9.
What is the solution set for this inequality?
negative five D plus five and one over two symbol seventeen.
Answer:
Step-by-step explanation:
Find the average rate of change for the given function. f(x) = x² x + 6x between x = 0 and x = 7 The average rate of change is 13. (Simplify your answer.)
The average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is 13.
To find the average rate of change for the given function f(x) = x² + 6x between x = 0 and x = 7, you can follow these steps: Calculate the value of the function at the given points.
f(0) = 0² + 6(0) = 0
f(7) = 7² + 6(7) = 49 + 42 = 91
Use the average rate of change formula, which is (f(b) - f(a)) / (b - a), where a and b are the given points.
Substitute the values into the formula:
Average rate of change = (f(7) - f(0)) / (7 - 0) = (91 - 0) / 7 = 91 / 7 = 13
Therefore the average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is calculated to be 13.
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Quadrilateral ABCD is a square with diagonals AC and BD. If A(4, 9) and C(3, 2), find the slope of BD.
Using the given information from #13, find the length of BD. Give your answer in simplest radical form.
B
the location of point 0 on directed line segment PS such that PO: OS is divided into a ratio of 3:2
The length of BD is √(65)) and the slope of BD is 1/7.
What does Quadrilateral means ?
In geometry, a quadrilateral is a four-sided polygon with four sides (sides) and four angles (vertices). The word is derived from the Latin words quadri, the form of four, and latus, meaning "side". Different types of quadrilaterals include trapezoid, parallelogram, rectangle, rhombus, square, kite
To find the slope of the diagonal BD of square ABCD, you must first find the coordinates of points B and D. Since ABCD is a square, all sides are the same length and the diagonals bisect each other at 90 degrees.
The midpoint M of AC is the intersection of the diagonals, so we can find the coordinates of M by taking the average of the x-coordinates and the average of the y-coordinates:
M = ((4 +3)/2, (9+ 2)/2) = (3.5, 5.5)
Since BD bisects AC, the coordinates of the midpoint M are also the coordinates of both B and D. Hence we have:
B = D = (3.5, 5.5)
The slope of the line passing through points A and C is:
m_AC = (2-9)/(3-4) = -7
Since the diagonals of the square are perpendicular, the slope of BD is the negative inverse of m_AC:
m_BD = -1/m_AC = 1/7
We can use the Pythagorean theorem to find the length of BD. Let x be the length of BD. Then we have:
AC² + BD² = 2x²
Since AC is the diagonal of the square, its length is:
AC = square((3-4)²+ (2-9)²) = square(65)
Substituting this into the above equation and solving for x, we get:
√(65) x² = 2x²
x² = square(65)
x = square (square(65))
Therefore, the length of BD is √(65) and the slope of BD is 1/7.
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How much would you have to deposit in
an account with a 4.75% interest rate,
compounded continuously, to have
$20,000 in your account 20 years later?
Answer:
Pe^(.0475 × 20) = $20,000
P = $7,734.82
6. A certificate of deposit (CD) pays 2. 25% annual interest compounded biweekly. If you
deposit $500 into this CD, what will the balance be after 6 years?
The balance of the CD after 6 years will be $678.35.
To calculate the balance of the CD after 6 years, we need to use the formula:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)
Plugging in the values, we get:
A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35
Therefore, the balance of the CD after 6 years will be $678.35.
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Sara is studying for her dba. she studied for 31/2 hours before dinner, then for another
45 minutes after dinner. how long did sara study in all?
To find out how long Sara studied in all, we need to add the time she studied before dinner and after dinner.
Sara studied for 3 1/2 hours before dinner and 45 minutes after dinner.
We can convert 3 1/2 hours to minutes by multiplying it by 60:
3 1/2 hours = 3 × 60 + 30 = 180 + 30 = 210 minutes
So, Sara studied for 210 minutes before dinner and 45 minutes after dinner.
To find the total time, we add these two values:
Total time = 210 minutes + 45 minutes = 255 minutes
Therefore, Sara studied for 255 minutes in all.
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Emir earned some money doing odd jobs last summer and put it in a savings account that earns 10% interest compounded monthly. After 9 years, there is $400. 00 in the account. How much did Emir earn doing odd jobs?
Round your answer to the nearest cent
Emir earned approximately $207.05 doing odd jobs.
Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:
x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05
Therefore, Emir earned approximately $207.05 doing odd jobs.
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Please find x ASAP please please please
Answer:
GiveN:-Sides of triangles are √80 , 8 and xTo FinD:-Value of x = ??SolutioN:-we know that given triangle is right angled triangle.
➢ By using Phythagoras Theorem:-
[tex] \sf \longrightarrow \: (AC)^2 = (AB)^2 + (BC)^2[/tex]
[tex] \sf \longrightarrow \: ( \sqrt{80} )^2 = (x)^2 + (8)^2[/tex]
[tex] \sf \longrightarrow \: 80 = (x)^2 + (8)^2[/tex]
[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 8^2[/tex]
[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 64[/tex]
[tex] \sf \longrightarrow \: 80 \: - 64 = x^2 \:[/tex]
[tex] \sf \longrightarrow \: 16 = x^2 \:[/tex]
[tex] \sf \longrightarrow \: x^2 \: = 16[/tex]
[tex] \sf \longrightarrow \: x \: = \sqrt{16} [/tex]
[tex] \sf \longrightarrow \: x \: = 4 \: units [/tex]
Assuming an approximately normal data set, find the 68% confidence interval for systolic blood pressure in
women given a sample size of 1000 with a mean of 123.4 and a standard deviation of 19.9.
There is not enough evidence to conclude that Devon's true proportion of good serves is greater than 72%.
Find out the 68% confidence interval for systolic blood pressure in women from the given samples?The correct conclusion for Devon to reach is: Because the P-value of 0.06 > a (where a = 0.05), Devon should fail to reject H0. There is no convincing evidence that the proportion of services that are good is more than 72%.
The null hypothesis, H0, states that the true proportion of good serves for Devon is equal to 72%. The alternative hypothesis, Ha, states that the true proportion of good serves for Devon is greater than 72%.
The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming that the null hypothesis is true. In this case, the P-value is 0.06, which means that if the true proportion of good serves for Devon is actually 72%, there is a 6% chance of observing a sample of 50 serves with 42 or more good serves.
Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.
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The 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03)
How to find a confidence interval for systolic blood pressure in women?To find the 68% confidence interval for systolic blood pressure in women, we can use the standard formula:
Confidence Interval = Mean ± (Z * (Standard Deviation / √n))
Where:
Mean = 123.4 (sample mean)
Standard Deviation = 19.9 (sample standard deviation)
n = 1000 (sample size)
Z = Z-score corresponding to the desired confidence level (in this case, 68% corresponds to 1 standard deviation on each side of the mean)
To find the Z-score, we can refer to the standard normal distribution table or use a calculator. For a 68% confidence level, the Z-score is 1.
Plugging in the values, we get:
Confidence Interval = 123.4 ± (1 * (19.9 / √1000))
Calculating the square root of 1000, we have:
Confidence Interval = 123.4 ± (1 * (19.9 / 31.62))
Simplifying further, we get:
Confidence Interval = 123.4 ± (0.6301)
Therefore, the 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03).
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If x = 3 centimeters, y = 5 centimeters, and z = 5 centimeters, what is the area of the object?
A. 40 square centimeters
B. 50 square centimeters
C. 45 square centimeters
D. 25 square centimeters
The area of the object is 40 square centimeters
The correct answer is an option (B)
We know that the formula for the area of trapezoid is,
A = ((a + b)/2) × h
where a and b are the two parallel bases
h is the height of the trapezoid
From the attached figure, first we determine the length of the two parallel bases.
Let us assume that 'a' represents the length of the upper base and 'b' represents the length of the bottom side of the trapezoid
We can observe that a = 2x
so the length of a = 6 centimeters
And b = 2z
So, the length of b = 2(5)
= 10 cm
Here, the height h of the trapezoid is given by y = 5 cm
Using above formula for the area of trapezoid, the area of the object would be,
A = ((a + b)/2) × h
A = ((6 + 10)/2) × 5
A = (16/2) × 5
A = 40 cm²
Therefore, the correct answer is an option (B)
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Find the complete question below.
Fill in the blank: Some of the most common symbols used in formulas include (addition), - (subtraction), * (multiplication), and / (division). These are called _____
The basic arithmetic operators (+,-,*,/) are commonly used in formulas to perform mathematical calculations. They are collectively known as "operators" and are an essential component of mathematical formulas, allowing us to perform complex calculations quickly and efficiently.
The symbols mentioned in the question, i.e., (+,-,*,/) are the basic arithmetic operators that are used in mathematical formulas to perform different types of calculations. These symbols are collectively referred to as "operators" or "mathematical operators."
Operators are an essential part of mathematical formulas as they allow us to perform complex mathematical calculations in a concise and efficient manner. They act as a shorthand way of representing mathematical operations and make it easier to perform calculations without having to write out the entire equation every time.
In addition to the basic arithmetic operators mentioned above, there are other types of operators that can be used in formulas depending on the specific mathematical operation being performed. For example, there are logical operators like AND, OR, and NOT that are used in Boolean algebra to perform logical calculations.
Other operators that can be used in formulas include exponentiation (^), which is used to raise a number to a certain power, and modulo (%), which is used to find the remainder when one number is divided by another.
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A translation is applied to the square formed by the points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6) . Select the phrase from the drop-down menu to correctly describe the translation. The square was translated Choose... .
The square was translated 2 units downwards.
Describing the transformationFrom the question, we have the following parameters that can be used in our computation:
Points A(−3, −4) , B(−3, 5) , C(6, 5) , and D(6, −4) . The image is the square that has vertices A′(−3, −6) , B′(−3, 3) , C′(6, 3) and D′(6, −6)The square was translated 2 units downward since all the y-coordinates of the vertices of the image square are 2 units less than the corresponding y-coordinates of the vertices of the pre-image square.
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the line is parallel to the graph of 2x-3y=7 and contains the point (-3, -3)
The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.
What is the Equation of Parallel Lines?To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
This implies that the slope of this line is m = 2/3.
Thus, the equation of the line we are to find will take the following form:
y = (2/3)x + b
where b is the y-intercept of the line.
To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:
-3 = (2/3)(-3) + b
-3 = -2 + b
b = -1
Substitute m = 2/3 and b = -1 into y = mx + b:
y = (2/3)x - 1
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How many outcomes are there in a 5 digit license plate if the first 2 digits must be letters and the last 3 digits are numbers?
The letters and numbers can be repeated.
100
B 260
676,000
D 1,757,600
PLEASE HELP!!
Solve for measure of angle a.
a = [?]°
Answer:
∠ a = 125°
Step-by-step explanation:
the measure of chord- chord angle a is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ a = [tex]\frac{117+133}{2}[/tex] = [tex]\frac{250}{2}[/tex] = 125°
Find the perimeter of the rectangle, in feet.
L: 3 1/4 FT
W: 7/8 FT
Answers:
A. 8 1/4 ft
B: 8 1/5 ft
C: 8 1/2 ft
D: 8 1/3 ft
The perimeter of the rectangle is 8 1/4 feet. the correct answer is A.
Perimeter is the total length of the sides of a two-dimensional shape. In a rectangle, opposite sides are equal in length, so the perimeter can be found by adding the lengths of all four sides. To find the perimeter of a rectangle, we use the formula:
Perimeter = 2(length + width)
In this case, the length is given as 3 1/4 feet and the width is given as 7/8 feet. To find the perimeter, we substitute these values into the formula:
Perimeter = 2(3 1/4 + 7/8)
To simplify, we need to convert the mixed number to an improper fraction and find a common denominator for the fractions:
Perimeter = 2(13/4 + 7/8)
Perimeter = 2(26/8 + 7/8)
Perimeter = 2(33/8)
Now we can simplify the expression by multiplying 2 by the fraction:
Perimeter = 66/8
We can reduce this fraction by dividing both the numerator and denominator by 2:
Perimeter = 33/4
Therefore, the perimeter of the rectangle is 8 1/4 feet, which is answer choice A.
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() Jamison works as a server at a local restaurant. He made $42.80 in tips on
Thursday night. He made 2 1/4 times that amount in tips on Friday night. How much
in tips did he earn on Friday?
Therefore, Jamison made $96.30 in tips on Friday night.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.
Here,
Jamison made $42.80 in tips on Thursday night.
To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.
$42.80 x 9/4 = $96.30
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Use the order of operations to find the value of the expression. 12 ÷ 2 × 3 − ( 7 − 5 ) a. 0 b. 6 c. 16 d. 19
Answer:
Step-by-step explanation:
12 ÷ 2 × 3 − ( 7 − 5 )
= 6 × 3 - 2 (since 7 - 5 = 2)
= 18 - 2
= 16
Answer is C
The value of the expression is 16.
What is the value of the expression 12 ÷ 2 × 3 − (7 − 5) using the order of operations?The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules used to determine the sequence in which calculations are performed.
In this case, we start with the parentheses first: 7 - 5 = 2. Then, we perform multiplication and division from left to right: 12 ÷ 2 = 6, 6 × 3 = 18. we subtract the result of the parentheses: 18 - 2 = 16. Therefore, the answer is c. 16.
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3−(−1)+(−1)−33, minus, left parenthesis, minus, 1, right parenthesis, plus, left parenthesis, minus, 1, right parenthesis, minus, 3
The calculated value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
Finding the value of the expression 3 - (-1) + (-1) - 3From the question, we have the following parameters that can be used in our computation:
The expression 3 - (-1) + (-1) - 3
We can add the numbers using a calculator
So, we have the following representation
Value = 3 - (-1) + (-1) - 3
Using the above as a guide, we have the following:
Value = 0
This means that the value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0
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The heights of 14 plants, in inches, are listed.
12, 14, 15, 15, 16, 16, 16, 17, 18, 18 ,19, 20, 22, 25
If another plant with a height of 13 inches is added to the data, how would the mean be impacted?
The mean would stay the same value of about 17.1 inches.
The mean would decrease in value to about 17.1 inches.
The mean would stay the same value of about 17.4 inches.
The mean would increase in value to about 17.4 inches.
Answer:
The mean would decrease in value to about 17.1 inches.
Step-by-step explanation:
If we add a smaller data to the mean of a numerical data set, the mean will decrease.
Hope this helps.
How do I do number 3?
3.) The volume of the triangular prism = 6,480 mi³
The surface area of the triangular prism = 1,872mi²
How to calculate the surface area of the triangular prism?To determine the surface area of the given triangular prism, the formula that should be used is given as follows:
Surface area = bH + (b1+b2+b3)×l
where ;
b= 8 mi
b1 = 18 mi
b2 = 24 mi
b3 = 30 mi
Height = 18 mi
length = 24 mi
Surface area = 8×18 + ( 18+24+30)× 24
= 144 + 1728
= 1,872mi²
To calculate the volume of a triangular prism, the formula the should be used is given as follows;
Volume = 1/2 × b× h × L
where;
b = 24 ni
h = 18 mi
l = 30 mi
volume = 1/2 ×24×18×30
= 6,480 mi³
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Compute the number of 12 letter combination of the 26 letters in alphabet.
key answer:
9,675,700
To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).
Using this formula, we can plug in the numbers:
26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700
Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.
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A contractor is building a rectangular patio. If
t^2+19t+84/4t-4 represents the length of the patio
and 2t-2/t^2+9t+14 represents the width, write and
simply an expression that represents the area of
the patio. Leave simplified answers in factored form
The expression that represents the area of the rectangular patio in factored form is: area = [(t + 4)(t + 21) / 2(t + 7)(t + 2)]
What is an expression?An expression is a grouping of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division in mathematics.
Exponents, functions, and other mathematical symbols may also be included.
In mathematical equations and formulas, expressions are used to represent numbers, calculations, and relationships.
The length of the rectangular patio is given by the expression:
length = (t^2 + 19t + 84) / (4t - 4)
The width of the rectangular patio is given by the expression:
width = (2t - 2) / (t² + 9t + 14)
The area of the rectangular patio is given by the product of its length and width:
area = length x width
By substituting, we get:
area = [(t² + 19t + 84) / (4t - 4)] x [(2t - 2) / (t² + 9t + 14)]
We can factor the numerator and denominator of both fractions to simplify the expression:
area = [(t + 4)(t + 21) / 4(t - 1)] x [2(t - 1) / (t + 7)(t + 2)]
We can then simplify the expression by canceling out the common factors of (t - 1) in the numerator and denominator:
area = [(t + 4)(t + 21) / 4] x [2 / (t + 7)(t + 2)]
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Determine if the sequence is a geometric sequence. If it is, find the common ratio and write the explicit formula and recursive definition. 45, 15, 5, 5/3
The type of sequence is a geometric sequence with a common ratio of 1/3
Checking the type of sequenceTo determine whether the given sequence is a geometric sequence, we need to check if there is a common ratio between any two consecutive terms.
The common ratio, denoted by "r", is calculated by dividing any term of the sequence by its preceding term.
Let's check if there is a common ratio between any two consecutive terms of the given sequence:
15/45 = 1/3
5/15 = 1/3
5/3 / 5 = 1/3
Since the ratio between any two consecutive terms is the same (1/3), the sequence is a geometric sequence.
To find the explicit formula for a geometric sequence, we use the formula:
an = a1 * r^(n-1)
So, we have
an = 45* (1/3)^(n-1)
For the recursice sequence, we have
an = a(n - 1) * 1/3
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What is the value of 6x*2 +17 when x=8
Answer:
113 or 401: see below for explanation
Step-by-step explanation:
x = 8
The way you wrote it with the " * " symbol, it means the multiplication of 6x and 2. This is what I did in the line below.
6x × 2 + 17 = 6 × 8 × 2 + 17 = 48 × 2 + 17 = 113
If by " * " you actually meant an exponent, such as 6x², then here is the calculation using 2 as an exponent. For exponent, we normally use ^, such as 6x^2 to mean 6x².
6x² + 17 = 6 × 8² + 17 = 6 × 64 + 17 = 384 + 17 = 401
Find the amount of tin needed to make a milk can that has a diameter of 4cm and height of 5cm
In the surface area, the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here we know that the tin is in the shape of cylinder.
Now to find the amount we need to determine the surface area of the cylinder.
Now Height h = 5 cm, Diameter = 4 cm then radius r = d/2 = 4/2 = 2 cm.
Now using formula then,
Surface Area = 2[tex]\pi\\[/tex]r(h+r) square unit.
=> Surface area = [tex]2\times3.14\times2(5+2)=2\times3.14\times2\times7[/tex] = 87.92 [tex]cm^2[/tex]
Hence the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].
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Kevin has three classes in a row. Eight classes two hours long. Kevin’s first class is at seven. When will Karen’s last class and?
Karen's last class will end at three in the afternoon.
At what time will Karen’s final class conclude?Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.
Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.
Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.
Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.
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the following list shows the number of goals scored by a soccer team in each of 9 games. 0 0 1 1 1 3 3 4 5 how does the median number of goals scored compare with the mean number of goals scored? responses
The median number of goals scored is 1, and the mean number of goals scored is 2. The median is less than the mean, indicating a right-skewed distribution.
To find the median, we need to first put the numbers in order
0, 0, 1, 1, 1, 3, 3, 4, 5
There are an odd number of values, so the median is the middle value, which is 1.
To find the mean, we add up all the values and divide by the number of values
(0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5) / 9 = 2
So the mean number of goals scored is 2.
Since the median (1) is less than the mean (2), we can say that the distribution is skewed to the right. This is because the high value of 5 pulls the mean up, while the median is not affected as much by outliers.
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will mark brainlist to the correct person who does the step by step correctly and also the correct answer
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
Answer:
answer choice C
Step-by-step explanation:
The playground is a rectangle.
To find the area of a rectangle, we use the formula:
Area = Length x Width
The length is 25 yards.
The width is 68 yards.
Plugging these into the area formula:
Area = 25 x 68 = 1,700 square yards
Of the options, the closest choice is:
1,710 square yards
The area is 1,710 square yards.
A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the standard deviation of X, the number of draws until the first red marble? 0. 4852 0. 9704 2. 0770 1. 5172
The standard deviation of X to be approximately 0.4852. The correct answer is option (A).
To calculate the standard deviation of X, we need to first calculate the probability of drawing a red marble on the first draw, which is 11/29. The probability of not drawing a red marble on the first draw is 18/29. The probability of drawing a red marble on the second draw, given that we did not draw a red marble on the first draw, is 11/29. Using the formula for the geometric distribution, which models the number of trials until the first success, we can calculate the expected value of X, which is 1/p, where p is the probability of success (11/29 in this case).
Therefore, the expected value of X is 29/11. To calculate the standard deviation of X, we use the formula sqrt(q/p^2), where q is the probability of failure (18/29) and p is the probability of success (11/29). Plugging in these values, we get the standard deviation of X to be approximately 0.4852. Therefore, the correct answer is option A, 0.4852.
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