Answers
Answer: D (t−3)(t−5)(t+4)
Step-by-step explanation:
Hope this helps! :)
Related Questions
London practices the piano 525 minutes in 3 weeks. Assuming she practices the same amount every week, how many minutes would she practice in 4 weeks?
Answers
Answer:
700 minutes
Step-by-step explanation:
First you need to see how much London even practices in one week. So we will divide the total minutes (t) 525 from the total weeks (w) 3:
t / 3 = m
where m equals the amount of minutes London practices in 1 week.
1) rewrite:
t / 3 = m
2) plug in variables:
525 / 3 = m
3) divide:
525 / 3 = 175
Therefore every week, London practices for 175 minutes.
Secondly, we are going to add 1 more week (175) to the total minutes London spent practicing for the 3 weeks (525).
t = m + m
Where t = total minutes altogether (4 weeks) and m equals the minutes of the 3 weeks and the minutes of 1 week.
1) rewrite:
t = m + m
2) plug in:
t = 525 + 175
2) add:
t = 700
Therefore, London would practice 700 minutes in 4 weeks if she practices the same amount every week.
e) Write a proof to show AABC~ ACFD.
f) What is the longest cart that can pass through the second doorway?
Explain.
Some of the factory's products are long fragile rods that are carried through
the door by hand. The first door is 72 inches west of the start of the second
door. Assume the rod has zero width and BA = 13 in.
Answers
The longest cart that can pass through the second doorway is 85 inches or less in length.
e) To demonstrate that AABC~ACFD, we want to show that they have the very shape and that their comparing sides are corresponding.
To start with, we can see that point An is normal to the two triangles. Moreover, point BAC is harmonious to point FDC in light of the fact that they are both right points.
Additionally, point ABC is consistent to point ACF on the grounds that they are substitute inside points framed by the cross-over AC converging equal lines Stomach muscle and FD.
Then, we want to show that the relating sides are corresponding. We can begin by contrasting Stomach muscle and FD. We are given that Stomach muscle = 13 inches, and we can see that FD is the flat distance between the two entryways.
How about we call this distance x. Then, at that point, we can set up an extent:
Stomach muscle/FD = 13/x
To find the length of AC, we can utilize the Pythagorean Hypothesis. We know that BC = Cd = 60 inches, so:
[tex]AC^2 = AB^2 + BC^2[/tex]
[tex]AC^2 = 169 + 3600[/tex]
[tex]AC^2 = 3779[/tex]
[tex]AC = \sqrt{(3779)[/tex]
Presently, we can set up another extent:
AC/CF = Stomach muscle/FD
Subbing the qualities we viewed as before, we get:
[tex]\sqrt{(3779)}/CF = 13/x[/tex]
Increasing the two sides by x, we get:
[tex]x * \sqrt{(3779)}/CF = 13[/tex]
Addressing for CF, we get:
[tex]CF = x * \sqrt{(3779)}/13[/tex]
Thus, we have shown that AABC~ACFD on the grounds that they have similar shape and their comparing sides are relative.
f) The longest truck that can go through the subsequent entryway is a truck whose length is equivalent to or not exactly the level distance between the two entryways. This is on the grounds that the entryways are lined up with one another, so the main limitation on the length of the truck is the level distance between the two entryways.
We are given that the main entryway is 72 inches west of the beginning of the subsequent entryway, and we know that BA = 13 inches. In this way, the flat distance between the two entryways is:
FD = 72 + BA = 85 inches
Subsequently, the longest truck that can go through the subsequent entryway is a truck that is 85 inches or less long.
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the sum of two consecutive odd numbers is 124 what equation would you use to solve this problem
Answers
Answer:
x + (x+2) = 124
Step-by-step explanation:
Let x be the first odd number, then the next consecutive odd number would be x+2.
According to the problem, the sum of these two numbers is 124.
So, we can set up the following equation:
x + (x+2) = 124
Simplifying this equation:
2x + 2 = 124
Subtracting 2 from both sides:
2x = 122
Dividing both sides by 2:
x = 61
Therefore, the first odd number is 61, and the next consecutive odd number is 63.
To check, we can add them together:
61 + 63 = 124
So the solution is x = 61.
