classified into four types, three of which are unique. The four distinct shapes are parallelograms, squares, rectangles, and rhombuses. A quadrilateral is a parallelogram when it has two sets of parallel sides. The opposing sides and angles of a parallelogram are both the same length. The internal angles on the same side of the horizontal line are also angles. The total number of internal angles is 360.
Let's start with the formula for parallelogram area:
Base x Height = Area
We know that the parallelogram's height is 1/6 inch and its area is 23/42 inch to the power of 2. So, by plugging these values into the formula, we get:
23/42 inches multiplied by 2 Equals base x 1/6 inch
6 x 23/42 inches multiplied by 2 = base
(6/42) x 23 inches multiplied by 2 = base
base = (1/7) x 23 inches
Base x Height = Area
(1/7) × 23 inches x (1/6) inches Equals 23/42 inches to the power of 2
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a sample of 100 shoppers showed a sample mean waiting time of minutes. assume a population standard deviation of minutes. what is the -value?
A population standard deviation of 8.5 minutes. Then, the p-value is 0.0436.
We know the length of the show based on the assumption that shoppers spend an average of 8 minutes in line at the store checkout.
A sample of 100 buyers reported an average sample wait time of 8.5 minutes. For example, the population standard deviation is 3.2 minutes.
Null Hypothesis, H₀: μ =8 minutes {means that the actual mean waiting time does not differs from the standard}
Alternate Hypothesis, Hₐ: μ ≠ 8 minutes {means that the actual mean waiting time differs from the standard}
The test statistics that would be used here are One-sample z-test statistics as we know about the population standard deviation;
T.S. = x-μ/σ/√n ~ N(0,1)
where, X = sample mean waiting time = 8.5 minutes
σ = population standard deviation = 3.2 minutes
n = sample of shoppers = 100
So, test statistics = 8.5 -8/3.2/√100
= 1.75
The value of t-test statistics is 1.75.
Now, the P-value of the test statistics is given by;
P-value = P(Z > 1.71) = 1 - P(Z ≤ 1.75)
= 1 - 0.9568 = 0.0438
Complete Question:
A sample of 100 shoppers showed a sample mean waiting time of 8.5 minutes. Assume a population standard deviation of 3.2 minutes. What is the p-value?
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in a study, 40% of adults questioned reported that their health was excellent. a researcher wishes to study thehealth of people living close to a nuclear power plant. among 13 adults randomly selected from this area, only3 reported that their health was excellent. find the probability that when 13 adults are randomly selected, 3 orfewer are in excellent health.a) 0.112 b) 0.169
If 40% of adults questioned reported that their health was excellent, then the probability that when 13 adults are randomly selected, 3 or fewer are in excellent-health is (b) 0.169.
The number of adults randomly selected is = 13 adults,
We need to find probability of getting 3 or fewer people reporting excellent health which is considered as success , in 13 trials
The probability of success = 0.4 ...because proportion of adults reporting excellent health in general population.
We use "binomial-probability" formula to calculate probability:
⇒ P(X ≤ 3) = ΣP(X = k), for k = 0, 1, 2, 3
where X = number of successes = people reporting excellent health and P(X = k) = probability of getting exactly k successes;
⇒ P(X = k) = C(n,k) × p^k × (1-p)^(n-k),
where n = number of trials, p = probability of success, and
substituting values,
We get,
⇒ P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3),
⇒ C(13,0) × (0.4)⁰ × (0.6)¹³ + C(13,1) × (0.4)¹ × (0.6)¹² + C(13,2) × (0.4)² × (0.6)¹¹ + C(13,3) × (0.4)³ × (0.6)¹⁰,
≈ 0.1686 ≈ 0.169.
Therefore, the required probability is approximately 0.169, the correct option is (b).
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I need step by step detailed solution to the given question.
we can shown that the areas of △PMS and △SOR are equal, and the areas of △MQT and △NRT are equal,
we can then conclude that △PMS+△MQT = △SOR + △NRT.
How do we calculate?We will label the points in the figure as follows:
PQ = RS (given that PQRS is a parallelogram)
MN = OS (given that MNOS is a parallelogram)
T is the point of intersection of MQ and PR
R is the point of intersection of PS and NT
considering △PMS and △SOR. We can see that they share a base, PS, and that the heights of both triangles are equal, since PS is parallel to MN and therefore the distance between PS and MN is the same at both ends. Therefore, the areas of these two triangles are equal.
Also considering △MQT and △NRT.
It is obvious that they share a base, QT, and that the heights of both triangles are equal, since QT is parallel to RS and therefore the distance between QT and RS is the same at both ends.
Therefore, the areas of these two triangles are also equal.
Since we have shown that the areas of △PMS and △SOR are equal, and the areas of △MQT and △NRT are equal, we can conclude that △PMS+△MQT = △SOR + △NRT.
