The probability that the students will be arranged in order from shortest to tallest is 1/(8!) or 1/40320.
What is student?Student is an individual who is enrolled in an educational institution such as a university, college, or a trade school. A student typically takes courses in order to further their knowledge and skills, to prepare for further education or training, or to receive credentials necessary to pursue a job or career. Students can include both full-time and part-time learners. Depending on the institution, a student may also be referred to as a pupil, student-athlete, or scholar. Students can also take part in a variety of student-led activities and organizations, both on-campus and off-campus.
This is because there are 8! (8 factorial) ways in which the students can be arranged in order from shortest to tallest.
Therefore, the probability of any one arrangement is 1/8!
Thus, the probability of the students being arranged in order from shortest to tallest is 1/8! or 1/40320.
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An ABS (Australian Bureau of Statistics) employee wishes to test the speed (in minutes) with which different online survey designs can be completed. Three different online survey designs have been proposed. One complication in assessing the surveys is the notion that individual differences might influence the speed with which the online forms are completed. To account for individual differences an experiment is arranged so that a survey from each design is completed by each individual. The following results are extracted from a randomised block experiment with three treatment levels (i.e. three types of online survey designs) and five blocks (i.e. 5 individuals). SSBL (sum of squares between blocks) = 3738, SSB (sum of squares between groups) = 1048.93 and SST (sum of squares total) = 5391.33. Based on this information, what is the critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance? Use our textbook statistical table to answer the question.
The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.
The critical value can be determined using a statistical table.
The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).
The critical value for a 5% level of significance is 10.76.
This value can be found in the statistical table given in the textbook.
The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.
The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).
The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).
In this case,
The F statistic is 3738/1048.93 = 3.56.
The critical value for a 5% level of significance can be found using a statistical table.
According to the table,
The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76
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a report claims that the proportion of all adults who are vegetarians is 0.12. believing this claimed value is incorrect, a researcher surveys a large random sample of 1,000 adults and finds that 140 of the adults in the sample are vegetarians. what will the test statistic be equal to in this example? as you are engaging in calculations, try not to do a lot of rounding until you get to the very end, and choose the answer below that is closest to what you calculate. a. 2.5 b. 1.4 c. 1.9 d. 0.3 d. less than 0.1
The correct answer is (c) 1.9
How to calculate the test statistic?To calculate the test statistic in this example, we can use the formula for a z-test for proportions:
[tex]z = (p - P) / \sqrt{[P(1-P) / n][/tex]
where:
p is the sample proportion of vegetarians (140/1000 = 0.14)
P is the hypothesized population proportion of vegetarians (0.12)
n is the sample size (1000)
Substituting these values into the formula, we get:
[tex]z = (0.14 - 0.12) / \sqrt{[0.12(1-0.12) / 1000][/tex]
z = 0.02 / 0.0110
z = 1.818 (rounded to three decimal places)
Therefore, the test statistic in this example will be approximately equal to 1.818. The answer closest to this value is (c) 1.9
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how many intervals (or 'bins' or 'classes') should be chosen when creating a histogram? question 1 options: most often, about 8-10. eleven. it can vary - it really depends on the distribution of the variable. a minimum of 5.
"It can vary - it really depends on the distribution of the variable."
The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.
Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.
Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.
The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.
While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.
In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.
A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.
Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.
There is no established guideline, however 8–10 intervals are typically utilized.
A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.
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Make a box-and-whisker plot of the data. 60,63,53,66,65,58,51,55,58,51,58,62,53,66,61,51,65,52,54,50
Minimum value is 50, maximum value is 66, median is 59, Q1 is 53.5 and Q3 is 65. Box-and-whisker plot:
Define whisker plot?A box plot, often referred to as a whisker plot, shows the distribution of a continuous variable along with details like the median, quartiles, and outliers. A set of data's variety is shown graphically in this way. The plot, often known as a five-number summary, presents five bits of information. The fundamental benefit of box whisker plots is that the overlap between the distributions of various qualities may be calculated by comparing them side by side.
You must determine the minimum value, maximum value, median, and quartiles in order to create a box-and-whisker plot of the provided data.
The base number is fifty.
The highest number is 66.
