[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{"x" varies}\\ \textit{inversely with "y"} \end{array}\implies x=\cfrac{k}{y}\hspace{5em}\textit{we also know that} \begin{cases} x=32\\ y=3 \end{cases} \\\\\\ 32=\cfrac{k}{3}\implies 96=k\hspace{10em}\boxed{x=\cfrac{96}{y}} \\\\\\ \textit{when x = 11, what's "y"?}\qquad 11=\cfrac{96}{y}\implies y=\cfrac{96}{11}[/tex]
A shipping container will be used to transport several 60 kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24500 kilograms. Other shipments weighing 14600 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 60 kilogram crates that can be loaded into the shipping container.
The inequality which can be used to determine x, the number of 60 kilogram crates that can be loaded into the shipping container is
60x ≤ 9900 where x is less than or equal to 165
What is an Inequality?
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
According to the given question:
The greatest weight that can be loaded into the container is 24500 kilograms.
Other shipments weighing 14600 kilograms have already been loaded into the container.
24500 - 14600 = 9900 kg can be the weight of 60 kg containers
Now, the number of 60 kilogram crates that can be loaded into the shipping container can be represented as
60x ≤ 9900
where x is number of 60 kg containers
Solving for x we get
x ≤ 165
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HELP
Select all the equivalent solution sets to the compound inequality 27>−1/2(4x+6)≥100?
A. −15
B. −10.5
C. −10.5
D. −15
E. −10.5
F. −15
G. −15
x:2 + 8 =-24[tex]x/2 + 8 =-24.which step should sammy complete first
The step which Sammy should complete first in a bid to solve the equation is; subtraction 8 from both sides of the equation.
Which step should Sammy complete first to solve the equation?It follows from the task content that the step which Sammy should complete first in a bid to solve the equation.
Since the given equation is;
x/2 + 8 = -24
Therefore, in a bid to solve the equation; the first step which Sammy must complete first in a bid to solve the equation is;
Subtract 8 from both sides of the equation; so that we have;
x/2 = -24 -8
x/2 = -32
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correlation will not show whether or not there is weight loss. which tool would be more appropriate?
The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.
What is meant by weight loss?Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.
A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.
You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.
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if a true-false test with questions is given, what is the probability of scoring (a) exactly 80% just by guessing?
The probability of scoring exactly 80% is 0.04395 as per the given data.
Given: 10 true-false questions
So, we will have 50% chances (probability = 0.5) of being correct.
P( 80% score) = P( 8 answers correct)
As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)
So, P( 80% score) = P( 8 answers correct)
= 0.0439453125
= 0.04395
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Probability basically refers to the degree to which something is likely to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will discover the possible results for a random experiment. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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At a clothing store, ted bought 4 shirts and 2 ties for a total price of $95. At the same time store, stephen bought 3 shirts and 3 ties for $84. Each shirt was the same price, and each tie was the same price. Which system of equations can be used to find s, the cost of each shirt in dollar, and t, the cost of each tie in dollars ?.
The required system of equation for the cost of shirt and tie are-
4s + 2t = 953s + 3t = 84 Explain the term system of equations?simultaneous equations, or a system of equations, In order for two or so more equations in algebra to be solved jointly, the system's equations must all be satisfied by the solution. The quantity of equations must match the number of unknowns for a system to have a singular solution.For the stated question-
Ted spent a total of $95 on 4 shirts and 2 ties from a clothes store. Stephen spent $84 on three shirts and three ties at the same time store. Each shirt and each tie cost the same amount.Let 's' be the cost of each shirt.
Let 't; be the cost of each tie.
Then, the equations become-
4s + 2t = 95
3s + 3t = 84 are the required system of equation.
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Question 10 of 10
What is the slope of a line that is parallel to y = 3x+ 5?
Answer:
[tex]\huge\boxed{\sf 3}[/tex]
Step-by-step explanation:
Given slope-intercept equation:y = 3x + 5
Comparing it with standard form of slope-intercept equation i.e. y = mx + b.
Where,
m = slope = 3
b = y-intercept = 5
A line that is parallel to this line will have the same slope as this line.
So, it will also have a slope of 3.
[tex]\rule[225]{225}{2}[/tex]
Subtract and choose the answer in simplest form.
1\frac {(3)} {(4)}-\frac {1} {3}
(4)
(3)
−
3
1
The required evaluation to the given expression is 5/12.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The expression is given in the question as:
1 3/4 - 1/3 (4)(3) - 1/3
We have to determine the evaluation to the given expression
As per the given question, we have
⇒ 1 3/4 - 1/3 (4)(3) - 1/3
⇒ 7/4 - 1/3 (12) - 1/3
Apply the subtraction operation,
⇒ 7/4 - 4 - 1/3
Take the LCM in the above fractions,
⇒ (21 - 12 - 4)/12
⇒ 5/12
Thus, the required evaluation to the given expression is 5/12.
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Mary has 7 1/12 square feet of wrapping
paper. If she needs 1 3/5 times more paper
than what she has, how many more feet of paper does she need?
Answer: 12
Step-by-step explanation:
Convert both mixed numbers to improper fractions:
7 1/12= 85/12
1 3/5= 8/5
Multiply:
84 x 8 = 680
12 x 5 = 60
As a fraction:
680/60
Simplified:
11 1/3 ft. of paper needed
Forty-five percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 125 randomly selected individuals and found 50 believed that there is life on other planets. At α=0.10, is there sufficient evidence to conclude that the percentage differs from 45%? Use the P-value method with tables.
Hypothesis test is a two-tailed test. Compute the test value. Always round z score values to two decimal places.
We will reject the H0 as there sufficient evidence is obtained that the percentage of people who believe that there is life on planets differs from 50%.
It is given that the sample size, (N) is 125
Probability (P)= 0.50 or 50%
P'= 50/120= 0.4166
Significance level ([tex]\alpha[/tex])=0.10
If we consider the null and alternative hypotheses, they are:
H0= 0.50
H1≠ 0.50
For conducting the test statistics:
Z= [tex](P'-P)/\sqrt{P*(1-P)/N}[/tex]
Z= [tex](0.41-0.50)/\sqrt{0.50*0.50/125}[/tex]
Z= -2.01
The critical value of Z at [tex]\alpha[/tex]=0.10 is 1.645 or -1.645
And the P- value at Z= 2.01 is 0.04
Decision Criteria: If the P-value is less than the significance level, we reject the H0. Also, if the Z is found to be greater than the critical value, we will reject H0.
Thus, in this case, we see that, the P-value, 0.04 is less than the significance level, i.e., 0.10, we will reject the H0.
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What is h, the height of the tree? use the law of sines to first find at. Then use that measure to find the value of h. 3. 0 yards 3. 2 yards 3. 8 yards 4. 4 yards.
The measured height of the tree is found as 3.2 yards.
Explain the term trigonometric relation?Trigonometric ratios are based on the measurement of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. These trigonometric ratios of a given acute angle are the ratios of the sides of such a right-angled triangle in respect to that angle.Let 'h' be the height of the three.
Let distance between student A and tree = x.
Using trigonometric relation;
tan 57 = h/x
x = h/tan 57 ......eq 1
tan 46 = h/(x + 1)
x + 1 = h/tan 46 ......eq 2
Equation eq 1 and eq 2.
h/tan 57 + 1 = h / tan 46
h / tan 46 - h / tan 57 = 1
Further solving,
h(tan 57 - tan 46) = tan 46.tan 57
h = tan 46 tan 57 / (tan 57 - tan 46)
h = 3.2 yards
Thus, the measured height of the tree is found as 3.2 yards.
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The complete question is-
Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.
What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.
A) 3.0 yards
B) 3.2 yards
C) 3.8 yards
D) 4.4 yards
Answer: 3.2 is correct
Step-by-step explanation:
edge 2023
g consider a disk queue holding requests to the following cylinders in the listed order: 94, 169, 39, 135, 22, 133, 69, 65. using each of the following scheduling algorithms, what is the order in which the requests will be serviced? (assume that the disk head is currently located at cylinder 50 and is moving toward higher numbered cylinders).
For FCFS (First Come, First Served):The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65.
SSTF (Shortest Seek Time First):
The requests will be serviced in the following order: 39, 22, 65, 69, 94, 133, 135, 169
SCAN:
The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22
C-SCAN:
The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65
LOOK:
The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22
C-LOOK:
The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65
In FCFS and C-SCAN, the requests are serviced in the same order as they were received. In SSTF and LOOK, the requests are serviced in an order that minimizes the seek time of the disk head. In SCAN and C-LOOK, the requests are serviced in an order that moves the disk head in one direction (towards higher numbered cylinders in this case) until the end of the disk is reached, and then moves the disk head in the opposite direction to service the remaining requests.
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a research firm determined that the equation y=2x+80 can be used to model the total amount of spending by tourist in florida,y, in billions of dollars, for the years 2013-2017 where x is the number of years since 2013.
determine the key features for the context
domain? range? as x values increase,y values ? slope? x intercept? y intercept? thank ya
The slope and intercept of the line will be 2 and 80 respectively.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that, the total amount of tourist spending in Florida from 2013 to 2017 can be predicted using the equation y=2x+80, where x is the number of years since 2013, to the tune of billions of dollars.
Compare the equation with the standard equation,
y=mx+ c
Where m is the slope and c is the intercept of the line.
Thus the slope and intercept of the line will be 2 and 80 respectively.
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how many three-digit numbers can be formed using the digits 1 through 9 if no digit can appear twice in a number?
Total 504 three digit numbers can be formed if no digit appear twice
What is Permutation?
The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.
Solution:
Total Numer of Digits = 9
Number of Characters in the number = 3
Total Numbers = 9P3 = 9! / 6!
9P3 = 504
Total 504 three digit numbers can be formed
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PLEASE HELP 5 QUESTIONS PLEASE ILL GIVE BRAINLY IF IT SHOWS
1.
Which one is a proportion?
A. 1/2 = 2/3
B. 3/4 = 12/16
C. 19/15 = 54/85
D.2.5/7=5/12
-------------------
2.
Solve the proportion for the missing value of y.
3/12 = y/8
y =_________|
----------------------
3.
Solve the proportion for the missing value of w.
5/w = 8/4
w =__________|
-------------------------------
4.
If Mr. Argo went 20 miles on 2.5 gallons of gas, and he wants to know how far he can go on 9 gallons of gas. Which proportion would be helpful to solve the problem?
A.20/9 = 2.5/x
B. 9/2 = 20/x
C. 20/2.5 = x/9
D.9/20 = x/2
Answer:
3/4 = 12/16, y = 2, w = 2.5, 20/2.5 = x/9
Step-by-step explanation:
The first question is asking which is proportional.
B. 3/4 = 12/16
We know this is proportional because 4 can be multiplied by 4 to get 16, and the same can be applied to 3 to get 12.
The second question is asking for the missing value of y.
3/12 = y/8
y = 2
We can solve this by looking at the 12 and the 8.
8 is 2/3 of 12.
2/3 of 3 is 2
The third question is asking for the missing value of w.
5/w = 8/4
w = 2.5
We can solve this by looking at the 8/4.
8/4 is the same as 2/1.
Using this, we can conclude that w = 2.5
The fourth question is asking for the correct proportion.
If Mr. Argo can go 20 miles on 2.5 gallons of gas:
20/2.5
And he wants to know how many miles he can go with 9 gallons:
x/9
We can use the equation: C. 20/2.5 = x/9
Hope this helps!!
a cake recipe calls for 472 ml of milk. you dont have a metric measuring cup at home, so you need to convert milliliters to cups. you know that 1 l equals 1.06 quarts and that there are 4 cups in 1 quart. how many cups of milk will you need to use
Number of cups of milk that will you need to use is 2.001 cups
Total quantity of milk needed for the cake = 472 milliliter
we know
1 liter = 1.06 quarts
1 quart = 4 cups
Convert the given quarts to cups
Then 1.06 quarts = 4 × 1.06
Multiply the numbers
= 4.24 cup
Here the total quantity of milk needed for the cake is 472 milliliter
We have to use the unitary method here
1 liter = 4.24 cups
472 milliliter = 4.24 × 0.472
Multiply the numbers
= 2.001 cups
Therefore, he need 2.001 cups of milk to make a cake
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a variable is normally distributed with mean 19 and standard deviation 5. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 16. b) find the area to the left of 14. c) find the area to the right of 15. d) find the area to the right of 27. e) find the area between 14 and 30.
The areas are
(a) 0.2743
(b) 0.1587
(c) 0.8413
(d) 0.0548
(e) 0.8274
What is standard deviation ?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
Use TI 84 plus calculator to find the following areas
(a) Entering the values
Lower : -999999999
Upper : 16
Area (probability): 0.2743
(b) Entering the values
Lower : -999999999
Upper : 14
Area (probability): 0.1587
(c) Entering the values
Lower : 15
Upper : 999999999
Area (probability): 0.8413
(d) Entering the values
Lower : 27
Upper : 999999999
Area (probability): 0.0548
(e) Entering the values
Lower : 14
Upper : 30
Area (probability): 0.8274
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identify the expression as a numerical expression or a variable expression. for a variable expression, name the variable. 9 10 variable expression; j is the variable. variable expression; i is the variable. variable expression; there is no variable. numerical expression
As there is no variables, so the given expression 9 + 10 is the numerical expression.
What is numbers ?An object can be counted, measured, or labelled using a number, which is a mathematical value. Arithmetic calculations are often done with numbers. Natural numbers, whole numbers, rational and irrational numbers, among other types of numbers, are examples. A null value is also represented by the integer zero, or 0.
What is numerical expression ?Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.
Mathematical operations like add, subtract, multiply, and divide can be used to mix integers with numbers to create a numerical expression.
Given Expression 9 + 10
As it contains only numbers and mathematical operators,
So, it is the numerical expression.
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What is 1\3x + y = 4
Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare
The social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots
Main body:
Cumulative Earnings before this pay period = $128,300
pay amount this period = $3000
tax rate of 6.2% on social security = 6.2%
effective earning = 128300 = 3000
= 125300
social security deduction = 6.2 % of 125300
⇒ 6.2 *125300 /100
⇒$7768
Medicare deductions = 1.45%
⇒ 1.45*125300/100
⇒$1816
Hence , the social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
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a four digit personal identification number (pin) is selected. what is the probability that there are no repeated digits? do not round
If a four digit personal identification number is selected, then the probability that there are no repeated digits is 0.504
Number of digits in the identification number = 4
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
There are 10 digits
The probability = Number of favorable outcomes / Total number of outcomes
Total number of outcomes = 10 × 10 × 10 × 10
= 10000
Number of outcomes that digits wont repeat = 10 × 9 × 8 × 7
= 5040
Substitute the values in the equation of probability
The probability = 5040 / 10000
= 0.504
Therefore, the probability there are no repeated digits is 0.504
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Helpppppppppp meeeeee
Answer:
1.07 maybe... don't trust me on that
Answer:
x = -6
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation based on this information to calculate value of x:
64 + 27 = 97 + x
Add like terms91 = 97 + x
subtract 97 from both sides91 - 97 = 97 - 97 + x
-97 will eliminate the 97 on the right side of the equation-6 = x
of the 459,000 people living in miami, 68%indicated on a recent, city-wide survey that they were employed for a random sample of size 490 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
The standard deviation of the sampling distribution of sample proportions is 0.21
Given,
Number of people living in Miami = 459,000
Sample size, n = 490 people
Population proportion, p = 68% = 68
We have to find the standard deviation for the sampling distribution of the sample proportions;
Here,
Standard deviation of the sampling distribution of sample proportions is
σpˆ=√p(1−p)/n
σpˆ=√.68(1-.68)/490
σpˆ= .021
That is,
0.21 is the standard deviation of the sampling distribution of sample proportions.
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a child has a box full of colored building blocks. he will choose one block without looking. the odds against choosing a blue block are 47. what is the probability of choosing a blue block?
7/11 is the probability of choosing a blue block.
Given:
a child has a box full of colored building blocks. he will choose one block without looking.
the odds against choosing a blue block are 47.
We need the probability of choosing a blue block,
Odds:
The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.
The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.
So, the probability of not choosing the blue block is 4/11.
Probability of choosing blue block: complement of 4/11 which is equal to 7/11.
Hence we get the required answer.
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You have blue ribbon and red ribbon in the ratio 1/2:1/5 . Your friend finds the value of the ratio. Is your friend correct? :
Answer:
No.
Step-by-step explanation:
Below I should you two ways to get the correct answer.
if olive construction company gets the job, what is the probability that base construction company did not bid?
If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
So, the probability that the base construction company did not bid:
[tex]\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}[/tex]
Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.
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chegg the number of successes and the sample size for a simple random sample from a population are given below. x, n, : p, : p, a. determine the sample proportion. b. decide whether using the one-proportion z-test is appropriate. c. if appropriate, use the one-proportion z-test to perform the specified hypothesis test.
Since, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.
What is a left-tailed test?
When the alternative hypothesis asserts that the true value of the parameter indicated in the null hypothesis is lower than the null hypothesis indicates, a left-tailed test is utilized.
This is a left-tailed test.
Test statistics
[tex]z = (\hat p - p_{0} ) / \sqrt{} p_{0}*(1-p_{0}) / n[/tex]
= [tex]\sqrt{} (0.4*0.6) / 45[/tex][tex]= ( 0.2 - 0.4) \div \sqrt{} (0.4*0.6) / 45[/tex]
= -2.74
The critical value of the significance level is α = 0.01, and the critical value for a left-tailed test is:
[tex]Z_{\alpha} = -2.33[/tex]
Hence, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.
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when transforming a shape twice, do you transform it from the pre image or image?
The mean number of hours watching TV per week for a sample of 153 teenagers is 27. If the margin of error for the population mean with a 98% confidence interval is 1.2, construct a 98% confidence interval for the mean number of hours watching TV per week for all teenagers.
With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).
98% confidence interval can be calculated as
Point estimate± Error margin
Point estimate=mean number of hours watching TV
students=28.
Error margin=1.4.
As per given data, the 98% confidence interval for all teenagers is
=28± 1.4
=(28-1.4,28+1.4)
=(26.6,29.4)
Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.
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A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle isA1+√32B5−2√3C 2D 1+√3
An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.
A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.
The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.
Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.
From the diagram, let GH be x. The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3
[tex]\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}[/tex]
By Pythagoras' theorem, from ΔHEF,
[tex]\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}[/tex]
The radius of the circle (HE) is 2-√3+√3=2.
The answer is 2 cm. Therefore, option C is correct.
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