The probability is 0.8427.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.
Here we are total number of insurance agents = 89
And number of insurance agents do own a handgun = 75
So we asked probability that a insurance agent will own a handgun
Probability = no.of insurance agents/no.of insurance agents who owns a handgun
Probability = 75/89 = 0.8427
The probability that the agent will own a handgun is .84
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What are the 5 properties of rhombus and rectangle?
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
Properties of rhombus:
1. All sides are equal in length.
2. Opposite angles are equal.
3. Diagonals bisect each other at 90°.
4. Diagonals are respective angle bisectors.
5. Any two adjacent angles add up to 180 degrees.
6. The area of the rhombus is a product of the lengths of the 2 diagonals divided by 2.
Properties of rectangle:
1. Opposite sides are equal in length.
2. All the angles are 90°.
3. Diagonals bisect each other.
4. Any two adjacent angles add up to 180 degrees.
Hence, the common properties are
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
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The height (in feet) attained by a rocket 1 seconds into flight is given by
h(t)
13+2112+ 431+ 20. When is the rocket ascending and when is it descending?
--313
Hint: you will first need to determine the time the rocket hits the ground.
==
We can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
What is a derivative of a function?
The derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
To determine whether the rocket is ascending or descending at a given time, we need to find the derivative of the function h(t) and determine whether it is positive or negative.
The derivative of h(t) is given by h'(t) = -t²+42t+43. This is the rate of change of the height of the rocket at any given time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
At t = 1 second, h'(t) = -1 + 42 + 43 = 44. Since the derivative is positive at t = 1, we know that the rocket is ascending at this time.
Hence, we can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
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i need help quick pls
Answer: 20
Step-by-step explanation: If you look at how 4 got to 8 you multiplied it by two, so therefore, you multiply 10 by 2 also to get twenty.
Answer:
Step-by-step explanation
if in triangle 1 it’s four and its 8 in the 2nd one
multiply each number on the first triangle
f-e 20
The National Association of Realtors estimates that 31% of all homes purchased in 2016 were considered investment properties. If a sample of 600 homes sold in 2016 is obtained what is the probability that 200 or fewer homes were purchased as investment properties? 0.3333 0.4066 0.9106 O 0.8917
The probability that 200 or fewer homes were purchased as investment properties is 0.937. This is calculated using the binomial distribution formula, where n = 600, p = 0.31, and x = 200.
1. The binomial distribution formula for calculating the probability of an event occurring is:
P(x) = nCx * p^x * q^(n-x)
where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure (1 - p).
2. In this problem, n = 600, p = 0.31, x = 200, and q = 1 - 0.31 = 0.69.
3. Plugging these values into the formula, we get:
P(x) = 600C200 * 0.31^200 * 0.69^400
4. Solving this equation, we get P(x) = 0.937.
5. Therefore, the probability that 200 or fewer homes were purchased as investment properties is 0.937.
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Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is
Multiple Choice
$90,195.20
$93,932.28
$95,072.31
$88,555.42
After six years, Jim Moore's account will have a balance of $69,341 thanks to compound interest.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
The account in this issue is split up into two distinct investments. The first one is for $12,000 with a 12% compound interest rate over six years. Consequently, the criteria are as follows:
P = $12,000
r = 0.12
t = 6 years.
[tex]A_1(t)=P(1+\frac{r}{n} )^n^t[/tex]
[tex]A_1(6)=12000(1+\frac{0.12}{6} )^(^2^)^(^6^)[/tex]
A₁(6) = $15219.
The value of the second investment, which is $50,000 and is likewise compounded semi-annually at 12%, will be as follows at the conclusion of the fourth year:
[tex]A_2(t)=P(1+\frac{r}{n} )^n^t[/tex]
[tex]A_2(2)=50000(1+\frac{0.12}{6} )^(^2^)^(^2^)[/tex]
A₂(2) = 54122
Hence,
A(6) = A₁(6) + A₂(2)
A(6) = 15219 + 54122
A(6) = $69341
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Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
(x - 4)2 + y2 = 100
(x - 4)2 + y2 = 10
x2 + (y - 4)2 = 10
x2 + (y - 4)2 = 100
the set of hexadecimal digits consisting of from one through four digits can be thought of as broken up into disjoint subsets: s1, s2, and so forth, where each sk consists of the strings with k hexadecimal digits. there are $$ incorrect: your answer is incorrect. strings in s1, $$ incorrect: your answer is incorrect. strings in s2, and so forth. thus, by the addition correct: your answer is correct. rule, the total number of strings is .'