You must sort the data from smallest to largest in order to determine the median. The listed data are:
50, 51, 51, 52, 53, 53, 54, 55, 58, 58, 58, 60, 61, 62, 63, 65, 65, 66, 66
The middle value of the ordered data is the median. Finding the average of the two middle values is necessary since the data set (18 values) contains an even number of values:
(58 + 60) ÷ 2 = 59
Divide the ordered data into four equal sections before calculating the quartiles. The median of the lower half of the data set is the first quartile (Q1). The median of the data set's upper half represents the third quartile (Q3).
The data set's lower half consists of:
50, 51, 51, 52, 53, 53, 54, 55
The data set's upper half is as follows:
58, 58, 58, **60**, **61**, **62**, **63**, **65**, **65**, **66**, **66**
First quartile (Q1):
(53 + 54) ÷ 2 = **53.5**
Third quartile (Q3) comprises:
(65 + 65) ÷ 2 = **65**
With all of this knowledge at hand, you can now develop a box-and-whisker plan.
Given below:
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the standard deviation of a normal distribution group of answer choices is always 0. is always 1. can be any value. cannot be negative.
The standard deviation of a normal distribution group of answer choices is always 1.
What is the standard deviation of a normal distribution group of answer choices?In a normal distribution, the standard deviation is a measure of the spread or dispersion of the data. The standard deviation is defined as the square root of the variance, which is the average of the squared differences from the mean.
For a standard normal distribution, which has a mean of 0 and a standard deviation of 1, the area under the curve between any two values represents the probability of getting a value between those two values. This property of the standard normal distribution is useful for calculating probabilities in statistics.
However, for a normal distribution that is not standard, the standard deviation can be any positive value. In this case, the mean and standard deviation defines the shape and location of the distribution. A larger standard deviation indicates that the data is more spread out, while a smaller standard deviation indicates that the data is more tightly clustered around the mean.
Therefore, the standard deviation of a normal distribution group of answer choices can be any positive value, but it is often standardized to 1 for ease of calculation and interpretation.
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Tell whether a triangle can have the given angle measures. 115. 1∘, 47. 5∘, 93∘
No, a triangle cannot have the given angle measures, 115. 1∘, 47. 5∘, 93∘, as sum of these is greater than 180°.
The angle sum of a triangle will always be equal to 180°. The angle sum of a quadrilateral is equal to 360°, and a triangle can be created by slicing a quadrilateral in half from corner to corner. Since a triangle is essentially half of a quadrilateral, its angle measures should be half as well.
The sum of the angles in a triangle is always 180°, and 115.1° + 47.5° + 93° = 255.6°, which is greater than 180°.
Therefore, it is not possible for a triangle to have these angle measures.
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you are constructing a box from a piece of cardboard with dimensions 5 by 7 meters. you cut equal-size squares from each corner of the cardboard so you may fold the edges to construct the open top box. what are the dimensions of the box with the largest volume?
3.1634 m , w = 1.1634 , h = 1.91834 m are the dimensions of the box with the largest volume.
What is a simple volume definition?
Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The basic formula for the area of a rectangle is length x width, but the basic formula for volume is length x width x height.
Length of cardboard = 7 m
width of a cardboard = 5 m
let x be the side of square of piece cut from each corner
length of box = (7 -2x) m
width of box = (5 - 2x) m
height of box = x
volume V = (7 -2x) * (5 - 2x) * X
= (35 - 14X - 10X + 4X²) * X
= 4X³ - 24X² + 35X
If v is max v' = 0 and v'' < 0
v' = 12x² - 48x + 35
x = 6.0816 or 1.91834
if x = 6.0816 , box will not be follow.
x = 1.91834
v''(x) = 24x - 48
= 46.04 - 48 = -1.95 < 0
V is max.
length = 7 - 3.8366 = 3.1634 m
width = 5 - 3.8366 = 1.1634 m
height = 1.91834 m
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En el año 2018. Un electricista cobraba $10 000 por uno de sus trabajos. En la actualidad cobra $12 500 por el mismo trabajo. ¿En qué porcentaje aumentó su tarifa respecto de lo que cobraba en el año 2018?
The electrician's rate experienced a 25% increase compared to what he charged in the year 2018.
A percentage is a number or ratio expressed as a fraction of 100, used to indicate the portion of something in relation to its whole.
To find the percentage increase in the rate, we need to calculate the difference between the two rates and express it as a percentage of the original rate.
