The percentage of the whole population voted. A pie chart is best used to show the percentage of the whole that different categories represent, in this case the percentage of the whole population that voted.
A pie chart is one of the most commonly used types of data visualization because it provides an easy way to understand the proportional distribution of the data that is being presented. In a presentation about voter turnout, a pie chart would be an excellent way to illustrate what percentage of the whole population voted. Pie charts can be used to show how a whole is divided into different categories, and how much of the whole each category represents. This type of chart is especially useful for presenting data in a visually appealing way and for making comparisons between different categories. In the case of voter turnout, a pie chart would be ideal for showing the percentage of the population that voted, and for comparing the proportions of those who did and did not vote.
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if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the ---select--- point determined by t
If we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
What is a terminal point?
The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle is the ray that has reached its terminal point. The most typical acute-angle measurements are represented by the sine and cosine values.
The coordinates of the terminal point come from the coordinates of the reference point (positive or negative depending on the quadrant.)
We know that a unit circle is the circle of radius 1 which is centered at the origin in the xy-plane.
General equation of a unit circle is: x^2+ y^2 = 1
Starting at the point (1,0),
If t≥0, then, t is the distance along the unit circle in clockwise direction
If t<0, then mod t is the distance along the unit circle in clockwise direction.
Here, role="math" , localid="1648202152711"t is a real number by which a point P(x,y) is generated. This point is known as the terminal point which is determined by the real number t.
Hence, if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the terminal point determined by t.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent are:
2 + x = 5
x + 1 = 4
-5 + x = -2
How to Determine Equivalent Equations?If any two or more equations are equivalent, they would have the same value when evaluated.
To find which equations are equivalent, solve to find the value of x in each given equation.
A. 2 + x = 5
x = 5 - 2
x = 3
B. x + 1 = 4
x = 4 - 1
x = 3
C. 9 + x = 6
x = 6 - 9
x = -3
D. x + (-4) = 7
x = 7 + 4
x = 11
E. -5 + x = -2
x = -2 + 5
x = 3
The equivalent equations are:
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ivan had scores of 62, 75 and 90 on three of four tests. if his average on all four tests was 80.5, his score on the fourth test was
The score of fourth test is 95
what is mean?The mean, also known as the average or the arithmetic mean, is a measure of central tendency that represents the sum of a set of values divided by the number of values in that set. It is one of the most common ways to summarize a set of data and is often used as a reference point for other measurements such as standard deviation. It is represented by the Greek letter "mu" (µ) for population mean and "x bar" for sample mean.
Given mean of the score is 80.5
mean of score is given as (∑ score) / n
where ∑ score is sum of score of all marks and n is the number of test he had attempted
∑ score = 62 + 75 +90 +x
where x is marks in fourth subject
so ∑ score = mean * 4
=> 227 + x = 80.5 *4
=> x = 322 -227
so x = 95
so the marks of the fourth test is 95.
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use the regression equation to predict the head circumference of a child who is 24.25 inches tall. y
The regression equation to predict the head circumference of a child who is 24.25 inches tall y=17.20 inches
The regression line with the least squares
y = 0.1827*x + 12.4932
Children that are 25.25 inches tall should have a mean head circumference that we can anticipate.
Let x = 25.75
y is thus equal to 0.1827*25.75 plus 12.4932.
b) The mean head circumference of kids who are 25.25 inches tall falls within the 95% confidence interval of
The Mean of the head circumference is 17.327, the standard deviation is 0.219, there are 11 participants, and there are 10 participants in step c.
y = 0.1827*x + 12.4932
The head circumference of a youngster who is 25.25 inches tall must be predicted.
Let x = 25.75
y is thus equal to 0.1827*25.75 plus 12.4932.
y=17.20 inches.
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if a to b ratio, b to c ratio, c to d ratio, are given, then express a to d in terms of given ratios
The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).
The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.
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Suppose that the price elasticity of demand for mystery novels is 3. If we observe the quantity of mystery novels sold falling by 9%, what must have happened to price?
A. Price decreased by 3%.
B. Price increased by 3%.
C. Price decreased by 27%.
D. Price increased by 1%.
// Economics question but yeah.
find the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon,
The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time.
