The probability of a lion living longer than 10.1 will be 0.1585.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years.
The lifespan of a lion in a particular zoo is normally distributed with average lion lives:
Mean u = 12.5 years
Standard deviation s = 2.4 years
We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.
The empirical rule ( 68-95-99.7% ) states:
P ( u - s < X < u + s ) = 68%
P ( u - 2s < X < u + 2s ) = 95%
P ( u - 3s < X < u + 3s ) = 99.7%
The test has the following number of standard deviations (s):
u - s < X < u + s = 12.5 - 2.4 < X < 12.5 + 2.4 = 10.1 < X < 14.9
u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8 = 7.7 < X < 17.3
u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2 = 5.3 < X < 19.7
Then the probability is calculated as,
P ( 10.1 < X < 14.9 ) = 0.68
P ( 7.7 < X < 17.3 ) = 0.95
P ( 5.3 < X < 19.7 ) = 0.997
We need P ( X < 10.1 ) and P ( X < 5.3 ):
P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2
P ( X < 10.1 ) = [ 1 - 0.68 ] / 2
P ( X < 10.1 ) = 0.16
P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2
P ( X < 5.3 ) = [ 1 - 0.997 ] / 2
P ( X < 5.3 ) = 0.0015
P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )
P ( 5.3 < X < 10.1 ) = 0.16 - 0.0015
P ( 5.3 < X < 10.1 ) = 0.1585
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A researcher has collected the following sample data. The mean of the sample is 5 "3 5 12 3 2" Refer to Exhibit 1. The range is: O 1 O 2 O 10 O 12
The range of a sample data collected by a researcher is 10 . So, correct answer is option (C).
Range of a sample data is calculated by using the formula to determine the difference between the highest and lowest value in sample set of values.
R = Highest Value (H) - Lowest Value (L)
Range Formula, R = H - L
Where, R --> range
H --> the highest value
L --> the lowest value
We have, a reaseacher collected a sample data .
Sample data values are following,
3 5 12 3 2
The mean of sample data = 5
Range of sample data = highest data value - lowest data value
There is highgest data value = 12
and lowest data value = 2
Range = 12 - 2 = 10
So, the required range of sample data is 10.
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Complete question:
A researcher has collected the following sample data. The mean of the sample is 5
"3 5 12 3 2"
Refer to Exhibit 1. The range is:
A)1
B)2
C)10
D) 12
According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval?
Select one:
A. [8.75, 13.25]
B. [10.353, 11.647]
C. [10.5, 19.5]
D. [6.5, 15.5]
c) A concern or risk of reporting significant mean differences between groups is that people may
If Joseph collects data from 186 students from a medium sized school in Iowa and finds that only 11% students has reported rate of bullying , then the 95% confidence interval is option (b) [tex](10.353, 11.647)[/tex] .
the students who report bullying in middle sized school is ⇒ [tex]15[/tex] percent ;
the standard deviation is given as ⇒ 4.5% = 0.045 .
the sample size is ⇒ 186 students ;
the sample proportion is ⇒ 11% = 0.11 .
we know that the for the 95 percent confidence interval the value of z score is 1.96 .
The formula to calculate the upper and lower limit of 95 percent confidence interval is :
= [tex]( Sample Proportion \pm \frac{Zscore \times Standard Deviation}{\sqrt{Population Size} })[/tex]
So , the lower limit of the interval will be calculated as :
= [tex]( 0.11 - \frac{1.96 \times 0.045}{\sqrt{186} })[/tex]
On simplifying ,
we get
= [tex]0.1035[/tex] = [tex]10.35\%[/tex] ;
So , the upper limit of the interval will be calculated as :
= [tex]( 0.11 + \frac{1.96 \times 0.045}{\sqrt{186} })[/tex]
On simplifying ,
we get ;
= [tex]0.1165[/tex] = [tex]11.65 \%[/tex]
Therefore , the required interval is [tex](10.353, 11.647)[/tex].
The given question is incomplete , the complete question is
According to a "how to stop bullying" Web site, 15% of students report experiencing bullying one to three times within the most recent month. Let's assume the standard deviation is 4.5% of students. Joseph collects data from 186 students at a medium-sized school in Iowa and finds that only 11% reported this rate of bullying. What is his 95% confidence interval ?
(a) (8.75, 13.25)
(b) (10.353, 11.647)
(c) (10.5, 19.5)
(d) (6.5, 15.5)
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In a jar, the ratio of dimes to nickels is 3.4. Given that there are 60 nickels in the jar, how many more nickels are in the jar than dimes?.
Answer:
15
Step-by-step explanation:
the nickels ratio is 4. I then divided 60 : 4 = 15. I then timesed 15 with 3 and then came out 45. I then subtracted 60 with 45 which gave me the answer of 15.