The difference between the two rates is
$12,500 - $10,000 = $2,500
To express this difference as a percentage of the original rate, we need to divide it by the original rate and then multiply by 100:
($2,500 / $10,000) x 100% = 25%
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The diameter of a circle is 3.6 m. Find the radius, circumference and area. Show your working.
Step-by-step explanation:
Given :
d = 3.6m
r = d/2
r = 3.6/2
r = 1.8 m
We know that,
C = 2πr
C = 2 * 22/7 * 1.8
C = 11.3 m
Now,
A = π r²
A = 22/7 × (1.8)²
A = 22/7 × 3.24
A = 10.1 m²
Answer:
The Radius is 1.8, The circumference is 11.3 ,The area is 10.2
Step-by-step explanation:
The radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .
To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.That's it; you found the circumference of the circle.Or you can use the circle's diameter:Multiply the diameter by π, or 3.14.The result is the circle's circumference.
Diameter of circle= 3.6cm So, radius of circle=3.6/2Radius of circle = 1.8 Now ,Area of circle =πr². [r=radius] so 3.14 times 1.8 times 1.8 and you get 10.17 then round it to the nearest tenth and it is 10.2
I need help with these problems
a) x= 20, y=20√3 b) x=2, y=2/√3 c) x=9, y=√162 is the correct answer.
What is right triangle?Right triangle is that triangle in which one angle has to be 90 degree.The side opposite the right angle is called the hypotenuse, while the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
a)sinα= perpendicular/hypotenuse
sin30°=x/40
1/2=x/40
2x=40
x=20
tanα= perpendicular/base
tan30°=x/y=20/y
1/√3=20/y
y=20√3
b) tanβ=⊥/base
tan60°=2√3/x
x√3=2√3
x=2
tanγ=⊥/base
tan30°=y/x=y/2
1/√3=y/2
y=2/√3
c) tanω=⊥/base
tan45°=9/x
1=9/x
x=9
y²=9²+x²
y²=81+81
y=√162
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1. Decide if each quadrilateral is a paranciogram. Explain
1 Pt
105
DOOOO
B
A
75
DE
1 Pt
OO
A B
4/7 -
11
65°
E
1 Pt.
For what value of x must the quadrilateral be a parallelogram?
A
O
B
с D E
A. Yes the quadrialateral is a parallelogram, because consecutive angle are supplementary.
B. Yes the quadrialateral is a parallelogram, because one pair of opposites sides is both
parallel and congruent
C. Yes the quadrialateral is a parallelogram, because opposite angles are congruent.
D. Yes the quadrialateral is a parallelogram, because diagonals bisect each other.
E. No we do not have enough information to prove this is a parallelogram.
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For all given Quadrilaterals none has enough information provided in the problem to definitively say - if they are a parallelogram.Hence, option E is correct for all.
How to determine if Quadrilateral is a parallelogram?If a quadrilateral is a parallelogram, it satisfies the following properties:
Opposite sides are parallel.Opposite sides are equal in length.Opposite angles are equal.Diagonals bisect each other.It is important to note that in order to definitively conclude that a quadrilateral is a parallelogram, all four properties must be satisfied. If only one or some of the properties are met, it does not necessarily guarantee that the quadrilateral is a parallelogram.
Figure 1-: Adjacent angles are 105 and 75 degrees, which satify the condition of opposite angles being equal but except this no other information is provided, Hence, we don't have enough information to say figure 1 is a parallelogram.
Figure 2-: Diagonals bisect each other and make angle 65 degree with each other. Given that Diagonal 1 bisects Diagonal 2 and the opposite sides of the quadrilateral are equal, by using SAS criterion, the congruency of triangles formed by the diagonals can be derived to say that the opposite angles of the quadrilateral are also equal . However, we still need more information about parallelism of sides to definitively say given quadrilateral is a parallelogram.
Figure 3-: One pair of opposite side is equal in length ,while other pair of line is parallel to each other.This information is insufficient to determine if given quadrilateral is a parallelogram.
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the graph below displays the amount of time to the nearest hour spent on homework per week for a sample of students. which measures of center and variability would be most appropriate to describe the given distribution?
The measures of center and variability that would be most appropriate to describe the given distribution is D) Median and IQR.
What is median and IQR?The middle value in a set of data is represented by the median, a measure of central tendency. It is the value that, when a dataset's values are ranked from lowest to highest, distinguishes the lower from the upper half of the dataset.