The angle of elevation is the angle formed by the rope attached to the boat and the horizon. It is measured from the horizon line and can be used to measure the height of the boat relative to the horizon. The rate of change of the angle of elevation is the rate at which the angle between the rope and the horizon changes over time. This rate of change can be calculated by measuring the change in the angle over a specific time period and dividing it by the time period. This rate of change can be used to determine the speed at which the boat is moving up or down relative to the horizon. It can also be used to measure the rate of acceleration or deceleration of the boat.
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The complete question is
What is the rate of change of the angle of elevation, which is the angle formed by the rope attached to the boat and the horizon, given the speed of the boat and the distance from the boat to the horizon?
0.125 less than 0.127
Answer: 0.002. 0.127 - 0.125 is 0.002
Use the ALEKS calculator to evaluate each expression.
Round your answers to the nearest thousandth.
Do not round any intermediate computations.
log √7=
Log 23/6=
The values would be
log √7= 0.291
log 23/6= 0.585
What is a logarithm?
A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The most common base used in logarithms is base 10, but logarithms can be defined with any base. If the base of a logarithm is not specified, it is assumed to be base 10. The logarithm of a number is represented by the symbol log.
log √7 = (1/3)log7
Log 23/6 = log(23) - log(6)
The logarithm of a number is the exponent to which the base must be raised to produce that number. If the base of the logarithm is not specified, it is assumed to be base 10.
The square root of 7 is around 2.646, and log2.646 is around 0.874, so
log √7 = (1/3)log7 = (1/3)*0.874 ≈ 0.291
The logarithm of 23 is around 1.363 and the logarithm of 6 is around 0.778, so
Log 23/6 = log(23) - log(6) = 1.363 - 0.778 = 0.585
Hence, the values would be
log √7= 0.291
log 23/6= 0.585
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Writing and solving radical equations: Mastery Test
The solutions to this equation are x=5 and x=2.
What is the factor of the equation?
A factor in an expression is something that is multiplied by something else. It can be a number, variable, term or any other longer expression. For example, the factors of 2xy are 2, x and y.
We have,
(√x-1) - 5 = x - 8
To solve this equation, you can start by isolating the variable (x) on one side of the equation.
You can begin by adding 5 to both sides of the equation, which will give you (√x-1) = x-3.
Then, you can square both sides of the equation, which will give you x-1 = x^2-6x+9.
To solve for x, you can add 1 to both sides, which will give you x^2-6x+10=0.
You can then factor this equation to get (x-5)(x-2)=0.
Hence, The solutions to this equation are x=5 and x=2.
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a botanist wanted to know if plants with mycorrhizae have a higher rate of respiration and photosynthesis than do plants without mycorrhizae. the data he collected is below. determine the sample size, mean, standard deviation, and standard error for each data set
The sample size of the data set is the total number of plants in the experiment. The mean is the average of the data set, the standard deviation is the measure of how much the values in the data set vary from the mean, and the standard error is a measure of the accuracy of the mean.
The sample size of the data set is the total number of plants in the experiment and can be determined by counting the total number of plants in the experiment. The mean is the average of the data set and can be calculated by taking the sum of all the values divided by the sample size. The standard deviation is the measure of how much the values in the data set vary from the mean and can be calculated by taking the square root of the sum of all the squared differences divided by the sample size minus one. The standard error is a measure of the accuracy of the mean and can be calculated by taking the standard deviation divided by the square root of the sample size.
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suppose you take a random sample of size 25 from a population with mean of 120 and a standard deviation of 15. your sample has a mean of 115 and a standard deviation of 13.8. which of the following has a mean of 120 and a standard deviation of 3?
3 has a mean of 120 and a standard deviation of 3.
Describe standard deviation using an example?
The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.
mean of sample means = true mean = 120
std dev of sample mean = true std / sqrt(n)
= 15/5 = 3
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Determine whether the matrix is in row-echelon form. if it is, determine whether it is also in reduced row-echelon form. (select all that apply.)
1 0 0 0
0 1 1 7
0 0 0 0
- row echelon form
- reduced row echelom form
- neither
It is neither row echelon form nor reduced row echelon form matrix
How do you know if a matrix is in echelon form or reduced echelon form matrix ?
A matrix is in reduced row-echelon form if it satisfies the following:
In each row, the left-most nonzero entry is 1 and the column that contains this 1 has all other entries equal to 0. ...