Before beginning a unit of frog anatomy, a seventh grade biology teacher gives each of the 24 students in the class a pretest to assess their knowledge of frog anatomy. The teacher wants to compare the effectiveness of an instructional program in which students physically dissect frogs with the effectiveness of a different program in which students use computer software that only simulates the dissection of a frog. After completing one of the two programs, students will be given a posttest to assess their knowledge of frog anatomy. The teacher will then analyze the changes in the test scores (score on posttest minus score on pretest). a) Describe a method for assigning the 24 students to two groups of equal size that allows for a statistically valid comparison of the two instructional programs. b) Suppose the teacher decided to allow the students in the class to select which instructional program on frog anatomy (physical dissection or computer simulation) they prefer to take, and 11 students choose actual dissection and 13 students choose computer simulation. How might that self-selection process jeopardize a statistically valid comparison of the changes in the test scores (score on posttest minus score on pretest) for the two instructional programs? Provide a specific example to support your answer.
The following method for assigning the 24 students to two equal-sized groups allows for a statistical valid comparison of the two instructional programmes.
What is instructional program?An instructional programme is a course of study that requires the completion of a specified number of course credits from a prescribed group of courses and results in a formal award.
A) Each student will be given a unique random number generated by a random number generator on a calculator, statistical software, or a random number table. The assigned numbers will be listed in ascending order. Students with the lowest 12 numbers on the ordered list will be assigned to the instructional programme that requires physically dissecting frogs.
Students with the highest 12 numbers will receive an instructional programme that simulates frog dissection using computer software.
B) By not randomizing and allowing students to self-select, there is the possibility of changes in the differences between pre test and post test scores for a specific group due to the characteristics of students who choose a particular instructional method, rather than the instructional method itself.
For example, suppose frog-loving students already know a lot about frog anatomy; these students would be less likely to show a large difference between pre and post test scores. Assume that the frog-loving students prefer the computer simulation method (perhaps because they do not like the notion of dissecting the frogs they love).
The possible low change in pre- and post-test scores for the computer simulation group could then be attributed to the students' prior knowledge of frog anatomy, rather than to the instructional method itself. Because the students entering the frog dissection group have lower pre-test scores (less prior knowledge), they are more likely to show greater improvement between pre-test and post-test scores.
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the graph shows the total weight of abox of cereal, y, as a function of the amount of cereal in the box, x. what is the weight of the box when it is empty?
Answer:
3
Step-by-step explanation:
A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
Answer:
The probability of winning a straight bet is 1/100, and the payout is $50, so the expected value of a winning bet is (1/100) * $50 = $0.50.
The probability of losing a straight bet is 99/100, and the cost of the bet is $1, so the expected value of a losing bet is (99/100) * -$1 = -$0.99.
Therefore, the expected value of a straight bet is $0.50 - $0.99 = -$0.49.
I need help with this please
Answer in explanation:
*change the problem to [tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]
(change 3 into a fraction by putting 1 in the place of a denominator)
next cross multiply
5 x /1
/2 1
3 can go into 6- 1 time
since anything multiplied by 1 is 1, the answer is [tex]\frac{5}{2}[/tex]
Hope this helps ya!
*(disclaimer lol: alternatively, you could cross multiply without changing 3 to a fraction and get the same answer-- however, I wanted to explain as clearly as possible, and figured it was less confusing this way!)
Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it. What fraction of the voters voted in favor of the measure?
Enter the fraction in simplest form.
The fraction of the voters who voted in favor of the measure will be 1/5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.
The fraction of the voters who voted in favor of the measure will be given as,
⇒ 20%
⇒ 20 / 100
⇒ 1 / 5
The fraction of the voters who voted in favor of the measure will be 1/5.
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Which expression is equivalent to 12x2+x−20
If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.
What other expression is the same as 3 5?6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
The given quadratic expression 12x^2+x-20
now, 12x^2 + 16x - 15x - 20
4x (3x+4) - 5(3x+4)
(4x-5) (3x+4)
the root of the equation is (4x-5) (3x+4)
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In binomial distribution, the probability is .2, P(x is greater than or equal to 1)>.75, find the least possible value of n
The approximate shape of the sampling distribution of the sample will be normal.
Option E is correct.
Sampling distribution:
It is a statistic that determines the probability of an event based on data from a small group within a large population.
Given that, is greater than or equal to 15 and is greater than or equal to 15.
and
So that the new mean and standard deviation will be,
Thus, the approximate shape of the sampling distribution of the sample will be normal.
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Which of the following is a factor of 2x^2 3x 5?