Answer:
x + x + 2 = 124
(and then you could solve that x=61 and the two numbers are 61 and 63)
Step-by-step explanation:
"sum" means adding. "consecutive" means the two numbers are in a row, or one right after the other. Like 3 and 4 are consecutive numbers and 3 and 5 are consecutive odd numbers. 3 and 11 are not consecutive.
So let one number be x.
Then next odd number after that is +2...so the 2nd number is x+2.
And they add up to 124. Write the equation like this:
x + x + 2 = 124
If you want or need to solve then:
combine like terms.
2x +2 = 124
subtract 2.
2x = 122
divide by 2.
x = 61
then x+2 is 63.
A company's monthly profit, P, from a product is given by P = -x^2+105x-1050, where x is the price of
product in dollars. What is the lowest price of the product, in dollars, that gives a monthly profit of $1550?
Answers
Answer:
We are given that the monthly profit, P, from a product is given by the quadratic function:
P = -x^2 + 105x - 1050
To find the lowest price of the product that gives a monthly profit of $1550, we need to solve the equation:
x^2 + 105x - 1050 = 1550Rearranging this equation, we get:
x^2 + 105x - 2600 = 0To solve for x, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -1, b = 105, and c = -2600.
Substituting these values, we get:
x = (-105 ± sqrt(105^2 - 4(-1)(-2600))) / 2(-1)
x = (-105 ± sqrt(11025 - 10400)) / (-2)
x = (-105 ± sqrt(625)) / (-2)
We can simplify this expression to:
x = (-105 ± 25) / (-2)
Therefore, the two possible values of x are:
x = (-105 + 25) / (-2) = 40
x = (-105 - 25) / (-2) = 50
Since we are looking for the lowest price that gives a monthly profit of $1550, the answer is $40. Therefore, the lowest price of the product that gives a monthly profit of $1550 is $40.
Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5.
Answers
Answer:
The given line has a slope of 1/4. The slope of any line perpendicular to this line will have a slope equal to the negative reciprocal of 1/4, which is -4.
We are also given that the line passes through the point (0, 2). Using point-slope form, we can write the equation of the line as:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point (0, 2). Substituting the values, we get:
y - 2 = -4(x - 0)
Simplifying, we get:
y - 2 = -4x
Adding 2 to both sides, we get the final equation of the line:
y = -4x + 2
Therefore, the equation of the straight line passing through the point (0, 2) which is perpendicular to the line y = 1/4x + 5 is y = -4x + 2.
4-1
Find the critical value(s) and rejection region(s) for the type of z-test with level of
significance x. Include a graph with your answer.
Right-tailed test, a = 0.01
Answers
The critical value is Z = 2.331. The rejection region is Z > 2.33
What is meant by critical value?
A critical value is a value used in hypothesis testing to determine whether to reject or fail to reject the null hypothesis.
What is meant by rejection region?
The rejection region is the set of values that lead to the rejection of the null hypothesis in favor of the alternative hypothesis.
According to the given information
To find the critical value(s) and rejection region(s) for a right-tailed z-test with level of significance x = 0.01, we can use the following formula1:
Critical value: Z = Zα where α = x and Zα is the Z-score that corresponds to an area of α in the standard normal distribution table
Rejection region: Z > Zα
For a right-tailed test with α = 0.01, we can find the critical value using a standard normal distribution table1. The critical value is Z = 2.331. The rejection region is Z > 2.33
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5(98) =___(100-2)
USE THE DISTRIBUTIVE PROPERTY TO FIND EAch product
Answers
Answer:
To solve 5(98) =___(100-2) using the distributive property, we can distribute the 5 to both the 100 and the -2:
5(98) = 5(100 - 2)
Now, we can use the distributive property to simplify the right side:
5(98) = 5(100) - 5(2)
Multiplying, we get:
490 = 500 - 10
Simplifying further, we get:
490 = 490
Therefore, the equation is true, and we have verified the distributive property.
PLEASE HELP!! ASAP PLEASW
Answers
Total recycling = 237 pounds + 192 pounds + 179 pounds = 608 pounds
Next, we need to calculate the fraction of recycling each class collected:
Mr. Brogle's class: 237 pounds / 608 pounds = 0.389
Mrs. Abiola's class: 192 pounds / 608 pounds = 0.316
Mr. Wheeler's class: 179 pounds / 608 pounds = 0.295
These fractions represent the proportion of the prize money each class should receive. To determine how much money each class should get, we can multiply each fraction by the total prize money of $800:
Mr. Brogle's class: 0.389 x $800 = $311.20
Mrs. Abiola's class: 0.316 x $800 = $252.80
Mr. Wheeler's class: 0.295 x $800 = $236.00
Therefore, Mr. Brogle's class should receive $311.20, Mrs. Abiola's class should receive $252.80, and Mr. Wheeler's class should receive $236.00.
GASES The volume V of a gas varies inversely as its pressure P. If V=80 cubic centimeters when P = 2000 millimeters of mercury, find V when P=320 millimeters of mercury.
A. 500cm3
B. 12.8cm3
C. 8000cm3
D. 80cm3
Answers
Answer:
A. 500 cm3
Step-by-step explanation:
The general inverse variation equation is
y = k/x, where y varies inverse as x and k is the constant of proportionality.
Thus, if we substitute V for y and P for x in the equation, we have
V = k / x
To find k, we can plug in 80 for V and 2000 for P and solve for k:
80 = k / 2000
160000 = k
Finally, to find V when P = 320 millimeters, we can plug in 160000 for k and 320 for P and solve for V:
V = 160000 / 320
V = 500 cm3
How many ways can 5 students line up for a picture?
Answers
Let’s say the students are numbered 1-5
you would do 1x2x3x4x5, which would give you a total of 120.
if you don’t understand: Think of it this way. How many different people can be first in line? 5. 4 now remain. Next position 4 possibilities, 3 remain. 3 possibilities for next position. 2 remain. 2 possibilities for next position. 1 left for the last position. This gives us 5 X 4 X 3 X 2 X 1 which can be written as 5! (5 factorial). This is equal to 120. This is normally known as a permutation.
I’m so sorry if this doesn’t help!
Write the following as an algebraic expression. Simplify if possible.
Subtract 5y−6 from y−3.
Answers
Answer:
Algebraic expression:
y - 3 - (5y - 6)
Simplified: -4y + 3
Step-by-step explanation:
"Subtract 5y−6 from y−3" means the 5y-6 is being taken away from the y-3.
y-3 up front and then minus 5y-6. Use parenthesis to keep things organized.
(y-3) - (5y-6)
This is the algebraic expression.
well, tbh, we don't really need the first set of parenthesis.
y-3 - (5y-6)
This is good enough.
Then, to simplify use distributive property. That minus that we wrote in the middle, it has to go to both the 5y and also to the -6.
y-3 - 5y - -6
= y - 3 - 5y + 6
combine like terms
= -4y + 3
Solve for x round to the nearest tense, if necessary
Answers
Using a trigonometric relation we can see that x = 83.7
How to find the value of x?We can see that x is the hypotenuse of the given angle, and we know the measure of the adjacent catehtus to the given angle, then we can use the trigonometric relation:
cos(48°) = 56/hypotenuse
cos(48°) = 56/x
Solving that for x, we will get:
x = 56/cos(48°) = 83.7
That is the value.
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What would the answer be?
Answers
The length of the arc CD is 14.13 centimeters.
How to find the length of CD?Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:
L = (a/360°)*2*pi*R
Where pi = 3.14
Here the angle is a = 45°
And R = 18cm, so we can replace that in the formula above to find the length.
L = (45°/360°)*2*3.14*18cm = 14.13cm
That is the length of the arc CD.
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Helppppppopppopppoo please
Answers
This tetrahedron is known as a triangular pyramid and it has four triangular faces, four vertices, and six edges.
How are the sides of the triangular pyramid classified ?We can name the faces of the triangular prism as:
V1 for vertex A.V2 for vertex B.V3 for vertex C.V4 for vertex DThe edges would be:
E1 for connecting V1 and V2.E2 for V1 and V3.E3 for V1 and V4.E4 for V2 and V3.E5 for V2 and V4.E6 for V3 and V4.The faces would be:
F1 triangle formed by vertices V1, V2, and V3F2 triangle by V1, V2, and V4F3 triangle by V1, V3, and V4F4 triangle by V2, V3, and V4Find out more on triangular pyramids at https://brainly.com/question/30615121
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HOCKEY Andrew went to the hockey game. He paid $13.50 for admission. He bought a program for $4.75, a bag of a popcorn for $3.50, and a large drink for $3.35. How much did he spend in all ?
Answers
Answer:
$25.10
Step-by-step explanation:
We can find the total amount Andrew spent at the hockey game by finding the sum of each individual cost, including the costs for admission, the program, the popcorn, and the large drink
Total amount spent = 13.50 + 4.75 + 3.50 + 3.35
Total amount spend = $25.10
A cylinder with a radius of 4 cm and a height of 6-cm is inside of a
sphere with a radius of 10 cm. How much space is inside the sphere,
but outside the cylinder? Round to the nearest tenth if necessary. Use 3.14 for π.
Answers
The volume of the cylinder is given by:
V_cylinder = πr^2h
Substituting the given values, we get:
V_cylinder = π(4^2)(6) = 96π cubic cm
The volume of the sphere is given by:
V_sphere = (4/3)πr^3
Substituting the given value, we get:
V_sphere = (4/3)π(10^3) = (4000/3)π cubic cm
The space inside the sphere but outside the cylinder is therefore:
V_space = V_sphere - V_cylinder
V_space = (4000/3)π - 96π
V_space = (4000/3 - 288)π
V_space ≈ 869.6 cubic cm (rounded to the nearest tenth)
Therefore, the space inside the sphere but outside the cylinder is approximately 869.6 cubic cm.
+
P
8
2. Find the interest earned on a $25,000 deposit for 2 years at 4.7%
2
interest, compounded continuously?
(25000) (4.7
25,000
P
P(25,000) (47)
+-117500
= 117
com
or
Answers
Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.
What is compounding interest?Compound interest is the term for interest that is earned on interest.
This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.
At the end of the second year, you will have $110.25.
So, we know that:
Principal amount = $25000
Interest rate = 4.7%
Time = 2 years
Compounded annually
Then, using the compounding calculator:
(Refer to the graph attached below)
The amount after 2 years will be $27,405.23.
Interest in this is:
$27,405.23 - $25,000
$2,405.23
Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.
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Correct question:
Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.
The radius of a circle is 19 m. Find its area to the nearest whole number
Answers
Answer:
7.07cm
Step-by-step explanation:
What is the solution to -2(8x - 4) < 2x + 5?
O x
7/10 7/10
6
O
0 x < 1/1/201
O x > 6
O x < 6
Answers
The solution for the inequality -2(8x - 4) < 2x + 5 is x > 1/6.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Let's simplify the inequality -
-2(8x - 4) < 2x + 5
Distribute the -2 -
-16x + 8 < 2x + 5
Subtract 2x from both sides -
-18x + 8 < 5
Subtract 8 from both sides -
-18x < -3
Divide both sides by -18, remembering to reverse the inequality because we're dividing by a negative number -
x > 3/18
Simplifying, we get -
x > 1/6
Therefore, the solution to the inequality is -
x > 1/6
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In a classroom survey of twelve students, it was determined that one-half of the students belong to the Chess Club, one-third belong to the Drama Club,
and one-fourth belong to both clubs. How many students are not in either club?
4). 5). 6). 7). 13).
Answers
The number of students who belong to neither club is 6 students.
The number of students who are not in either club is 6.
Let's say that there are x students in the classroom.
We know that 1/2 of the students belong to the Chess Club, so 1/2 * x = 6 students belong to the Chess Club.
We also know that 1/3 of the students belong to the Drama Club, so 1/3 * x = 4 students belong to the Drama Club.
Since 1/4 of the students belong to both clubs, then 1/4 * x = 3 students belong to both clubs.
Therefore, the number of students who belong to only one club is 6 - 3 = 3 students.
The number of students who belong to neither club is 6 + 3 - 3 = 6 students.
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Q22: In a company, the ratio of the number of men to the number of women is 1:3
20% of the men are under the age of 25
80% of the women are under the age of 25
What percentage of all the people in the company are under the age of 25?
Answers
From the given information, we know that the ratio of men to women is 1:3, so we can set up the equation:
x/4x = 1/3
Solving for x, we get:
x = 1/3 * 4x
x = 4/3x
Multiplying both sides by 3/4, we get:
x = 3/4x
So, x represents 4/7 of the total employees in the company, and 3/7 are women.
Now we can calculate the percentage of people under the age of 25:
Number of men under 25 = 0.2x
Number of women under 25 = 0.8(4x/3) = 1.067x
Total number of people under 25 = 0.2x + 1.067x = 1.267x
Therefore, the percentage of people under 25 is:
(1.267x / 5x) * 100% = 25.34%
So, approximately 25.34% of all the people in the company are under the age of 25.
Dwane uses 2/6 of a jar of tomato sauce for his pasta. He uses the rest to make pizza. On paper, complete the number bond to show the fraction of a jar of tomato sauce used for pasta and for pizza.
Answers
Answer:
Step-by-step explanation:
if he uses 2/6 for his pasta, he should use 2/6 on his pizza (assumption) therefore, he should have used 4/6 of his tomato sauce jar
Real-life Problems Question 6
Answers
The amount of money that Theresa has left is equal to £2,740.
How to write a linear equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:
Let the variable a represent cost of flights for each of them.
Let the variable f represent cost of accommodation for each of them.
Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;
y = 12(a + b)
y = 12(266 + 339)
y = £7,260
For the amount of money left, we have:
Amount of money left = £10,000 - £7,260
Amount of money left = £2,740.
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Students are given an IQ test. The data are normally distributed with a mean of 100 and a standard deviation of 12. Sally scores 114 on the test. The test is given to 300 students.
How many students would you expect to score between Sally’s score and the mean?(100-114)
Answers
we would expect about 36 students to score between Sally's score and the mean on the IQ test.
What is frequency distribution?
The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.
We can use the normal distribution formula to calculate the number of students who would be expected to score between Sally's score and the mean:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
First, we need to calculate the z-score for Sally's score:
z = (114 - 100) / 12 = 1.17
To find the number of students who would be expected to score in this range, we multiply this proportion by the total number of students:
0.1210 x 300 ≈ 36.3
So, we would expect about 36 students to score between Sally's score and the mean on the IQ test.
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Solve for x to the nearest 10th.
57 = 2070(0.93)^x - 11
Answers
The solution to the equation 57 = 2070(0.93)^x - 11 to the nearest tenth is x ≈ 86.5.
What is an equation?A mathematical assertion that two expressions are equal is known as an equation.
A typical equation contains one or more variables, which are elements with several possible values.
Finding the values of the variables that make an equation true is the aim of equation solving.
A linear equation, which has the form:, is the most widespread sort of equation.
ax + b = 0
where the objective is to find the value of the variable x and a and b are constants.
What are variables ?A variable in mathematics is a symbol or letter that designates a value that is subject to variation or change. In algebraic expressions and equations, variables are used to denote unknown or fluctuating quantities, such as a building's height or the number of apples in a basket.
Typically, letters from the alphabet, such as x, y, and z, are used to represent variables. Mathematical expressions can be created using variables, constants (numbers), and operators (+, -, x, /, etc.) in an algebraic expression. As an illustration, the phrase 2x + 3y - 5z combines the three variables x, y, and z in a linear fashion.
According to the question ,
By adding 11 to both sides, we may isolate the exponential term first:
57 + 11 = 2070(0.93)^x
Streamlining the left side: 68 = 2070(0.93)^x
By 2070, divide both sides: 0.03285024 = (0.93)^x
Using both sides' natural logarithms: ln(0.03285024) = ln[(0.93)^x]
By applying the logarithm property, which states that ln(ab) = b ln(a):
ln(0.03285024) = x ln(0.93)
By dividing both sides by ln(0.93), one can find x:
x = ln(0.03285024) / ln(0.93)
When we evaluate this expression with a calculator, we obtain:
x ≈ 86.5
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A hyperbola centered at the origin has vertices at (+/- [tex]\sqrt{7}[/tex] , 0) and foci at (+/- [tex]\sqrt{27}[/tex] , 0). Write the equation of this hyperbola.
Answers
The hyperbola equation centered at the origin with the vertices is x²/(t² + 22) - y²/(t² - 27) = 1
How to Solve the Problem?Because the hyperbola is centered at the origin, its standard form equation is:
(x²/a²) - (y²/b²) = 1
Where a denotes the distance between the center and the vertices and b denotes the distance between the center and the co-vertices.
Because the distance between the center and each vertex is √(t² + 72),
We get:
√(t² + 72) = a√(c² - a²) is the distance between the center and each focus, where c is the distance between the center and each focus.
We know that the distance between the center and each focus is √(27),
Thus we can calculate:
√(27 - a²) = √(27 - (t² + 72))
When we simplify, we get:
27 - a² = 27 - t² - 49
a² = t² + 22
When a² is substituted, we get:
(x²/(t² + 22)) - (y²/b²) = 1
Now we must locate b.
Because the distance between the center and each co-vertex is b, we get:
√(a² - 72) = b
√(t² + 22 - 49) = b
√(t² - 27) = b
When b² is substituted, we get:
(x²/(t² + 22)) - (y²/(t² - 27)) = 1
As a result, the hyperbola equation is: x²/(t² + 22) - y²/(t² - 27) = 1
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I need help with the first question of this problem.
Answers
Answer:
Step-by-step explanation:
hello, it seems this is problematic im sorry but I'm not sure if you could put a better picture.
Make up two data sets. List all the values in each dat set and write a story to describe where they may have come from. The data sets should meet the following conditions:
- The data should come from random samples taken from a population
- The centers of the distributions should be similar
- The variables of the distributions should be different
Pls show work
Answers
Answer:
- The centers of the distributions should be similar
Step-by-step explanation: - The centers of the distributions should be similar
PLEASE HELP ME WITH THIS DISCUSSION ASAP!!! 40 POINTS!!
Answers
The median is the middle value in a data set when the values are arranged in order, so it would help the real estate agent to set a price that is not too high or too low compared to other similar houses. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is often used to summarize a set of data with a single value that represents the "center" of the data.
Here,
1. For the first situation, the mode would be the most appropriate measure of central tendency because it would tell the supermarket manager which type of lettuce is purchased most often. The mode is the value that appears most frequently in a data set, so it would indicate which type of lettuce is the most popular among customers.
For the second situation, the mean would be the most appropriate measure of central tendency because it would give the average score of all the tests taken during the grading period. The mean is calculated by adding up all the scores and dividing by the number of scores, so it would give a good representation of the student's overall performance.
For the third situation, the median would be the most appropriate measure of central tendency because it would provide a value that is in the middle of the data set, with half of the comparable houses above and half below the selling price.
2. The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades, so in this case, the mean would be (97 + 97 + 75 + 70 + 55)/5 = 78.8%. However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%.
If we calculate the median instead, which is the middle value when the grades are arranged in order, we get 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set. The student is misrepresenting their performance by reporting the mean as the average, which does not accurately reflect their performance due to the outlier.
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The median is 77%, which is closer to the actual performance of the student.
what is mean?
In statistics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is calculated by adding up all the values in a data set and dividing by the total number of values. The mean is also known as the arithmetic mean or the average. It is commonly used to summarize data and is one of the most widely used measures of central tendency. However, the mean can be sensitive to outliers, which are extreme values that can skew the average and make it less representative of the data set.
The student is reporting the mean as the average. The mean is calculated by adding up all the grades and dividing by the number of grades. In this case, the mean would be:
(97 + 97 + 75 + 70 + 55) / 5 = 78.8%
However, this is not an accurate representation of the student's course performance because the mean is sensitive to outliers, which in this case is the low grade of 55%. If we calculate the median instead, which is the middle value when the grades are arranged in order, we get:
75%, 70%, 55%, 97%, 97%
The median is 77%, which is closer to the actual performance of the student. The median is not affected by outliers, so it provides a better representation of the center of the data set.
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Larry put $1,287 into a savings account 8 years ago. The account earned 4% simple annual interest. He made no additional deposits or withdrawals. Based on this information, what is the balance in dollars and cents in Larry's savings account at the end of these 8 years? Record your answer and fill in the box on your answer document. Be sure to use the correct place value. Answer:
Answers
Therefore, the balance in Larry's savings account at the end of 8 years is $1,699.84.
What kind of mathematics is employed in finance?
Algebra. A financial management expert is often required to solve for variables in banking and investing financial models. Even if most of the work is now done for us by programmes like Excel, having a solid grasp of the fundamentals of algebra is still commonly seen as being very beneficial.
After eight years, the balance in Larry's savings account can be determined using the straightforward interest formula:
A = P(1 + rt)
where A represents the final balance, P the initial principal, r the yearly interest rate expressed as a decimal, and t the period of time in years.
In this case, we have P = $1,287, r = 0.04, and t = 8.
A = $1,287(1 + 0.04*8)
= $1,287(1.32)
= $1,699.84
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