Answer:
Median: 85.5
Step-by-step explanation:
Knowledge Needed
Median is the middlemost value of the data set.
For example, we have a data set:
1, 7, 5
Line up in least to greatest.
1, 5, 7
Median is 5.
If there is an even amount of terms, the value of the median is the average of the 2 middlemost terms. For example:
1, 7, 16, 8
Line up in least to greatest.
1, 7, 8 , 16
(7 + 8)/2, average: 7.5
Median is 7.5
Question
Test Scores:
79 88 83 93 79 88 83 93 79 88 83 93 79 88 83 93 79 88
Line them up in least to greatest.
79 79 79 79 79 83 83 83 83 88 88 88 88 88 93 93 93 93
Middle of the set: 83 & 88 (Because there is an even amount of terms).
83 + 88 = 171
171/ 2= 85.5
Median: 85.5
Raul deposited $3000 into a bank account that earned simple interest each year. After 3.5 years, he had earned $262.50 in interest. No money was deposited into or withdrawn from the account.
What was the annual interest rate?
Enter your answer in the box.
Answer:
The annual interest rate is 0.018, or 1.8%.
Step-by-step explanation:
Let r be the annual interest rate, t be the number of years the money was in the account, and I be the amount of interest earned. Since the interest is simple interest, the amount of interest earned is given by the formula I = Prt, where P is the principal, or initial amount deposited. In this case, we know that P = $3000, t = 3.5 years, and I = $262.50. Substituting these values into the formula, we get:
262.50 = 3000r * 3.5
r = 0.018
Thus, the annual interest rate is 0.018, or 1.8%.
f(x) = (4x/9) -8
Find
f-¹(-10)
Answer:
Step-by-step explanation:
f x = (4x/9)
so it will be x into 4x = 9/f
so 4x square = 9/f
Solve the equation included in the picture
Answer:
[tex]C[/tex]
Step-by-step explanation:
[tex]|2x+2|=10\\\\2x+2=10,2x+2=-10\\\\2x=8,2x+2=-10\\\\x=4,2x=-12\\\\x=4,x=-6[/tex]
the table below shows the flight of a golf ball after it was hit from the tee toward the green
a) The graph is drawn and attached below by using graphing calculator:
b) The equation of the curve of best fit is y=0.75x
c) The horizontal distance of the ball travelled with this hit is 58.33
d) It does not touch the hall land on the green.
What is a graph?A relation is shown graphically in a function graph. In set theory and modern mathematics, a function is truly equivalent to its graph. For instance, a codomain should be considered while determining whether or not a function is onto (surjective). A function's graph by itself does not show the codomain.
a) The graph is drawn and attached below by using graphing calculator:
b) The equation of the line of best fit is:
Consider any points from the table,
(0,0) and(30,22.5)
y=mx+c
(0,0) -----> 0=0+c
c=0
(30, 22.5)
m=0.75
y= (0.75)x
c) The horizontal distance of the ball travelled with this hit is 58.33
d) For 10m ------>5.8m
For 20m ------->x
x=11.6m
For 120m it will be near to the ground,
16.7-11.6
=5.1m
It does not touch the hall land on the green.
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Calculate the perimeter of the irregular shape . Please show ur work Bc I have too !!
Therefore, the perimeter of the irregular shape is 34cm .
What is perimeter?Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. The outermost border of an ellipse or circle is its circumference.
Here,
The perimeter of the irregular shape is
Given:
9 cm is the length of the below line and 4cm , 3cm and x is the length of the above line .
So x value is => 9 = 4 + 3+x
=> 9-7 = x
=>x= 2cm
and
thus we get all the length of the irregular shape
so adding =>
=> 4+2+3+2+3+6+5+9= 34 cm
Therefore, the perimeter of the irregular shape is 34cm .
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HELPPPPP!! A company makes different sized shoeboxes in the shape of rectangular prisms. Match the area of the material needed to make each box to the box’s dimensions.
The area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in², 16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Given
A company makes different-sized shoeboxes in the shape of rectangular prisms.