The factor of the given expression is -1 and 5/2 first we try to solve given expression as a quadratic equation then we make 2 terms equal to 0.
first, try to understand what is the factor of a quadratic equation.
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
The roots of a quadratic equation are known as a factor. This means if we put the value of x to factor then the quadratic equation will become zero.
2x^2 - 3x - 5 = 2x^2 - (5-2)x - 5
3 can be written as 5-2.
2x^2 - 5x + 2x - 5
x(2x - 5) +1(2x-5)
(2x - 5)(x + 1)
So the factors is 2x - 5 = 0 or x + 1 = 0.
2x - 5 = 0 , x = 5/2.
x + 1 = 0 , x = -1.
Given question is incomplete complete question here:
Which of the following is a factor of 2x^2 - 3x - 5?
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-2(4 - 3x) - 6x = 10
Answer:
this is a problem with no solution look it up if you dont beleve me
Step-by-step explanation:
when journalizing an accounts payable account what account is debited
a. accounts payable
b. it depends on the transaction
c. cash
d. accounts receivable
I'm need help asap! i dont get the question, i would appreciate it if somebody could help me( giving brainilest & 20 points)!!!
Look at picture below
Answer:
215/100
Step-by-step explanation:
it is asking for improper fraction
improper fractions are just the bottom number multiplied by the number outside of the fraction so in this case it is
2*100 which is 200 then add that to the top number
which leaves you with 215/100
x - (-3) + 8 - 2x - 6 =
Answer:
-x + 5
Step-by-step explanation:
x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5
Answer:
[tex] \sf \: -x + 5 [/tex]
Step-by-step explanation:
Given expression,
→ x - (-3) + 8 - 2x - 6
Let's simplify the expression,
→ x - (-3) + 8 - 2x - 6
→ x + 3 + 8 - 2x - 6
→ (x - 2x) + (3 + 8 - 6)
→ (-x) + (5)
→ -x + 5
Hence, the answer is -x + 5.
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer: 5$ for 52 days
Step-by-step explanation: (5 x 52) + 90 = 350
How do u work this out ?
Answer:
[tex]\frac{d}{c}[/tex]
Step-by-step explanation:
[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex] You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom. It now looks like this
[tex]\frac{d}{c}[/tex]
How does the parabola open? Is the vertex a minimum or maximum value?
f(x) = 5x²-3x
The parabola is open upward direction. The vertex is the minimum value of the parabola.
What is a parabola?
A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
Given quadratic function is
f(x) = 5x² -3x
The leading term of the given function is 5x².
The sign of the leading term is positive, thus it is open upward direction.
Rewrite the given function in the form f(x) = a(x - h)² + k
f(x) = 5x² -3x
f(x) = 5( x² - 3/5 x)
f(x) = 5( x² - 3/5 x + 9/100 - 9/100)
f(x) = 5( x² - 3/5 x + 9/100) - 5 × 9/100
f(x) = 5( x - 3/10)² - 9/20
f(x) = 5( x - 3/10)² + (-9/20)
The vertex of the parabola is (3/10, -9/20).
Since the parabola opens upward direction, thus the vertex of the parabole is a minimum value.
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Use the illustration below to determine which statements are true. Select the two statements that are true statement 1: Points A, E, and C are collinear. statement 2: Lines I and m intersect at point D. statement 3: AE and DC are line segments on line I. statement 4: EA and EC are rays on the line m.
The required true statements for the given lines are 1 and 4.
What is line segments?An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
According to question:Statement A: E and C are co-linear.
It is true, E and C are lie in same line
statement 2: Lines I and m intersect at point D.
It is false, I and m intersect at point E.
statement 3: AE and DC are line segments on line I
It is false,because AE and DC are line segments placed in different line.
statement 4: EA and EC are rays on the line m.
It is true, as EA and EC are in same line m.
Thus, required true statements are 1 and 4.
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Answer:
1 and 4
Step-by-step explanation:
What is the variable in 2x 3 7?
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.
if we solve the above equation, we get
2x + 3 = 7
or, 2x = 7 - 3
or, 2x = 4
or, x = 2
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1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms?
In response to the question, we may say that As a result, the orangutan's expression mass in kilogrammes is roughly 64.55 kg.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To convert pounds to kilogrammes, divide the pound weight by the conversion ratio of 2.2.
Hence, to calculate the orangutan's mass in kilos, do the following:
Divide the orangutan's weight in pounds by the conversion ratio of 2.2:
142 pounds divided by 2.2 is 64.54545... kilos (rounded to the nearest hundredth)
As a result, the orangutan's mass in kilogrammes is roughly 64.55 kg.
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Select the correct answer.
Which expression is equivalent to √48x^5, if x > 0?