It is possible to think of the set of hexadecimal digits, which includes one through four digits, as being divided into disjoint subsets: s, Sa, and so forth, strings in S,, strings in fourth, where each S, is made up of the strings with k hexadecimal digits. There are v rules, there are S2 total strings, and so on.
What is the hexadecimal system of numbers?Hexadecimal number system is one of many sorts of ways for representing numbers that has a base-16 value. Hexadecimal numerals therefore contain 16 symbols or digital values, namely 0 through 1, 2, 3, 4, 5, 6, 7, 8, 9, A–F. Single bit representations of 10, 11, 12, 13, 14, and 15 are A, B, C, D, E, and F, respectively.
How is hexadecimal pronounced?It can occasionally be spoken as "hex." There are only 16 used to represent hexadecimal integers. A, B, C, D, E, and F are the following values or symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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seven teams play a soccer tournament in which each team plays every other team exactly once. no ties occur, each team has a 50% chance of winning each game it plays, and the outcomes of the games are independent. in each game, the winner is awarded 1 point and the loser gets 0 points. the total points are accumulated to decide the ranks of the teams. in the first game of the tournament, team a beats team b. the probability that team a finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$
The team a finishes with more points than team b with a probability of 319/512
seven teams play a soccer tournament in which each team plays every other team exactly once
in the first game of the tournament, team a beats team b
We need to find the probability that team a finishes with more points than team b
Both teams, a and b play 6 matches each
In the first match, a wins. Now they can play 5 matches each
Of the remaining 5 games
a win 0 and b win zero
P(a > b) = 5C1/2^5 x 5C1 / 2^5 = 1/1024
a win 1 and b win 1 or zero
P(a > b) = 5C1/2^5 x(5C0 + 5C1) / 2^5 = 30/1024
a win 2 and b win 2 or 1 or zero
P(a > b) = 5C2/2^5 x(5C0 + 5C1 + 5C2) / 2^5 = 160/1024
a win 3 and b win 3 or 2 or 1 or zero
P(a > b) = 5C3/2^5 x(5C0 + 5C1 + 5C2 + 5C3) / 2^5 = 260/1024
a win 4 and b win 4 or less
P(a > b) = 5C4/2^5 x(5C0 + 5C1 + 5C2 + 5C 3 + 5C4) / 2^5 = 155/1024
a win 5 and b win 5 or less
P(a > b) = 5C1/2^5 x(5C0 + 5C1+ 5C2 + 5C3 + 5C4 + 5C5) / 2^5 = 32/1024
P(a> b) = (1 + 30 + 160 + 260 + 155 + 32)/1024 = 638/1025 = 319/512
Therefore, the the probability that team a finishes with more points than team is 319/512
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alpha can produce either 18 oranges or 9 apples an hour, while beta can produce either 16 oranges or 4 apples an hour. which of the following statements is true?
If alpha specialize in growing apples beta specialize in growing oranges the both could gain profit by the trade is true for the statement
Comparative advantage describes a situation in which a person or a country involved in trade processes may not have an absolute advantage, but can still benefit from trade on a comparative basis.
The nations frequently trade goods based on their comparative advantages so that both parties can benefit from trade.
According to the stated information,
Alpha can produce either 18 oranges or 9 apples per hour, while beta can only produce 16 oranges or 4 apples per hour, it is stated.
so ,If alpha specialize in growing apples and beta specialize in growing oranges the both could gain profit by the trade
Hence, option C is true
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Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line
with a slope of 5.9. See the figure below.
With 48 gallons of fuel in its tank, the airplane has a weight of 2383.2 pounds. What is the weight of the plane with 77 gallons of fuel in its tank?