The middle 50% of a dataset's interquartile range (IQR) is a measure of variability that captures this dispersion. It is the difference between the data's first (Q1) and third (Q3) quartiles. The number that divides the lowest 25% of the data from the remaining data is known as the first quartile, and the value that separates the highest 25% of the data from the remaining data is known as the third quartile.
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The complete question is:
The dolphins at the San Diego zoo eat 3 1/8 buckets of fish each day. The killer whales eat 2 3/5 times as much fish as the dolphins
how many buckets of fish do the killer whales eat each day?
If line segment AC = 9 and Angle A = 34°, find line segment BC. Round to the nearest tenth.
Answer: BC ≈ 6.4 units
Step-by-step explanation: We can use trigonometry to find the length of line segment BC.
Since we know the length of AC and the measure of angle A, we can use the trigonometric function cosine (cos) to calculate BC.
Using the formula: cos(A) = Adjacent / Hypotenuse, we have
cos(34°) = BC / 9.
Solving for BC, we get BC ≈ 6.4 units (rounded to the nearest tenth).
Here is an article on trigonometry basics: https://byjus.com/maths/trigonometry/#:~:text=Trigonometry%20Basics,are%20based%20on%20these%20functions.
A ( x + 3 ) < 5x + 15 - x
find the value for a for which the solution of the inequality is all real numbers
The value of a for which the solution of the inequality is all real numbers is a = 5.
We have to first simplify the inequality:
A(x + 3) < 5x + 15 - x
Ax + 3A < 4x + 15
Ax - 4x < 15 - 3A
Simplifying further:
x(A - 4) < 15 - 3A
Now, we need the inequality to hold for all real values of x. This means that the coefficient of x, (A - 4), must have a fixed sign, and that the right-hand side, 15 - 3A, must be unbounded.
For the coefficient of x to have a fixed sign, we need either A - 4 < 0 or A - 4 > 0. This means that A must be less than 4 or greater than 4.
For the right-hand side to be unbounded, we need 15 - 3A to be equal to positive or negative infinity. Since 15 - 3A is a linear function of A, this only occurs when A = 5.
So, the solution to the inequality for all real numbers is:
if A < 4, then the solution is x < (15 - 3A) / (4 - A)
if A > 5, then the solution is x > (15 - 3A) / (4 - A)
if A = 5, then the solution is all real numbers.
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The hour marks on a clock face are 30° apart. What is the angle a line from the four o'clock mark to the twelve o'clock mark makes with a horizontal line?
SOMEONE HELP!!!!!!!!!!!!
Answer: It's none of these because the answer is 30.
consider a dataset of towers in every state which is normally distributed. consider a sample of 40 towers. the sample data has a mean of 68 with a standard deviation of 15. how many degrees of freedom we use to find the t-critical statistic value?
39 degrees of freedom will be used to find the t-critical statistic value.
We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.
The degrees of freedom (df) for a t-distribution are calculated as given below:
df = n - 1
where n is the sample size of the problem.
In this case, the sample size is 40, so the degrees of freedom would be:
df = 40 - 1 = 39
Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.
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What is the surface area of this right rectangular prism?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
[tex]2((1 \frac{1}{3} )(1 \frac{1}{2} ) + (1 \frac{1}{2} )(5) + (1 \frac{1}{3}) (5))[/tex]
[tex]2(( \frac{4}{3} )( \frac{3}{2} ) + ( \frac{3}{2} )(5) + ( \frac{4}{3} )(5))[/tex]
[tex]2(2 + \frac{15}{2} + \frac{20}{3} )[/tex]
[tex]2( \frac{12 + 45 + 40}{6} )[/tex]
[tex] \frac{97}{3} = 32 \frac{1}{3} [/tex]
The surface area of this rectangular prism is 32 1/3 square feet.
Himpunan penyelesaian dari :
18 - 2x < 3.(2x - 1) - 3
adalah ….
Step-by-step explanation:
18-2x<3(2x-1)-3
21-2x<6x-3
24<8x
3<x
Interval notation
(3, ∞)
AD BE
DC EC
Given:
Prove: AB || DE
A
MN
2
E
3 C
B
Complete the steps of the proof.
1.
2
3.
4.