The leading 1 in the second row or beyond is to the right of the leading 1 in the row just above.
if you look at the two row echlon form you can see that it has leading entries(starting form left) that all one and there are no-zero elements above diagonal which can be any numbers (2,3,4, 6, x,y,x).
However reduced row echelon of has always leading elements 1 and are on diognal, this form is always like this therefore we can infer that reduced row echlon form is always uniqe as oppose to row echelon form.
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for the sequence 11,13,15,_,_,_, find the formula for the nth term
Answer:
aₙ = 9 + 2n
Step-by-step explanation:
Formula for the nth term of an arithmetic sequence, aₙ with a common difference of d and first term of a₁ is
aₙ = a₁ + d(n-1)
The common difference is the difference between two consecutive terms and is a constant
Here d = 13- 11 = 15-13 = 2
First term is 11
nth term:
aₙ = 11 + 2(n-1)
aₙ = 11 + 2n -2
aₙ = 9 + 2n
So if you wanted the 10 term say it would be
a₁₀ = 9 + 2x 10 = 9 + 20 = 29
Which equation matches the graph of the greatest integer function given
below?
The greatest integer function is a function that gives the greatest integer less than or equal to a given number. The standard graph is in the picture.
The graph you have is that function, shifted down by 2 units.
The answer is c.
The length and breadth of a cuboid shaped paper are 1m and 60 cm respectively. If 1920 small cubes of 5 cm each can be placed in the box, find the height of box.
Answer:
h = 40 cm
Step-by-step explanation:
1. Let's calculate the total volume of 1920 cubes, size 5 x 5 x 5 cm:
V one = 5 cm x 5 cm x 5 cm = 125 cm³
V all = 1920 x 125 = 240,000 cm³
2. Divide this volume by the area of the paper to get the height, given that 1 m = 100 cm:
S paper = 100 cm x 60 cm = 6,000 cm²
h = V all / S paper = 240,000 / 6,000 = 40 cm
A students tuition was $4263 a loan was obtained for 4/7 of the tution how much was the Loan?
FILL IN THE BLANK if the dollar price of the euro increases from $1.50 to $2.00, the dollar is _______ and european goods are ____expensive to americans. (5 points)
The dollar is weakening in comparison to the euro, making European goods more expensive for Americans. American consumers must spend more to purchase the same amount of goods from Europe.
When the dollar price of the euro increases from $1.50 to $2.00, it means that the euro has strengthened relative to the dollar. This means that the dollar has weakened in comparison to the euro. This weakened dollar results in American consumers needing to spend more to purchase European goods. As the dollar price of the euro increases, it takes more dollars to purchase the same amount of euros, meaning the same amount of goods from Europe will cost more dollars. This means that European goods become more expensive to Americans as the dollar price of the euro increases. This is a result of the weakened dollar and the strengthened euro in comparison to each other.
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−4≤−2(y−1)<2
Step 2 of 2 : Graph the solution set.
Answer:
draw a line between an empty point at 0 and a filled point at 3
Step-by-step explanation:
To graph this inequality we first want to isolate the y variable to make it a bit easier to deal with. This is a compound inequality and when isolating the y variable instead of just doing an operation on both sides, we do it to all sides which follows the same principle of maintaining equality.
We start with the original inequality:
[tex]-4 \le -2(y-1) < 2[/tex]
From here we divide by -2 on all sides, but since we're dividing by a negative we would flip the way the inequality is pointing so we get:
[tex]2\ge y-1 > -1[/tex]
From here we add 1 to all sides.
[tex]3 \ge y > 0[/tex]
Although generally we would write this as:
[tex]0 < y \le 3[/tex]
Now to graph this we would draw a hole on the number line at the point zero, and a filled point on the number line at 3, since 3 is included (since less than or equal to 3) and then just connect the two points. I'll include an image that demonstrates this.
Calculate the angle EOD in the figure above
2. Calculate the angle DOC In the angle above
Answer:
Step-by-step explanation: Hello!
To find angle EOD, you are already given two angle measurements. The measure of angle AOB is 55 degrees and the measure of angle BOC is 30 degrees. The important thing that you have to remember to solve this problem is that vertical angles are congruent. (I won't be explaining the definition of vertical angles, but you can find a lot of images and explanations online). This means the two angles formed by two lines intersecting each other in any way is always congruent. Angles AOB and EOD are congruent by the definition of vertical angles. This means that the measure of angle EOD is 55 degrees.
Now, you have to find the measurement of angle DOC. By the definition of straight lines, you know that the angles formed by a straight line all add up to 180 degrees. This means that:
EOD + DOC + COB = 180 degrees. You are already given two of these measurements. (Angle EOD which you just figured out and Angle COB which was already given). Fill these numbers in the equation.
55 + DOC + 30 = 180. Combine like terms (55 + 30)
85 + DOC = 180. Then subtract 85 from both sides using the subtraction property of equality.
(85 - 85) + DOC = (180 - 85)
DOC = 95.
The measure of angle DOC = 95.
You can check this by substituting the new measurement for angle DOC back into the equation.
Does 55 + 30 + 95 = 180?
85 + 95 = 180
180 = 180.
The measure of angle DOC is 95 degrees and the measure of angle EOD is 55 degrees.
rewrite the equation in slope-intercept form
3x - 2y = 8
[tex]y=\frac{3}{2}x-4[/tex]
Step-by-step explanation:Linear functions can be written in different forms such as standard and slope-intercept form.
Rewriting the Equation
To rewrite standard form (Ax + By = C) into slope-intercept, simply solve for y. To solve for y, we need to isolate it. We can do this using the properties of equality. Firstly, move x to the opposite side.
Subtract 3x from both sides.
-2y = -3x + 8Then, divide both sides by -2.
[tex]y=\frac{3}{2}x-4[/tex]This is the slope-intercept form.
Interpreting the Values
Slope-intercept form is written as y = mx + b, m is the slope and b is the y-intercept. This means that the slope of the line we were given is 3/2. Additionally, the y-intercept is -4.
Answer:
y = 3/2 x - 4
Step-by-step explanation:
The given equation is:
Recall that the slope-intercept form is of the form:
Therefore the equation can be rewritten as follows:
What type equation is this is it a rational ?
Answer:
A rational equation is an equation containing at least one fraction whose numerator and denominator are polynomials, \frac{P(x)}{Q(x)}. Q(x)P(x). These fractions may be on one or both sides of the equation.
Find the surface area of the solid.
The surface area of the cuboid is 94 m² while The surface area of the triangular pyramid is 259.695 in²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Surface area is the sum of each area of the solid surface.
7) For the cuboid:
Surface area = 2(3 m * 4 m) + 2(3 m * 5 m) * 2(4 m * 5 m) = 94 m²
The surface area of the cuboid is 94 m²
8) For the triangular pyramid:
Surface area = 3(1/2 * 17.4 in * 8.7 in) + (1/2 * 8.7 in * 7.5 in) = 259.695 in²
The surface area of the triangular pyramid is 259.695 in²
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Use determinants to decide if the set of vectors is linearly independent. -2 The determinant of the matrix whose columns are the given vectors is (Simplify your answer:) Is the set of vectors linearly independent? A The set of vectors is linearly dependent; because the determinant exists_ 0 B. The set of vectors is linearly independent; because the determinant exists_ O
c: The set of vectors is linearly independent, because the determinant is not zero_ 0
D: The set of vectors is linearly dependent, because the determinant is not Zero.
The determinant of a matrix is a scalar value that can be used to determine if a set of vectors is linearly independent.
It is calculated by taking the product of the elements in each row or column and subtracting the product of the elements in the other row or column. For example, if we have a matrix with two columns and two rows, A and B, the determinant can be calculated using the following formula: det(A) = (A11*A22) - (A12*A21). If the determinant is equal to zero, then the set of vectors is linearly dependent, as this implies that all of the elements in the matrix are multiples of each other. On the other hand, if the determinant is non-zero, then the set of vectors is linearly independent. This can be seen because all of the elements in the matrix are not multiples of each other and thus the set of vectors cannot be expressed as a linear combination of each other.
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In a city library, the mean number of pages in a novel is 525 with a standard deviation of 200.
Furthermore, 30% of the novels have fewer than 400 pages. Suppose that you randomly select 50 nov from the library.
What is the probability that at least 20 of the novels have fewer than 400 pages?
The probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
What is the normal distribution and the cumulative distribution?
The normal distribution, also known as the Gaussian distribution or bell curve, is a probability distribution that describes the distribution of a continuous random variable.