This was using the properties of parallelograms and the fact that the triangles share a common base with equal heights.
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Sakshi prepared some jam at home and filled it in bottle. After giving away 7of the bottle to her friend, she still has 12 for herself. How many bottle had she made in all? If she filled 250g of jam in each bottle, what was the total weight of the jam she made?
Answer:
4.75 kg
Step-by-step explanation:
Bottles of jam given by Sakshi to her friends =7
Bottles of jam prepare by sakshi for herself =12
Total bottles of jam made =7+12=19
Weight of jam in 1 bottles =250 gm
Total weight of jam made by sakshi
=250×19
=4,750 gm
Total weight of jam =4.75 kg.
1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ (Record your
The linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.
The surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.
Surface area is the combined area of all the faces of a three-dimensional object. It is the area that is visible when looking at the outside of the object. It is often used to calculate the amount of material needed for a certain project or product. It is also used to calculate the cost and energy required to heat or cool a certain space. Surface area can be calculated using geometry and calculus, or it can be measured directly.
1. Linear scale factor: The linear scale factor of the enlargement is the ratio of the volume of the larger jar to the volume of the smaller jar. The volume of the larger jar is 0.58 L which is equivalent to 580 cm³. The volume of the smaller jar is 87 cm³. Therefore, the linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.
2. Surface area scale factor: The surface area scale factor of the enlargement is the ratio of the surface area of the larger jar to the surface area of the smaller jar. The surface area of a jar depends on its radius. Since the radius of the larger jar is larger than the radius of the smaller jar, the surface area of the larger jar is larger than the surface area of the smaller jar.
Therefore, the surface area scale factor of the enlargement is greater than 1. To calculate this factor, we can use the formula for the surface area of a cylinder: A = 2πrh, where r is the radius and h is the height. The height of both jars is the same, so we can calculate the surface area scale factor by dividing the radius of the larger jar by the radius of the smaller jar. The radius of the larger jar is 0.29 L, which is equivalent to 290 cm³. The radius of the smaller jar is 8.7 cm³.
Therefore, the surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.
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Complete questions as follows-
Use the following information to answer the next two questions Raj Jars Ltd. Sells different types of similar jars. One of their jars has a volume of 87 cm³ and another has a volume of 0.58 L. 1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ 2. What is the surface area scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³
f(x)=x(x
2
+1)(x+5)(x
2
−3)
F(x) is a degree 6 polynomial having roots at x = 0, I -5, and 3.
As F(x) contains six elements in the form of (x-a), where an is a root, the degree of F(x) is 6. We discover that the roots are x=0, I -5, and 3 when we set each component to zero. By resolving each issue independently, their roots can be discovered. For instance, x=0, I is obtained from x(x2+1)=0. We obtain x=-5 from (x+5)=0. We get x=3 from (x2-3)=0. The roots of F(x) are significant because they reveal where the function crosses the x-axis and where its extrema are.
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Please help, see photo attached
The point (1, -5) is not a solution to the given system of inequalities.
How to determine and graph the solution for this system of inequalities?In order to graph the solution for the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then check the point of intersection;
y ≤ 3x + 2 .....equation 1.
y > -2x - 3 .....equation 2.
Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region below the solid and dashed line, and the point of intersection of the lines on the graph representing each, which is given by the ordered pair (-1, -2).
Next, we would use the point (1, -5) to test the system of inequalities mathematically:
y ≤ 3x + 2
-5 ≤ 3(1) + 2
-5 ≤ 5 (True).
y > -2x - 3
-5 > -2(1) - 3
-5 > -5 (False)
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Find the error in the work below. Then show the correct calculation. 8/12x6= 8x1/12x6= 8x1/72= 8/72= 1/9
The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division. the correct answer is [tex]4[/tex] , not [tex]1/9[/tex] .
What is the multiplication and division?The error in the calculation above is in the first step. When performing multiplication and division in the same step, you should always perform the multiplication before the division. This is known as the order of operations.
The correct calculation would be:
[tex]8/12 \times6 = (8/12) \times 6[/tex] (perform the multiplication first)
[tex]= (2/3) \times 6[/tex] (simplify the fraction)
[tex]= 12/3[/tex]
[tex]= 4[/tex]
The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division.
The correct calculation is as follows:
[tex]8/12 \times 6 = (8/12) x\times6[/tex] // Multiplication first
[tex]= (2/3) \times 6 /[/tex] / Simplify 8/12 to 2/3
= [tex]12/3[/tex] // Multiply 2/3 by 6
= [tex]4[/tex] // Simplify 12/3 to 4
Therefore, the correct answer is [tex]4[/tex] , not [tex]1/9[/tex] .
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