We have to match the area of the material needed to make each box to the box’s dimensions.
S₁ = 12in× 5in× 6in
S₁ = (12×5+12×6+6×6)×2
S₁ = 162×2
S₁ = 324in²
S₂ = 10in× 6in ×6in
S₂ = (10×6+10×6+6×6)×2
S₂ = 156×2
S₂ = 312in²
S₃ = 16in× 6in× 4in
S₃ = (16×6+16×4+6×4)×2
S₃ = 184×2
S₃ = 368in²
S₄ = 14in× 5in× 5in
S₄ = (14×5×2+5×5)×2
S₄ = 165×2
S₄ = 330in²
Hence, the area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in², 16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².
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Avicenna, a major inurance company, offer five-year life inurance policie to 65-year-old. If the holder of one of thee policie die before the age of 70, the company mut pay out $23,900 to the beneficiary of the policy. Executive at Avicenna are conidering offering thee policie for $956 each. Suppoe that for each holder of a policy there i a 4% chance that they will die before the age of 70 and a 96% chance they will live to the age of 70
Answer:
Step-by-step explanation:
E(x) = 791*0.97 - 23600*0.03 = 59.27. The answer is positive so they will make a profit of $59.27 for each policy sold.
However the correct answer is $83. By trial and error.
Write the point slope form of the equation of the line that passes through the point (2, 1) with m = 4.
y+2= 4(x+1)
y-1 = 4(x-2)
Use the display of data items to find the mean, median, mode, and midrange.
Stems
Leaves
The statistical measures for the data-set are given as follows:
Mean: 69.6.Median: 74.Mode: 74.Mid range: 37.5.How to obtain the statistical measures?From the stem plot, the observations of the data-set are given as follows:
45, 46, 48, 74, 74, 75, 76, 93, 95.
The mean is given by the sum of all observations divided by the number of observations, hence:
Mean = (45 + 46 + 48 + 74 + 74 + 75 + 76 + 93 + 95)/9 = 69.6
The median is the middle element of the data-set. The data-set has 9 elements, hence the median is the 5th element, which is of 74.
The mode is the element that appears the most times in the data-set, which is also 74.
The first quartile is the median of the first half of the distribution, which is the median of the first four elements, hence:
Q1 = (46 + 48)/2 = 47.
The third quartile is the median of the last four elements, hence:
Q3 = (76 + 93)/2 = 84.5.
Then the midrange is given as the difference of the quartiles, as follows:
IQR = Q3 - Q1 = 84.5 - 47 = 37.5.
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A pattern ue both addition and ubtraction a it rule. The rule i "Add 12, Subtract 3. " The pattern begin with 41. What i the ixth number in the pattern?
When the rule reads, "Add 12, Subtract 3," and the pattern begins at 41, the sixth number in the pattern is 71.
What is pattern?A pattern is defined in mathematics as a sequence of repeated objects, forms, or numbers. A pattern can be associated with any form of event or object. A pattern has a rule that informs us which items belong to the pattern and which objects do not. Patterns are items that repeat logically, such as vertical stripes on a shirt. They can take the form of numbers, pictures, or forms. A pattern constructed of plastic animals, for example, can alternate between two and four legged creatures, or animals that swim and animals that fly.
Here,
pattern begin at 41,
=41+12
=53
=53-3
=50
=50+12
=62
=62-3
=59
=59+12
=71
The 6th number in the pattern is 71 when the rule says, "Add 12, Subtract 3." and pattern start at 41.
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Please help with this
Answer:
x=45
Step-by-step explanation:
89+112+114+x=360(Sum of angles of a quadrilateral)
315+x=360
x=360-315
x=45
Hope this helps u
Use given information to prove that angle DHF = EHG. Write in two-column proof.
After solving the equation the required solution is ∠DHG = ∠EHG
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given, ∠1 = ∠3
now,
∠DHF = ∠1 + ∠2
and, ∠EHG = ∠3 + ∠2
∠EHG = ∠1 + ∠2 (As ∠1 = ∠3)
Hence, ∠DHG = ∠EHG
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What is the difference between a line and a line segment? Give an example of each.
The difference between a line and a line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.
Lines are the geometrical picture with non-terminating ends. A line runs in two opposite directions with endless. Both the points of a line can be extended to infinity.
The line is non-ending but it can be fractionally divided into different segments. These segments are known as the line segment which has two endpoints.
Difference between line and line segment:
A line segment can be taken as the shortest distance between two endpoints and they are the distance between two defined endpoints.
A line segment can be measured in length as it has two fixed endpoints, which are denoted by ‘_’ or \overline{xy}
A line extends up to infinity as it does not have any starting or endpoint, Which can be measured as it has no end and extends up to infinity, and is denoted by any two points lying on the line.
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What are the properties of the angles and sides of a triangle? How do you use these properties to solve problems involving triangles? Give an example and show your work.
The properties of the angles and sides of a triangle are as follows:
1. The sum of the three angles of any triangle is 180°
2. The longest side of a triangle is opposite the largest angle and the smallest side is opposite the smallest angle.
3. The sum of any two sides of a triangle is always greater than the third side.
These properties can be used to solve problems involving triangles by working out the angles or lengths of sides. For example, let's say we have a triangle with two sides of length 5 and 8, and we need to find the length of the third side. Using the third property listed above, we can set up the following equation:
5 + 8 > x
13 > x
Therefore, the length of the third side is greater than 13.
What is a triangle's rule?A triangle (of any kind) has a total angle of 180°. A triangle's two sides add up to a length bigger than its third side. In the same way, the length of the third side of a triangle's third side is shorter than the difference between its two sides.
What makes it a triangle, and why?Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."
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Which value represents a percentage between 11% and 17%?
Answer: 0.159
Step-by-step explanation:
0.159
The value of a percentage between 11% and 17% is,
⇒ 0.14
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
To find value of a percentage between 11% and 17%.
Now, We can formulate;
The value of a percentage between 11% and 17% is,
⇒ (11% + 17%) /2
⇒ 28% / 2
⇒ 14%
⇒ 0.14
Thus, The value of a percentage between 11% and 17% is,
⇒ 0.14
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What is the equation of the line that passes through the point (1,1) and has a slope of −5?
Answer: y=-5x+6
Step-by-step explanation:
a random sample of 1000 people was taken. 450 of the people in the sample favored candidate a. the 95% confidence interval for the true proportion of people who favor candidate a rounded to three decimal places is:
The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).
A random sample of 1000 people was condidered for testing.
Number of people in sample favoured candidate
= 450
So, sample proportion, p = 450/1000 = 0.45
Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..
Confidence interval formula,
CL = p ± Z× √(p×(1-p)/n)
Lower bound of interval is ,
=0.45 - 1.96× √(0.45× (1-0.45)/1000)
= 0.45 - 1.96× √(0.45× 0.55/1000)
= 0.45 - 1.96× √(0.0002475)
=0.419165~ 0.419
So the Upper bound is
= p + Z×√(p×(1-p)/n)
= 0.45 + 1.96× √(0.45× (1-0.45)/1000)
= 0.45 + 1.96× √(0.0002475)
= 0.480835 ~0.481
Hence, the required confidence interval is (0.419,0.481).
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Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
What is the range of this relation?
Answer:
c. 3 [tex]\leq[/tex] y [tex]\leq[/tex] 5
Step-by-step explanation:
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.
So, the range of this relation is 3 ≤ y ≤ 5.
Answer:
c
Step-by-step explanation:
the maximum of y is 5 the minimum of y is 3
At a book fair the ratio of the number of tudent to the number of adult i 4:3 after 169 tudent left the book fair the ratio became 4:5 how many adult were there at the book fair
If the ratio of the number of students and adults in the book fair is 4:3, the new ratio when 169 students left the fair is 4:5, then the number of adults in the book fair is 318
Let the number of students be 4x
Let the number of adults be 3x
When 169 students left the fair, number of students left = 4x - 169
According to question,
(4x-169)/3x = 4/5
⇒ 5(4x-169) = 4×3x
⇒ 20x - 845 = 12x
⇒ 20x - 12x = 845
⇒ 8x = 845
⇒ x = 845/8
⇒ x = 105.625
⇒ x = 106
Number of adults = 3x = 3×106 = 318
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A diver is at an elevation of -18 feet relative to sea level. The diver descends to an undersea cave that is 4 times as far from the surface
What is the elevation of the cave?
A: -14 feet
B: -18 feet
C: -22 feet
D: -72 feet
The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.
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.
A jumper is at a height of - 18 feet comparative with ocean level. The jumper plunges to an undersea cavern that is 4 times as distant from the surface
The elevation of the cave is given as,
Elevation = - 18 x 4
Elevation = - 72 feet
The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.
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WILL GIVE BRAINLIEST TO WHOEVER IS RIGHT. If you steal points, I WILL REPORT.
We created this inequality to represent how Amy can meet her revenue goals.
-100x^2 + 15,750x + 212,500 ≥ 243,600
This inequality can be used to find the minimum ticket price Amy should charge to meet her minimum revenue goal.
Write the inequality representing Amy’s revenue in factored form. Replace the values of a, b, and c to write the inequality.
By solving the inequality we get that the cheapest ticket is $29.
What is the inequality?Inequality is defined as a relationship between two expressions or values that are not equal to each other.When two or more algebraic expressions are compared using the symbols, <, > ≤, or ≥, an inequality is formed. They are mathematical expressions in which neither side is equal.Here given,
If x is the number of $2 dollar increases required to meet her goal, then the minimum number of increases required is:
-100x² + 15,750x + 212,500 ≥ 243,600
- 100x² + 15,750x - 31,100 ≥ 0
x² - 157.5x + 311 ≥ 0
x = (157.5 ± [tex]\sqrt{157.5^{2} - (4*1*311 }[/tex] ) / 2
x1 = 2
x2 = 155.5
The only conceivable value is x = 2 $2 increases
If the original cost was $25, the new rice needed to meet Amy's goal is:
P = 25 + 2 x 2
P = $29
The cheapest ticket is $29.
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For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution. {50, 46, 54, 51, 29, 52, 48, 54, 47, 48}.
According to the normal distribution, 68% of values should fall in one standard deviation from the mean.
Define the term standard deviation?The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the identical mean however a different range, it is helpful.The standard deviation and the mean of the provided data must first be determined.
Below are the standard deviation and mean
Mean = (50 + 46 + 54 + 51 + 29 + 52+ 48 + 54 + 47 + 48)/10
Mean x = 47.9
Standard deviation: √∑(x - x')²/(n - 1)
s = √(50 - 47.9)² + (46 - 47.9)² + (51 - 47.9)² + .....+ (48 - 47.9)²)/(9)
s = 7.20
We possess:
x' ± s = (47.9 ± 7.2)
x' ± s = (40.7, 55.1)
The proportion of values that are within 1 standard deviation of that mean is thus:
9/10 * 100 = 90%.
According to the normal distribution, 68% of values should fall in one standard deviation from the mean.
As a result, the percentage of values seen to be within 1 standard deviation of a mean is significantly larger than the percentage a normal distribution would predict.
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Write an equation of the line that passes through the points
(-1,7) (6,7)
Answer: y=7
Step-by-step explanation:
Slope intercept form
y=mx+b
m=slope
b= y-intercept
find the slope with the slope formula
y2-y1/x2-x1
7-7/6-(-1)
0/7
the slope is 0, meaning this is a horizontal line.
Find the y-intercept
7=0(-1)+b
b=7
y=7
Isabella is building a tree fort. The base of the fort is 78 inches wide by 92 inches long.
a What is the area of the base in square inches? Show your work
Answer: 7,176 inches
Step-by-step explanation:
Areas equation is Length times width so applying that we have 78 times 92 giving you the answer of 7,176
Two sides of a triangle measure 8 inches and 10 inches respectively which of these is NOTa possible length for the thirds side of a triangle . Please show ur work Bc I have too !!
A) 12 inches
B) 16 inches
C) 17 inches
D) 18 inches
18 inches is not a possible length for the thrid side of a triangle.
What is Triangle is?A triangle is a polygon with the 3edges and 3 vertices. It is 1 of the basic shaped on geometry. A triangle with vertices A, B, and C is denoted ∆ ABC. In Euclidean geometry, any 3 points, when non-colli early, determined a uniquely ∆ and simultaneously, to unique plane.
As we know in a ∆ if the measurement of two sides are given than the sum of these 2 sides.
Otherwise buliding of a triangle is never possible.
Here two side are 10 and 8 inches.
So, 3rd side of the triangle should be less than
10+8 = 18
Third sides=
2<x<18
Now we have to calculate the range of 3rd sides
2<x<18
Thus,3rd side of the measurement with 18 inches is not possible.
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Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). Find XU Y.
The number of elements of set (XUY) = 8
What is set?A set is simply an organized collection of distinct objects forming a group and can be expressed in set-builder form or roaster form.
Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). .
Means write all the elements in X and Y, then
X = {x|x is a whole number less than 10}
Means write the common elements in X and Y
Y= {-3, -2, 1, 3, 5, 7, 20).
Since there are no common elements in X and Y, then
(XUY) is null set.
The number of elements in (XUY) is 4 + 4 = 8 elements
Then (XUY) = 8
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Please respond to this two questions. Help me improve my grade :)
The percentile rank of a score of 71 on this test will be 33.33% and the score of the 60th percentile will be 84.
What is a percentile?Percentile is the amount to measure the rank of a student in respect to the other students.
For example, the 90 percentile score means that there is 10 percent of members higher than you.
As per the given test scores,
The score of 71 from left to is at the 5th number.
Percentile = 5/15 x 100 = 33.33%
If the percentile is 60%.
x/15 = 60/100
x = 9
The 9th from left to is 84
Hence "On this test, a score of 71 will yield a percentile rank of 33.33%, while an outcome of 84 will represent the 60th percentile.".
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Write a system of equations and then solve by the method of your choice:substitution or elimination
How to solve a system of equations by elimination.
Write both equations in standard form. If any coefficients are fractions, clear them.Make the coefficients of one variable opposites.Decide which variable you will eliminate.Multiply one or both equations so that the coefficients of that variable are opposites.Add the equations resulting from Step 2 to eliminate one variable.Solve for the remaining variable.Substitute the solution from Step 4 into one of the original equations. Then solve for the other variable.Write the solution as an ordered pair.Check that the ordered pair is a solution to both original equations.How to solve a system of equations by Substitution.
Let us take an example :
y = 3x - 4
2y = -x + 6
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionStep 1: Define Systems
y = 3x - 4
2y = -x + 6
Step 2: Solve for x
Substitution
Substitute in y: 2(3x - 4) = -x + 6[Distributive Property] Distribute 2: 6x - 8 = -x + 6[Addition Property of Equality] Add x on both sides: 7x - 8 = 6[Addition Property of Equality] Add 8 on both sides: 7x = 14[Division Property of Equality] Divide 7 on both sides: x = 2Step 3: Solve for y
Substitute in x [Original Equation]: y = 3(2) - 4Multiply: y = 6 - 4Subtract: y = 2Learn more about Substitution method at:
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The scale is 1ft:1.26cm and your school is 30 feet tall how tall will a model be with 6.3 cm tall toothpicks
Answer:
it will be 37.8 cm tall
wo cyclists leave towns kilometers apart at the same time and travel toward each other. one cyclist travels faster than the other. if they meet in hours, what is the rate of each cyclist?
one cyclist travels faster than the other. Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).
Let x = the rate of the faster cyclist, and y = the rate of the slower cyclist.
We can set up the equation:
x + y = (distance between towns) / (time they met)
x + y = (distance between towns) / (hours)
We can solve for x and y:
x = (distance between towns) / (2 * hours)
y = (distance between towns) / (2 * hours)
Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).
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