DC
Statements
BE
EC
+1= 8+1
-DC =BE+EC
BE+EC
EC
=
AD + DC
DC
5. AC=AD+DC;
BC=BE+EC
6. ACB
EC
7.23 23
8. AABC-ADEC
9.21 22
1. given
2. addition property
3. property of proportion
4. addition of fractions
5. segment addition
postulate
Reasons
6. substitution property
7. reflexive property
8.
9.+
The two statements that completes the above proof are:
ΔABC ~ ΔDEC - Side - Angle - Side Postulate
∠1≅∠2 - Corresponding angles.
What is the Side - Angle - Side postulate?The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.
Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.
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If s(d) represents the number of songs downloaded in a year d, what is the interpretation of s(2020) = 5,220,000.
A. 5,220,000 songs were downloaded in the year 2020.
B. There is not enough information to interpret the information.
C. In the year 2020 $5,220,000 was earned from downloaded songs.
D. 2,020 songs were downloaded at a cost of $5,220,000.
Answer: A. 5,220,000 songs were downloaded in the year 2020.
Step-by-step explanation: The interpretation of s(2020) = 5,220,000 is that in the year 2020, 5,220,000 songs were downloaded. The function s(d) represents the number of songs downloaded in a year d, so plugging in 2020 for d gives us the specific number of songs downloaded in that year.
MODELING REAL LIFE The volume of the largest of the six pyramids constructed by the Norte Chico people in Caral, Peru, is about 4,500,000 cubic feet. What is the height of the pyramid? A pyramid with the height h feet. Length of 8 h minus 30 feet. Width of 8 h plus 20 feet. Height: ft
The height of the pyramid whose volume is already given would be = 1,440,000 ft
How to calculate the height of the given pyramid?To calculate the height of the pyramid, the formula of the Volume of the pyramid should be used.
Volume = 1/3lwh
where l = base length = 8h-30 ft= 3.75 ft
w = base width= 8h+20 ft = -2.5 ft
h = h ft
The volume of the pyramid = 4,500,000 cubic feet
4,500,000 = 1/3 × (3.75)(-2.5)h
Make h the subject of formula;
h = 4500000×3/3.75×(-2.5)
h = 13500000/9.375
h = 1,440,000 ft.
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consider these functions f(x)=3x^3+8x-2 k(x)=4x what is the value of k(f(x)
The value of function k(f(x)) is 12x³ + 32x - 8.
What is Function composition:Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).
Here we have
Functions f(x)= 3x³ +8x -2 and k(x) = 4x
To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:
k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)
We can simplify this expression by distributing the 4:
k(f(x)) = 12x³ + 32x - 8
Therefore,
The value of function k(f(x)) is 12x³ + 32x - 8.
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the fruity tooty company claims that the population proportion for each of its five flavors is exactly 20%. jane counts 92 red candies in a 400-count sample.z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction using the formula and data provided, what is the value of the z-test statistic? answer choices are rounded to the hundredths place.
Value of the z-test statistic is 1.20.
How to find the value of the z-test statistic?To find the value of the z-test statistic, we need to calculate the sample proportion and the standard error of the proportion.
The sample proportion is:
p⁻ = 92/400 = 0.23
The standard error of the proportion is:
SE = √[(pq)/n] = √[(0.20.8)/400] = 0.025
where p = 0.2 and q = 0.8.
Now we can calculate the z-test statistic:
z = (p⁻ - p)/SE = (0.23 - 0.2)/0.025 = 1.2
Therefore, the value of the z-test statistic is 1.20.
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Question 4 Part A (2 points): Landon has $16 and wants to buy a combination of sandwiches and chips to feed his 4 teammates. Each sandwich costs $4 and each bag of chips costs $2. This system of inequalities models the scenario.
4x + 2y ≤ 16
x + y ≥ 4
Describe the graph of the system.
A.
A graph of two solid lines that intersect at point (0, 4).
B.
A graph of two solid lines that intersect at point (4, 0).
C.
A graph of one solid line and one dashed line that intersect at point (0, 4).
D.
A graph of one solid line and one dashed line that intersect at point (4, 0).
The correct statement about the graph is,
A graph of two solid lines that intersect at point (4, 0).
Given that;
This system of inequalities models the scenario.
4x + 2y ≤ 16
And, x + y ≥ 4
Now, We can draw the inequalities in graph, we get;
The intersection point of the inequality is, (4, 0)
Thus, The correct statement about the graph is,
A graph of two solid lines that intersect at point (4, 0).