The cumulative distribution function (CDF) is a function that gives the probability that a random variable is less than or equal to a certain value
To solve this problem, we can use the normal distribution and the cumulative distribution function (CDF) of a normal distribution. The normal distribution is a probability distribution that describes how many novels have a certain number of pages.
The mean number of pages in a novel is given as 525 and the standard deviation is 200. We know that 30% of the novels have fewer than 400 pages, which corresponds to a z-score of (400 - 525) / 200 = -0.75.
We can use the cumulative distribution function (CDF) to find the probability that at least 20 of the novels have fewer than 400 pages. The CDF of a normal distribution gives the probability that a random variable is less than or equal to a certain value.
The probability that at least 20 of the novels have fewer than 400 pages is the same as the probability that at most 30 of the novels have more than 400 pages. Using a standard normal table or software, we can find the probability that a standard normal random variable is less than -0.75 as P(X< -0.75) = 0.2266, this is the probability that less than 30 novels have more than 400 pages.
Hence, the probability that at least 20 of the novels have fewer than 400 pages is 1 - 0.2266 = 0.7734 or 77.34%.
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Which of the following scatterplots provides evidence that the condition of equal variance for inference for the slope of a regression line has not been met?
Such a plot is evidence of a linear relationship between the explanatory and response variables, which is a condition for these inference procedure
These are the four presumptions: Relatively linear residuals Continuity of residuals The residuals are distributed normally. residual variance is same.
Linearity: We plot the residuals and y values in a scatter plot. Y values are shown on the horizontal x axis and standardized residuals, or ZRESID in SPSS, are derived from the vertical y axis. The linearity assumption is satisfied if the scatter plot displays a linear pattern (rather than a curved pattern).
We generally have two types of data: cross sectional and longitudinal. Cross -sectional datasets are those where we collect data on entities only once. For example we collect IQ and GPA information from the students at any one given time.
Independence is a concern when working with longitudinal datasets. With a longitudinal dataset, observations are gathered from the same subject across time. For example, in stock price information, we gather price information on the same stock, the subject, throughout time.
The two forms of data that we typically use are longitudinal and cross sectional. Datasets that are cross-sectional are those for which entities' information is only collected once. For instance, we constantly get IQ and GPA data from the kids.
We gather GPA data from the same student over time in a longitudinal data set.
We do not need to worry about the Independence assumption in cross-sectional datasets. It is "assumed" that it will be.
Normality: First, we create a histogram of the residuals, and then we check to see if they are normal. The assumption is met if the residuals do not exhibit skewness.
A scatterplot of the residuals vs the explanatory variable values shows a haphazard distribution of dots around the line.
Correct. This inference technique requires a linear relationship between the explanatory and response variables, which is demonstrated by a plot like this.
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.
You have agreed to loan some money to a friend at a simple interest rate of 153% per year. Your friend hasn't taken this class; all they know is that they can pay you back $500 in 2 weeks.
How much money do you give your friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year? Round your answer to the nearest dollar.
The amount of money gives to my friend today so that the repayment of $500 in 2 weeks is equivalent to a simple interest loan with a rate of 153% per year is, $477.10
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Loan agreed on simple interest rate = 153% per year
He knows that he can pay me back $500 in 2 weeks or 2/52 years
Suppose, money given to him = P
So, simple interest of amount P in 2 weeks
I = P × 125 ×(2/52) /100
= 0.048P
Total repayment = P + 0.048P
He can pay back only $500
Total repayment = $500
P + 0.048P = $500
1.048P = 500
P = 477.10
Hence, the loan amount is $477.10
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A sociologist develops a test to measure attitudes towards public transportation, and n = 80 randomly selected subjects are given the test. Their mean score is = 84 and their standard deviation is s = 15.4. Find the margin of error E for the 95% confidence interval for the mean score of all such subjects, and round to the nearest tenth.
Answer:
Step-by-step explanation:
t%5Bc%5D=2.055
ME=SE%2At%5Bc%5D
ME=4.118%2A2.055
ME=8.463
.
.
.
(67.7,84.7)
a norman window has the shape of a rectangle surmounted by a semicircle. (thus the diameter of the semicircle is equal to the width of the rectangle. see exercise 1.1.72.) if the perimeter of the window is 30 ft, find the dimensions of the window so that the greatest possible amount of light is admitted.