Airplane
weight
(in pounds)
2383.2
48
Amount of fuel
(in gallons)
pounds
48
Answer:
To find the weight of the plane with 77 gallons of fuel in its tank, we can use the linear equation for the weight of the plane in terms of the amount of fuel in its tank. The equation has the form:Weight = m * Fuel + bWhere m is the slope of the line, which is 5.9, and b is the y-intercept, which is the weight of the plane when the amount of fuel is 0. We know that the weight of the plane with 48 gallons of fuel is 2383.2 pounds, so we can use this information to solve for b:2383.2 = 5.9 * 48 + b
b = 2383.2 - 5.9 * 48
b = 2383.2 - 280.8
b = 2102.4Now that we have the value of b, we can plug it back into the equation to find the weight of the plane with 77 gallons of fuel:Weight = 5.9 * 77 + 2102.4
Weight = 456.3 + 2102.4
Weight = 2558.7 poundsSo the weight of the plane with 77 gallons of fuel in its tank is 2558.7 pounds.
Step-by-step explanation:
the radius of a ping pong ball is ( blank) centimeters.
help a girl out pleasee!!
Answer:
3√3v/3x V
Step-by-step explanation:
d/dt[32/3π, sin (tim), 3√3v/3x, V]
Arezo borrowed $2,500 from her grandfather. This graph shows the balance remaining on Arezo’s debt after she makes each payment. Using this graph, how much will she owe after 4 payments?
Answer: May I see the graph?
Step-by-step explanation:
a) ( combining like terms)
Simplify (7a + 10b) − (4a − 6b).
b) Simplify the expression. ( combining like terms)
−5x + 8y + 2x − 3y
c) Solve and graph the inequality x - 4 ≤ -1 (the name of the game is ...)
a) Combining like terms (7a + 10b) − (4a − 6b) = 3a + 16b
b) The Simplify expression −5x + 8y + 2x − 3y the answer is -3x + 5y
c) The inequality x - 4 ≤ -1 Graph is given below.
What do you mean by algebraic expression?
When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
An algebraic expression is composed of various parts.
a) Given expression:
(7a + 10b) - (4a - 6b)
= 7a + 10b - 4a + 6b
On combining like terms we get,
(7a - 4a) + (10b + 6b)
= 3a + 16b
Therefore, (7a + 10b) − (4a − 6b) = 3a + 16b
b) Given expression :
−5x + 8y + 2x − 3y
On combining like terms we get,
-5x + 2x + 8y - 3y
= (-5x + 2x) + (8y - 3y)
= -3x + 5y
therefore, −5x + 8y + 2x − 3y = -3x + 5y
c) Given expression:
x - 4 ≤ -1
⇒ x ≤ -1 + 4
⇒ x ≤ 3
Graph of the function is given below:
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Factor 9-64u squared
Answer:
(3 + 8u)(3 - 8u)
Step-by-step explanation:
Conjugated binomials
[tex](9-64u^{2} ) =(3+8u)(3-8u)[/tex]
Hope this helps
Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 52 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.480. Determine if there is sufficient evidence to say that his batting average has improved at the 0.10 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2.
Step 1 of 3 :
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2
According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic.
The value of the test statistic is z = 1.65.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
Average of 0.48 in 25 at bats,
Test if there was improvement:
At the null hypothesis :
[tex]H_0 : P_1 - P_2 = 0[/tex]
At the alternative hypothesis:
[tex]H_1 : P_1 - P_2 > 0[/tex]
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
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what percent of a dollar is the value of each coin combination
a) A dollar is 40% of four dimes.
b) 8% of a dollar is equal to 1 nickel and 3 cents.
c) A dollar is equal to 135% of 5 quarters and 1 dime.
What is meant by percentage?A value or ratio stated as a fraction of 100 is known as a percentage in mathematics. Frequently, the percent symbol (%) or the abbreviation "pct" are used to indicate the percentage. The word "percent" derives from "percent," a contraction of "per centum," which meant per hundred.
1 dime equals 10 cents, as we all know. Thus, 4 dimes equal 40 cents. 4 dimes are consequently 40% of a $1.
We are aware that a nickel costs five cents and a penny one cent. Therefore, 8% of a dollar is equal to 1 nickel and 3 cents.
We are aware that a quarter equals 25 cents and a dime equals 10 cents. 5 quarters and 1 dime are therefore 135% of a dollar.
Therefore,
A dollar is 40% of four dimes.
8% of a dollar is equal to 1 nickel and 3 cents.
A dollar is equal to 135% of 5 quarters and 1 dime.
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The complete question is:
"What percentage of a dollar is the value of each coin combination?
a. 4 dimes
b. 1 nickel and 3 pennies
c. 5 quarters and 1 dime"
I need this please help me
Answer:
isnt it 72
Step-by-step explanation:
since it is that kind of triangle
show that cos4(t)+4cos2(t)=8cos^4(t)-3
Explanation:
You want to show cos(4t) +4cos(2t) = 8cos⁴(t).
Double-angle identityUse the cosine double-angle identity:
cos(2t) = cos²(t) -sin²(t) = cos²(t) -(1 -cos²(t)) = 2cos²(t) -1
Then
cos(4t) = 2cos²(2t) -1 = 2(2cos²(t) -1)² -1 = 2(4cos⁴(t) -4cos²(t) +1) -1
= 8cos⁴(t) -8cos²(t) +1
ApplicationSubstituting these expressions into the left side of the identity of interest, we have ...
cos(4t) +4cos(2t) = 8cos⁴(t) -3 . . . . . . . . . . . . . . . . . . identity to prove
(8cos⁴(t) -8cos²(t) +1) +4(2cos²(t) -1) = 8cos⁴(t) -3 . . . substitute
8cos⁴(t) -8cos²(t) +1 +8cos²(t) -4 = 8cos⁴(t) -3 . . . . . eliminate parentheses
8cos⁴(t) -3 = 8cos⁴(t) -3 . . . . . . combine like terms; Q.E.D.
Suppose the probability of success on each of 6 independent trials of an experiment is 0.2. (Round your answers to four decimal places.) (a) What is the probability of 4 successes? (b) What is the probability of at least 1 success?
a) the probability of 4 success = 0.00629
b)the probability of at least 1 success = 1.5726
In Probability, the set of outcomes of an experiment is called events. There are different types of events such as independent events, dependent events, mutually exclusive events, and so on.
If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.
given that
the probability of success on each of 6 independent trials of an experiment is 0.2.
a) the probability of 4 success
P(x=4) = 6[tex]C_{4}[/tex][tex](0.2)^{4}[/tex][tex](0.8)^{6}[/tex]
= 15×0.0016×0.2621
= 0.00629
b)the probability of at least 1 success
p(x≥1) = 1 - p(x<1)
= 1 - 6[tex]C_{0}[/tex][tex](0.6)^{0}[/tex][tex](0.8)^{6}[/tex]
= 1.5726
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If the average of 7 positive integers is 100, find the highest possible value of the largest number.
PLS ANSWER QUICKLY FOR THE SAKE OF THE GOD!!!1
Answer:
Step-by-step explanation:
What numbers have a LCM of 24?; What is the least common multiple of 2 6 and 12?; How do you find the LCM of 2 numbers?; What is the least common multiple of 12?
A LCM is smallest number among all common multiples of the given numbers. LCM of 24 is 2³ × 3
The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers
There are 3 methods to find the least common multiple of two numbers.
LCM by Listing MethodLCM by Prime Factorization MethodLCM using Division MethodAccording to the question,
(a) LCM of 24 : 2³ × 3
(b) LCM of 2 , 6 , 12 : 2 × 2 × 3
(c) To find the LCM of two number use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.
(d) Least common factor of 12 : 2 × 2 × 3
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a(n)___defines the form or protocol of an operation, but not its implementation. group of answer choices a. meta - operation b. inquisitor c. abstract operation
A meta - operation defines any form or protocol for the operation, but doesn't its implementation. Option (a) is correct.
Programmers reverence type of protocols. We think about protocols as some thing given to us from on excessive through the Cerfs, Postels, and Berners-Lees of the world. But the fact is that programmers construct protocols all of the time. Sometimes those are advert hoc and different instances they're constructed with the assist of a metaprotocol. Communication protocols in general, in addition to protection protocols, want a better degree of pliability to deal with evolution.
Many method will increase the extent of code sharing and reuse. I additionally observed that protection protocols are best-suitable for the utility of my framework due to the fact maximum protection protocols proportion a comparable set of capabilities and showcase not unusualplace sequences and styles withinside the manner they operate. Therefore, I proven the framework through making use of it to the implementation of numerous protection protocols: Needham-Schroeder Authentication Protocol, ISAKMP, and SSL.
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6) Pamela wants to buy a new Mercedes. The Mercedes wheel has a radius of
15", what is the area of the Mercedes wheel? (State answer to nearest tenth.)
Answer:
706.5 inches^2.
Step-by-step explanation:
The area of a circle is given by the formula A = πr^2, where A is the area of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.
To find the area of a Mercedes wheel with a radius of 15 inches, we can substitute these values into the formula:
A = πr^2 = π(15 inches)^2 = 706.5 inches^2
Rounding to the nearest tenth, the area of the Mercedes wheel is approximately 706.5 inches^2.
among both teenage boys and adult men, delinquency, hard drug use, and aggressive-bullying responses to frustration have been linked with higher-than-average levels of
Among both teenage boys and adult men, delinquency, hard drug use, and aggressive-bullying responses to frustration have been linked with higher-than-average levels of Testosterone.
The sex hormone testosterone has significant physiological functions. It is thought to control the creation of sperm, red blood cells, muscle mass, fat distribution, and sex drive (libido) in men.
Males and females may both have diminished bone mass and sex drive if a man has low testosterone, which can cause symptoms like erectile dysfunction.
Low sperm counts, testicular shrinkage, and impotence are issues connected to males having abnormally high testosterone levels. Cardiac attack risk is elevated when heart muscle is damaged. enlarged prostate and urination problems.
Therefore , Drug use and aggressive to frustration are licked with higher-than-average levels of Testosterone.
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All of the Pythagorean Identities are related. Describe how to manipulate the equations to get from sin^2t +cos^2t = 1 to the other forms.
[tex]1 + cot^{2}2t = csc^{2}2t[/tex] can be manipulated from [tex]sin^{2}2t +cos^{2}2t =1[/tex]
What is Pythagorean Identity?
An identity, in mathematics, is an equation that is true for all possible values.(It is always true regardless of the values that are substituted into the equation.)
A trigonometric identity is an equation that involves trigonometric functions and is true for every single value substituted for the variable (assuming both sides are "defined" for that value) You will find that trigonometric identities are especially useful for simplifying trigonometric expressions.
The most common trigonometric identities are those involving the Pythagorean Theorem.
When studying the unit circle (radius of 1), it was observed that a point on the unit circle (a vertex of the right triangle) can be represented by the coordinates (cos 2t, sin 2t ).
Since the legs of the right triangle in the unit circle have the values of sin 2t and cos 2t, the Pythagorean Theorem can be used to obtain [tex]sin^{2}2t +cos^{2}2t =1[/tex]
Given Equation : [tex]sin^{2}2t +cos^{2}2t =1[/tex]
To proof : [tex]1 + cot^{2}2t = csc^{2}2t[/tex]
[tex]1 + cot^{2} \alpha = csc^{2} \alpha [let \alpha =2t] \\\\1 + cot^{2} \alpha = 1 + \frac{cos^{2}\alpha }{sin^{2} \alpha } \\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha }{sin^{2} \alpha } + \frac{cos^{2}\alpha }{sin^{2} \alpha }\\\\1 + cot^{2} \alpha = \frac{sin^{2}\alpha + cos^{2} \alpha }{sin^{2} \alpha }\\ \\1 + cot^{2} \alpha = \frac{1 }{sin^{2} \alpha } [ since ,sin^{2}\alpha + cos^{2}\alpha = 1]\\\\1 + cot^{2}\alpha = sec^{2} \alpha\\\\or\\1 + cot^{2}2t = sec^{2} 2t[/tex]
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Need help answer please!
Answer:
The second option/ B
Step-by-step explanation:
6 coins plus 4 coins is 10 coins, and you can’t forget the x amount of pennies.
QUESTION 12/15 Which tools would you use to make Chart 1 look like Chart 2? Select all that apply.
The tool that is used to make Chart1 look like Chart2 is data lables .
What are Charts ?
Charts can be defined as graphical way that represents data elements.
the forms of charts are tables and graph .
From the attachment we can see that both the charts are circle graphs .
and the chart2's data label is visible and chart's 1 data label is not visible .
The data label of chart1 needs to be visible for both the chart to look alike .
Therefore , the tool that is used to make both the charts lookalike is data labels .
The given question is incomplete , the complete question is
Which tools would you use to make Chart 1 look like Chart 2 ?
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Let S be the set of all triangles that can be formed from three distinct vertices of a regular decagon. How many of those triangle are scalene?
The vertices of a regular decagon can only ever give rise to a maximum of zero scalene triangles at any one time.
What are triangles?Generally, An isosceles triangle has two sides with the same length. There are 10 ways to choose the vertex that is common to the two equal sides, and for each of these choices, there are 5 ways to choose the other two vertices (since they must be distinct from the first). Therefore, there are a total of
10* 5*5=250 isosceles triangles.
To get the final count of scalene triangles, we use the principle of inclusion-exclusion by subtracting the number of isosceles triangles from the total number of triangles.
This gives us a final count of 120-250=-130.
However, since we cannot have a negative number of triangles, the final answer is 0.
Therefore, there are 0 scalene triangles that can be formed from the vertices of a regular decagon.
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The article also reported that for a sample of 36 individuals who had taken quetiapine, the sample mean cholesterol level change and estimated standard error were 9.06 and 4.256, respectively. Make any necessary assumptions about the distribution of change in cholesterol level, test the hypothesis that the true average cholesterol level increases. Givens: State the appropriate hypotheses. (Use μD = μafter − μbefore.) H0: μD = 0 Ha: μD > 0 t value= 2.1 or 2.128759398 unrounded p value=? Identify the significance levels at which there is sufficient evidence to reject H0. (Choose all that apply.) ? = 0.1 ? = 0.05 ? = 0.01 ? = 0.001 For the sample of 45 individuals who had taken olanzapine, the article reported (7.520, 9.830) as a 95% CI for true average weight gain (kg). What is a 99% CI? (Round your answers to three decimal places.
P-value is equal to 0.0206 and the significance levels at which there is sufficient evidence to reject H0 are at = 0.05 and [tex]\alpha[/tex]=0.1 and value of 99% CI = 7.132, 10.218.
Here we have,
n= 36
e= 9.06
S.E. = 4.256
Hypothesis
H0: μD = 0
Ha: μD > 0
This a right-tailed test
Test statistics,
t = 2.12
P-value at t= 2.12 and degree of freedom(df) = n-1 =36-1 = 35
P-value = t-dist(t, df, tails)
= t-dist(2.12, 35, L)
= 0.020585
= 0.0206 Round to 4 decimals
If pvalue>[tex]\alpha[/tex], then we reject the null hypothesis.
So, [tex]\alpha[/tex]= 0.05 and [tex]\alpha[/tex]=0.1 we reject the H0.
For sample of n=45 df will be= 45 -1 =44
t0.025 = 2.015
Mean weight = (7.520 + 9.830)/2 = 8.675
Margin of error = 9.830 - 8.675 = 1.155
SE = 1.155/2.015 = 0.573
99%tc = 2.692
Margin of error = 2.692 x 0.573 = 1.543
99% CI = 8.675 ± 1.543
= 7.132, 10.218
99% CI = 7.132, 10.218.
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find the length of the hypotenuse of the triangle pictured below. give your answer accurate to at least 2 decimal places.
The length of the hypotenuse of the triangle is √181 cm
Pythagoras theorem states that in the right -angled triangle , the square of the hypotenuse side is equal to the sum of the square of other two sides.
Hypotenuse it the longest side , as it is opposite to the angle 90°
Pythagoras theorem formula :
Let a be the base
b be the perpendicular and c is hypotenuse
So, according to the Pythagoras
c² = a² + b²
According to the question,
We have to find the length of hypotenuse
Given that base = 10
Perpendicular = 9
Let Hypotenuse = x
Using above theorem
=> x² = (10)² + (9)²
=> 100 + 81 = x²
=> c = √181
The length of hypotenuse is √181
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