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Circle I and circle L are shown. Sector HIJ and sector KLM have the same area.
BLANK 1: Which formula should be used to solve this problem?
BLANK 2: What is the area of sector HIJ? Use 3.14 for pi.
BLANK 3: What is the measure of angle KLM?
1. Formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex] 2. The area of sector HIJ is 2.51 square units. 3. The measure of angle KLM is approximately 0.29 degrees
What is circle?A circle is a geometric shape consisting of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center).
According to given information:BLANK 1: To solve this problem, we can use the formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex], where θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).
BLANK 2: To find the area of sector HIJ, we need to know the radius of circle I and the measure of angle HIJ. From the given information, we know that circle I has a radius of 8, and angle HIJ is 45 degrees. Therefore, the area of sector HIJ is:
A = (45/360) x 3.14 x [tex]8^2[/tex]
A = 3.14 x 8 x (45/360)
A = 3.14 x 8 x 0.125
A = 2.51 square units (rounded to two decimal places)
Therefore, the area of sector HIJ is 2.51 square units.
BLANK 3: We know that sector KLM has the same area as sector HIJ, and circle L has a radius of 10. Therefore, we can use the formula for the area of a sector of a circle again to find the measure of angle KLM. Let x be the measure of angle KLM in degrees. Then:
A = (x/360) x 3.14 x [tex]10^2[/tex] = 2.51
Simplifying this equation gives:
(x/360) = 2.51/(3.14 x [tex]10^2[/tex])
(x/360) = 0.0008
x = 360 x 0.0008
x = 0.288
Therefore, the measure of angle KLM is approximately 0.29 degrees (rounded to two decimal places).
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PLS HELP SOLVE W STEPS!!!! THANK YOU
Answer:
see what you got to do is you have to find n
the rear window wiper blade on a car has a length of 10 inches. the blade is mounted on a 13 inch arm, 3 inches from the pivot point. if the wiper turns through an angle of 115 degrees, how much area is swept clean?
The area swept clean by the rear window wiper blade is approximately 91.37 square inches.
We'll calculate the area swept clean by the rear window wiper blade using the given information.
Convert the angle from degrees to radians:
115 degrees * (π radians / 180 degrees) = (23π/36) radians.
Find the length of the arc that the wiper blade traces out:
Arc length = (radius * angle) = (10 inches * (23π/36) radians) ≈ 20.08 inches.
Calculate the area of the sector formed by the arc and the pivot point:
Sector area = (1/2) * (radius² * angle) = (1/2) * (10 inches² * (23π/36) radians) ≈ 100.42 square inches.
Find the length of the arc that the mounting point of the blade traces out:
Arc length = (radius * angle) = (3 inches * (23π/36) radians) ≈ 6.02 inches.
Calculate the area of the sector formed by this arc and the pivot point:
Sector area = (1/2) * (radius² * angle) = (1/2) * (3 inches² * (23π/36) radians) ≈ 9.05 square inches.
Subtract the smaller sector area from the larger one to get the area swept clean by the wiper blade:
Area swept clean = 100.42 square inches - 9.05 square inches ≈ 91.37 square inches.
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The area swept clean by the rear window wiper blade is approximately 31.53 square inches.
To determine the area swept clean by the rear window wiper blade, we first need to find the length of the arc covered by the blade. We can use the formula:
arc length = radius * angle in radians
To convert the angle from degrees to radians, we multiply by[tex]\pi /180[/tex]:
115 degrees x [tex]\pi /180[/tex] = 2.007 radians
The radius is the length of the wiper arm, which is 13 inches minus the distance from the pivot point to the blade, which is 3 inches. Therefore, the radius is:
13 inches - 3 inches = 10 inches
Now we can calculate the arc length:
arc length = 10 inches x 2.007 radians = 20.07 inches
So the area swept clean by the wiper blade is approximately equal to the area of the sector formed by the arc and the two radii. The formula for the area of a sector is:
area = (angle in radians / [tex]2\pi[/tex]) x [tex]\pi r^2[/tex]
Plugging in values we have:
area = (2.007 / [tex]2\pi[/tex]) x [tex]\pi[/tex][tex](10 inches)^2[/tex] = 31.53 square inches
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What is the difference of the fractions? 4/7 - 10/7
Answer:
-6/7
Step-by-step explanation: