a) The proportion of the population that is less than 18 is 0.3085.
b) The probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
a) To find the z-score corresponding to the value of 18, we can use the standard normal formula:
z = (18 - mu) / sigma
Where mu is the mean and sigma is the standard deviation of the population.
To find the proportion of the population that is less than 18, we can use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives us the proportion of the population that is less than a given value.
For a standard normal distribution, we can use a standard normal table or a calculator to find the CDF.
Using the standard normal table, or a standard normal calculator,
we find that the CDF of the standard normal distribution at z = -0.6309 is 0.3085.
So, the proportion of the population that is less than 18 is 0.3085.
b) To find the z-score corresponding to the value of 25, we can use the standard normal formula:
z = (25 - mu) / sigma
Using a standard normal calculator or table,
we find that the z-score for 25 is 1.0538.
The proportion of the population that is greater than 25 is 1 - the CDF of the standard normal distribution at z = 1.0538.
Using a standard normal calculator or table, we find that the CDF of the standard normal distribution at z = 1.0538 is 0.8461.
So, the proportion of the population that is greater than 25 is 1 - 0.8461 = 0.1539.
To find the probability that a randomly chosen value is greater than 25, we can multiply 0.1539 by 100% to get 15.39%.
Therefore, the probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
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the first box has two white balls. the second box has two black balls. the third box has a white and a black ball. all boxes are labeled but all labels are wrong! you are allowed to open one box, pick one ball at random, see its color and put it back into the box without seeing the color of the other ball. how many such operations are necessary to correctly label the boxes?
To correctly label the boxes, you need to perform two operations. In the first operation, you can choose to open any of the three boxes. Regardless of which box you open, you will be able to determine the color of one ball.
Then, you can use that information to deduce which of the other two boxes must contain two balls of the same color and which must contain one ball of each color. In the second operation, you can choose to open the box which contains two balls of the same color. The color of the ball you take out will tell you the correct label of the box. By performing these two operations, you can correctly label the boxes with only two ball selections.
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I need help on this problem
The distance of Main Street is given by the equation D = 319.25 feet
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the distance of Main Street be D
Now , let the triangle be represented as ΔABC
The base of the triangle BC = 300 feet
The hypotenuse of the triangle AC = distance between First avenue and Canal street
The measure of angle ∠BAC = 70°
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin 70° = 300 / D
Multiply by D on both sides of the equation , we get
D ( sin 70° ) = 300
Divide by sin 70° on both sides , we get
D = 300 / ( sin 70° )
On further simplification , we get
D = 300 / 0.939692
D = 319.2535
D = 319.25 feet
Hence , the distance is 319.25 feet
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Do the following lengths form a right triangle?
The lengths form a right triangle are Triangle 2,3 and 4.
Side lengths a , b , c form a right triangle if, and only if, they satisfy a² + b² = c² . We say these numbers form a Pythagorean triple.
About Pythagorean theoremThe Pythagorean theorem reads:
"In a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides."
Thus the three sides of a right triangle have an interrelated relationship.
This theorem has two mandatory properties, namely it only applies to right triangles and you must know at least two sides first to be able to determine the other side.
While the purpose of this theory is basically to determine the length of one side of a right triangle. Whereas for a right triangle it is actually very easy because one of the characteristics of a right triangle is that it has one of the 90° angles.
However, this theory can also be used to calculate the length of the diagonal of a square or beam and cube which also looks like a right triangle.
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10 m
55 m
60 m
90 m
20 m
15 m
Whats the perimeter
The perimeter of the polygon is 250m
What is polygon? what its perimeter?A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface. The polygon can be divided into two different types, such as regular polygons and irregular polygons, depending on its sides and angles.
The total of a polygon's sides is referred to as the polygon's perimeter. If a polygon has regular sides, its perimeter may be calculated using the formula Perimeter of Regular Polygon = (Number of Sides) x (Polygonal Side Length) units.
Given the sides of the polygon are 10 m, 55 m, 60 m, 90 m, 20 m and 15 m.
The perimeter of the polygon = sum of all sides
The perimeter of the polygon = 10m + 55m + 60m + 90m + 20m + 15 m.
The perimeter of the polygon = 250m
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if there are 250 members of the 8th grade class, then what percent prefer either tennis or football? (the tennis is 20 and the football is 14)
The percentage of preference of tennis or football is, 13.6%
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
The total number of students who prefer tennis is 20.
And the total number who prefer football is 14,
so the total number who prefer either tennis or football is
⇒ 20 + 14
⇒ 34
To find the percentage of students who prefer either tennis or football, we can divide the number of students who prefer either by the total number of students and multiply by 100:
(34 / 250) x 100 = 13.6%
So, approximately 13.6% of the 8th grade class prefer either tennis or football.
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9 units to the left, 7 units up
The Equation of parabola is .y = a(x + 9)² + 7
What is Equation of Parabola?The general equation of a parabola is: y = a(x – h)² + k where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Given:
The general equation of a parabola is given by
y = a(x – h)² + k
Here (h, k) denotes the vertex.
We have 9 units to the left which is represented by '+9' and 7 units up which is represented by '+7'
So, the Equation of parabola is
y = a(x – h)²
y = a(x + 9)² + 7
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suppose the 99% confidence interval for the mean sat scores of applicants at a business college is given by [1,692, 1,842]. this confidence interval uses the sample mean and the sample standard deviation based on 25 observations. what are the sample mean and the sample standard deviation used when computing the interval?
The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.
Here, the two boundaries are 1692 and 1842.
Mean = (1692+1842) /2 = 1767
Here the degree of freedom, df = (n-1) = 25-1 =24
Margin of error = (1842-1692)/2 = 75
Confidence level = 99%
From the t table, value of T with confidence level 99% and df= 24 is 2.80
The equation for margin of error is M = Ts/√n
M= 75 , T= 2.80, n =25
75 = (2.80 × s) / √25
75 = 2.80s/ 5
s = (75×5)/2.80 = 133.928 = 133.93
So the sample mean is 1767 and the standard deviation is 133.93.
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Solve for x on the diagram below
Answer:
x = 60°
Step-by-step explanation:
the 'x' angle and the adjacent 120° angle form a straight line
a straight line consists of 180°
HELP THIS IS FOR EXTRA CREDIT AND ITS DUE TODAY
You spin a spinner that is equally divided into 11 parts. 3 parts are green, 3 parts are speckled, 2 parts are white, and 3 parts are yellow.
What is the probability of the spinner not stopping at a white section? Write your answer as a decimal rounded to the nearest hundredth.
Answer: The probability of the spinner stopping at a green section and then rolling a 3 is 1/22
Step-by-step explanation: A spinner stopping at a green section
B: rolling a 3
the spinner is divided into 11 parts, 3 of them are green, then:
P(A) = 3/11
the number cube has 6 numbers, then:
P(B) = 1/6
The two events are independent, then:
P(A∩B) = P(A)*P(B) = 3/11 * 1/6 = 1/22
Rule: 1, 2, 3, 5, 8,
Answer: 13, 21, 34...
Step-by-step explanation: 1+2 = 3, 2+3 = 5, 3+5 = 8, 5+8 = 13, 8=13 = 21, etc.
what is the unit of measurement for coding the length of lacerations? a. square inches b. inches c. square centimeters d. centimeters
The unit of measurement for coding the length of lacerations d)centimeters.
Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.
Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.
Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.
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Year 9 students from a school were asked to choose one language to study. The table shows information about their choices. Students in maths class 9s1 were told to draw a pie chart to ultralight
you can infer causality from a correlational result, but only when the r value is greater than
a.0
b.0.5
c.1
A correlational result can be used to infer causality, but only if the value of r is greater than 0.
What is infer causality?In statistics, a correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. A positive correlation coefficient implies that two variables are related (as one variable increases, so does the other), whereas a negative correlation value shows that two variables are inversely related (as one variable increases, the other decreases).A correlation value of zero shows that no relationship exists between two variables. However, a correlation coefficient greater than 0 does not imply causality, meaning that it cannot be concluded that one variable causes changes in the other variable. Establishing causality requires additional evidence and methods such as experimental designs or causal inference techniques.To learn more about infer causality refers to:
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Hexagon HEXAGZ has vertices H(3,0), E(1, -2), X(-1, -2), A(-3,0), G(-2,2), and Z(1,2). What are the coordinates of the image of HEXAGZ for a dilation with center (0,0) and a scale factor of 3.5?
Answer: ion know
Step-by-step explanation: 1 + 2 = 3
suppose that you are awarded prize money if you match at least three of the winning numbers. the probability that you will win some prize money is .
The frequency of winning numbers you can match, determines your chance of winning a prize.
The likelihood of earning some money is one if you can match three or more of the winning numbers (certain). However, the probability of winning any prizes is zero if you can only match two or fewer of the winning numbers (impossible).
Probability distribution: The probability that a random variable will take on a specific value or range of values is expressed mathematically as a probability distribution. It is often referred to as a probability mass function or a probability density function (PDF) (PMF). Each result of a random event, such as the roll of a dice, the toss of a coin, or a stock market return, is given a probability by the probability distribution.
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what is the probability that a standard normal random variable will be between .3 and 3.2?
0.3814 is the probability that a standard normal random variable .
What is the probability equation?
The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.
P(E) = positive outcomes/total outcomes is how it's expressed mathematically. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula. Mathematically speaking, it seems as follows: P(E) stands for positive outcomes/total outcomes.
P(0.3 < z < 3.2)
= P(z < 3.2) - P(z < 0.3)
= 0.9993 - 0.6179
= 0.3814
Probability = 0.3814
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Calculate the area of the figure below using the following information:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
Image of irregular pentagon with vertices points A, B, C, D, and E starting at upper left moving clockwise. Two dotted diagonal lines, one connecting vertices A and C, and the second connecting vertices A and D.
The area of figure ABCDE is 26.5 square units.
What is a Triangle?Three angles, three sides, and three vertices make up the closed shape of a triangle. It is one of the most fundamental geometric shapes, and the symbol for it is.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape
Given:
Area of triangle ABC = 7.95 square units
Area of triangle ACD = 9.8 square units
Area of triangle AED = 8.75 square units
To calculate the area of the figure we have to add the area of the individual triangles together.
So, Area of figure ABCDE
= Area of triangle ABC + Area of triangle ACD + Area of triangle AED
= 7.95 + 9.8 + 8.75
= 26.5 square units
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if the variance of the population a is 10 and the variance of the population b is 15, does it mean that population a has less variability than population b?
Yes, the given statement is true if the variance of the population 'a' is smaller than the variance of population 'b' it represents that population 'b' is more variable than 'a'.
Population variance represents the measurement of spread of group data points.It shows the average squared deviation from the given mean.Whenever data points are very near to the mean then the variance has smaller value.And when data points are far away to the mean then it has larger value of variance.Here variance of population 'a' is 10 which is smaller than the variance of population 'b' .It represents population 'a' is less variable than population 'b'.Therefore, the given statement is true for the variance of population 'a' and 'b'.
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Help with thisss pleasseeeee
Answer:
y[tex]\geq[/tex]2x-3
Step-by-step explanation:
y intersect is -3
slop is 2, which eliminates option 2 and 4
when plugging in the point 2,2 in the equation- its a true solution for option 3.
y[tex]\geq[/tex]2x-3
2[tex]\geq[/tex]4-3
2[tex]\geq[/tex]1 True.
lisle and linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and linda walks 2.8 kilometers every 30 minutes. how far apart are they after 1 hour?
The total distance between lisle and Linda will be 10.4 kilometers.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that lisle and Linda walk in opposite directions from the same point. lisle walks 0.8 kilometers every 10 minutes, and Linda walks 2.8 kilometers every 30 minutes.
lisle's distance in an hour:-
0.8 x 6 = 4.8 Km
Linda's distance in an hour:-
2.8 x 2 = 5.6 Km
Total distance = 4.8 + 5.6 = 10.4 Km
Therefore, there will be 10.4 kilometers between Lisle and Linda overall.
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the number of new cases of a disorder in a population that emerge in a particular time interval is called the:
The number of new cases of a disorder in a population that emerge in a particular time interval is called the incidence.
About incidenceIncidence refers to the rate at which a new event occurs in a population. Incidence takes into account the variable time period during which a disease-free individual becomes at risk of spreading the disease.
In incident calculations, the quantifier is the number of events that have occurred in a given time. Then the quantifier of the denominator is the population that is at risk of experiencing the event during this period.
Simply put, incidence refers to new cases and is used to determine the etiology of the disease. While prevalence is more widely used to refer to health status in certain populations.
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AC = 3x + 3, AB= -1 + 2x, and BC = 11.
The value of x is 7.
What are Collinear Points?Collinear points are the points which are formed on a straight line, whether they are close or far away.
Figure representing the question is given below.
From the figure, we have,
AB + BC = AC
(-1 + 2x) + (11) = 3x + 3
2x + 10 = 3x + 3
Like terms adding together,
2x - 3x = 3 - 10
-x = -7
x = 7
Hence the value of x is 7.
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Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 19, 13, 7,
An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 19 - 6(n - 1).
How to write an explicit formula for the arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.From the information provided, we have the following parameters:
First term, a₁ = 19
Second term, a₂ = 13
Next, we would determine the common difference as follows:
Common difference, d = a₂ - a₁
Common difference, d = 13 - 19
Common difference, d = -6
Substituting the parameters into the mathematical expression, we have;
aₙ = 19 + (n - 1)(-6)
aₙ = 19 - 6(n - 1).
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A coral reef is located near to a chemical plant. Scientists measure the number of colonies of coral over a period of 20 years. Each year, the
number of colonies is 5 times the previous year.
Which equation shows the number of colonies, c after t years?
c=5-25²
c=25-3²
c=25-5²
c=25+3t
c=25-20¹
SCALE:
0 - 1 - 2 - n
25-125-625-n
Find out which equation best suits N on the scale.
Answer:
c = 25 * 5^t
Step-by-step explanation:
c = 25 * 5^t
This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.
Write x^4 +5x^2-8 in quadratic form, if possible
Writing x^4 + 5x^2 - 8 in quadratic form will result to
y² + 5y - 8How to write the equation in quadratic formQuadratic equation involves having the variables to be in exponents of 2 as the maximum. That is making the equation degree 2
The equation x^4 + 5x^2 - 8 is rewritten by say
x² = y
then we have
y² + 5y - 8
The equation in quadratic form is y² + 5y - 8
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which variable is the dependent variable--the variable that responded to or depended on the treatment, and was measured by the researchers?
The dependent variable is the variable that responds to or depends on the treatment and is measured by the researchers.
The dependent variable is also known as the outcome variable, response variable, or dependent measure. The dependent variable is the result that the researchers are interested in observing and understanding the relationship with the independent variable, which is the variable that the researchers manipulate or control in the study. The dependent variable is what the researchers are trying to explain or predict based on the independent variable.
In other words, the value of the dependent variable is dependent on the independent variable.
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the dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. the data is divided into equal-sized subgroups with 25% of the adults in each subgroup. which measure of center can you most accurately estimate from this information?
which measure of center can you most accurately estimate from this information: Median
The median divides the data into equal-sized groups. So approximately 50% of the data is above the median and approximately 50% of the data is below the median.
Calculating the median
The median is the value in a data set, implying that half of data focuses have a value more modest or equivalent to the median and half of data focuses have a value higher or equivalent to the median.
For a little data set, you first count the quantity of data focuses (n) and organize the data focuses in expanding request. Assuming the quantity of data focuses is lopsided, you add 1 to the quantity of places and separation the outcomes by 2 to get the rank of the data point whose value is the median.
The rank is the place of the data point after the data set has been organized in expanding request: the smallest value is rank 1, the second-smallest value is rank 2, and so forth.
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the complete question is:
The dotplot above shows the distribution of calf measurements for 507 adults who attend a local gym. The data is divided into equal-sized subgroups with 25% of the adults in each subgroup.
Which measure of center can you most accurately estimate from this information?
1. mean
2. median
An item is regularly priced at $30. Maria bought it on sale for 80% off the regular price. How much did Maria pay?
Answer:
$24
Step-by-step explanation:
30 times .80=24
Which rectangular prism has the largest volume?
Answer:
The first one is largest volume: 27
Step-by-step explanation:
1) 3*3*3=27
2)4*4*1=16
3)2*4*2=16
4)1*6*2=12
Select the trigonometric equation that can be used to find x.
Answer:
tan(64)= x/11
Step-by-step explanation:
if we make 64 degrees are central angle then that means the side along the right angle is the adjacent and side x is the opposite
since tan∅ = opposite/adjacent
we know angle is 64 and adjacent is 11
thus,
tan 64 = x/11