The dimensions that maximize the area of the window are:
Width: 8.4 ftHeight: 4.2 ftWhat is diameter of the semicircle?If any of the following values are known, the diameter of a semicircle can be easily determined: Surface, bounds, or circumference. The diameter (d) is equal to ((8A/)) units if A is the semicircle's area. The semicircle's diameter (d) is calculated using the formula 2P/(+2) units if P is its perimeter. The equation (x - h)2 + (y - k)2 = r 2 is often solved for y to get a pair of equations with the form y = r 2 - (x - h)2 + k. A positive square root equation explains the upper semicircle, and a negative square root equation describes the lower semicircle.We have a Norman window, where the rectangle's width and the semicircle's diameter are the same.The rectangle's perimeter is made up of its two heights, one width, and half of its circumference.The perimeter can be expressed as follows if w is the semicircle's diameter (and the rectangle's breadth) and h is the other side of the rectangle:[tex]$P=2 h+w+\frac{\pi \cdot w}{2}=30$[/tex]
[tex]$2 h+(1+0.5 \pi) w=30$[/tex]
[tex]$h=\frac{30-(1+0.5 \pi) w}{2}=15-(0.5+0.25 \pi) w$[/tex]
With the restriction for the perimeter [tex]$(\mathrm{P}=30)$[/tex], we can express h in function of w. Now, we can express the area only in function of w and maximize its value:
[tex]& A=A_c / 2+A_r=\frac{1}{2} \cdot \frac{\pi w^2}{4}+h w=\frac{\pi w^2}{8}+\left[15-\left(\frac{1}{2}+\frac{\pi}{4}\right) w\right] \cdot w \\[/tex]
[tex]& A=15 w-\left(\frac{1}{2}+\frac{\pi}{4}-\frac{\pi}{8}\right) w^2=15 w-\left(\frac{1}{2}+\frac{\pi}{8}\right) w^2[/tex]
To maximize the area, we derive and equal to 0 :
[tex]$\frac{d A}{d w}=15(1)-\left(\frac{1}{2}+\frac{\pi}{8}\right)(2 w)=0$[/tex]
[tex]$$15-(1+\pi / 4) w=0$$[/tex]
[tex]$w=\frac{15}{1+\pi / 4} \approx 8.4$[/tex]
Now, we can calculate the height as:
[tex]$$h=15-(0.5+0.25 \pi) w$$[/tex]
[tex]$$h \approx 15-(1.2854) \cdot 8.4=15-10.8=4.2$$[/tex]
To learn more about diameter of the semicircle refer to;
https://brainly.com/question/20048128
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Given the function f(x) = 8x +5, evaluate and simplify the expressions below. See special instructions on how to enter your answers. Look at photo for the expressions and special instructions
Answer:
[tex]f(a)=8a+5\\\\f(x+h)=8x+8h+5\\\\\frac{f(x+h)-f(x)}{h}=8[/tex]
Step-by-step explanation:
Substitution:When we're asked to write what f(x+h) or f(a) is equal to, all we really have to do is substitution. The original function is provided as [tex]f(x)=8x+5[/tex], and all that "x" represents is input, now we can manipulate what that input is by simply substituting in new input. So if we want to write f(x+h), we substitute in "x+h" for "x".
f(a) = ?For this problem, we just do what was stated about and replace all of the x's, with a's, meaning: [tex]8x+5\to 8a+5[/tex].
f(x+h) = ?We essentially do the same thing here, although we will have to simplify more, but the first step is as follows: [tex]8x+5\to 8(x+h)+5[/tex], now from here we want to expand out the [tex]8(x+h)[/tex] by using the distributive property, so it becomes: [tex]8x+8h[/tex] and plugging this into our equation we get: [tex]8x+8h+5[/tex]
[f(x+h)-f(x)]/h = ?For this last question, I think it's also important to note that this is the formula to calculate the slope between point "x" and the point "h units away" or "x+h".
We already know what f(x+h) is and what f(x) is, so let's plug those into the equation:
[tex]\frac{(8x+8h+5)-(8x+5)}{h}[/tex]
Now let's distribute the negative sign to get:
[tex]\frac{8x+8h+5-8x-5}{h}[/tex]
Now let's group like terms:
[tex]\frac{(8x-8x)+(5-5)+8h}{h}[/tex]
Now let's simplify the grouped terms
[tex]\frac{8h}{h}[/tex]
Now let's divide by h to get:
[tex]8[/tex]
And this is our answer!