O A.12³√3x
OB. 42³√3
O c. 4x²√3x
OD. 12x²√x
Step-by-step explanation:
O c. 4x²√3x expression is equivalent to √48x^5, if x > 0?
A bag contains 18 red marbles. The ratio of red marbles to blue marbles is 6 to 9. Find the number of blue marbles in the bag.
How do you find mass using FG?
To find the mass of an object, one can use the formula (Force x Distance) / Gravitational Constant (FG). This formula involves multiplying the force applied to an object by the distance it moves, and then dividing the result by the gravitational constant (FG). The resulting number is the mass of the object in kilograms.
Mass can be found by using the formula (Force x Distance) / Gravitational Constant (FG).
For example, if a force of 10N is applied to an object that is moving 2 meters, the mass of the object can be calculated as follows:
Mass = (10 N x 2 m) / FG
Mass = 20 / 9.8
Mass = 2.04 kg
Finding mass using the force-distance formula (FG) is a simple process. To use it, one needs to know the force applied to an object, the distance it moves, and the gravitational constant (FG). The force and distance values can be measured or calculated depending on the situation. The gravitational constant is a fixed number and is equal to 9.8 m/s2. To calculate the mass, one needs to take the force multiplied by the distance and then divide it by the gravitational constant (FG). The resulting number is the mass of the object in kilograms. This formula is useful for calculating the mass of objects in a variety of situations. It is also useful for verifying the mass of an object that has already been measured.
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How to answer this question
The value of x to the nearest degree will be 112°.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
There are three angles are shown in figure.
That is,
⇒ 59°, 108°, and 81°.
Now, We know that;
Sum of all four angles is 360°.
So, We can formulate;
⇒ 59° + 108° + 81° + x = 360°
⇒ 248° + x = 360°
⇒ x = 360° - 248°
⇒ x = 112°
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How do I do this ? Because I’m having trouble with problems like this .
Answer:
[tex]\sqrt[3]{x^{9} x}[/tex]
Step-by-step explanation:
When you are multiplying powers that have the same bases (in this case x) you add the exponents. If you do not see an exponent, the exponent is 1.
9 + 1 = 10
A cube with volume 8 cubic centimeters is cut in half by a plane which contains two edges of the cube. What is the area of the rectangle formed by the intersection of the plane and cube ? express your answer in simplest radical form.
In simplest radical form as A = 22 = 4 cm2
The formula for the volume of a cube is V = a3, where a is the length of each of the cube's sides. In this case, we know that the volume of the cube is 8 cm3, so a3 = 8. When we take the cube root of 8, we get that a = 2 cm.
Therefore, the area of the rectangle formed by the intersection of the plane and cube is A = 2*2 = 4 cm2. This can also be expressed in simplest radical form as A = 22 = 4 cm2.
To calculate this step by step, we first use the formula V = a3 to find the length of each side of the cube. We plug in 8 cm3 for V and solve for a.
V = a3
8 cm3 = a3
Taking the cube root of both sides gives us:
a = ∛8
a = 2 cm
Next, we use the formula for the area of a rectangle, A = l*w, where l is the length and w is the width. We know that the length and width of our rectangle are both equal to 2 cm.
A = l*w
A = 2*2
A = 4 cm2
This can also be expressed in simplest radical form as A = 22 = 4 cm2.
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What is the inverse of the inverse of P → Q?
The inverse of ∼P→∼Q is P->Q.
Given ∼P→∼Q
Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.
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A patient recently diagnosed with Alzheimer's disease takes a cognitive abilities test and scores a 45.
The mean on this test is 52 and the standard deviation is 5. What percent of patients have his score and
below?
We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.
What does math's % mean?
In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
The Z-score formula is:
Z = (X - M) / SD
Where:
X = Patient's score (45)
M = Mean score (52)
SD = Standard deviation (5)
Plugging in the given values:
Z = (45 - 52) / 5
Z = -7 / 5
Z = -1.4
This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.
It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.
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Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.
The length of each of the four walls of the birdhouse is 5.5 inches, so the total length of all four walls is approximately 4 x 5.5 = 22 inches. Therefore, Javi's board is long enough to be cut into the four walls of the birdhouse.
What is the wall equation?Walls. Utilize the conventional equation Length x Width = Area to get the area of a wall. Next, apply the same calculation to each window and door's specific area. Subtract the area of the windows and doors from the overall size of the wall once you have recorded all of these dimensions.
The birdhouse must have four walls that are each 5.5 inches thick.
one room needs four walls because of the length of its four walls.
4*5.5=22
A board measuring 24.5 inches long is in Javi's possession. In order to cut through the birdhouse's four walls, it is sufficient.
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