We should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.
Describe Confidence Interval?In statistics, a confidence interval is a range of values that is used to estimate an unknown population parameter with a certain degree of confidence or probability. It is a statistical measure that indicates the level of uncertainty or variation associated with a particular estimate or sample.
A confidence interval is typically expressed as a range of values, along with a level of confidence, such as 95% or 99%. This means that if the same study were to be repeated many times, the calculated confidence interval would contain the true population parameter for the given confidence level in a specified proportion of the repetitions. For example, a 95% confidence interval means that if the same study were repeated many times, the interval would contain the true population parameter 95% of the time.
We can use the formula for the margin of error of a confidence interval to solve this problem:
Margin of error = z*(sigma/√(n))
where:
z = the z-score associated with the desired level of confidence (in this case, 1.96 for 95% confidence)
sigma = the population standard deviation (15 days)
n = the sample size we want to find
We want the margin of error to be no more than 7 days, so we can set up the following inequality:
7 <= 1.96*(15/√(n))
Solving for n, we get:
n >= (1.96*15/7)²
n >= 12.36²
n >= 152.7
Therefore, we should choose a sample size of at least 153 to be 95% confident that the true average waiting time is within 7 days of the sample mean.
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which of the following statements accurately describes the difference between interval measurement and ratio measurement? group of answer choices ratio measurement is used for continuous data, whereas interval measurement is used for noncontinuous data ratio measurement uses numeric values without fixed meaning, whereas interval measurement uses numeric values with fixed meaning interval measurement uses numeric values with equal intervals, whereas ratio measurement uses numeric values with unequal intervals interval measurement scales have an arbitrary zero point, whereas ratio measurement scales have an absolute zero point
Difference between interval measurement and ratio measurement is Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point. So, option C is correct.
Interval measurement uses numeric values with equal intervals.
This means that the difference between any two adjacent values on the scale is always constant.
However, the zero point on this scale is arbitrary, meaning it does not represent the absence of the characteristic being measured.
Ratio measurement, on the other hand, also uses numeric values with equal intervals, but it has an absolute zero point.
This means that the zero point on a ratio scale represents the complete absence of the characteristic being measured.
As a result, ratio scales can be used to perform more advanced mathematical operations, such as multiplication and division.
To summarize, the main difference between interval and ratio measurement lies in the zero point of their scales. Interval measurement scales have an arbitrary zero point, whereas ratio measurement scales have an absolute zero point.
The correct choice is option C . Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.
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Question:-
Which of the following statements describes the difference between interval measurement and ratio measurement?
A) Ratio measurement is used for continuous data, whereas interval measurement is used for noncontinuous data.
B) Interval measurement uses numeric values with equal intervals, whereas ratio measurement uses numeric values with unequal intervals.
C) Interval measurement scales have a zero point that is not absolute, whereas ratio measurement scales have an absolute zero point.
D) Ratio measurement uses numeric values without fixed meaning, whereas interval measurement uses numeric values with fixed meaning.
Which expression is equivalent to x-4?.
Answer:
x⁻²· x⁻²
Step-by-step explanation:
x⁻⁴ = x⁻²· x⁻² = x⁽⁻² ⁺ ⁻²⁾ = x⁻⁴
1 /4 of the schoolyard is used by the fifth graders for recess, as shown by the shaded part of the diagram. Teachers have 3 different activities planned for recess that will take up the same amount of space.
The shaded part of the figure in choice B is divided into three equal parts
There are 12 equal parts in total so each activity takes up 1/12.
What is the fraction?
A fraction is a part of a whole or a ratio of two numbers expressed with a horizontal line between them.
Part A: The shaded part of the figure in choice B
is divided into three equal parts
there are three kinds of activities
Part B: According to the choice B of part A. there are 12 equal parts in total so each activity takes up 1/12.
figure in all the parts of the choice up to B of part A, get 12 equal parts
Hence, The shaded part of the figure in choice B is divided into three equal parts
There are 12 equal parts in total so each activity takes up 1/12.
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If a function is increasing throughout its domain the y-value are greater and greater as x approaches infinity. Libby claims that any function that has all real number as a domain and is increasing everywhere must have all real numbers as it's range as well. Is Libby correct? Explain why or why
Not
Libby is correct in claiming that a function with a domain of all real numbers and is increasing everywhere must have all real numbers as its range.
Libby is correct. If a function is increasing throughout its domain, the y-values become greater as x approaches infinity.
This is because the function can take any y-value without restriction as x approaches positive or negative infinity.
The domain of the function is all real numbers, it means that the function is increasing for every x-value, and there are no limits to how large or small x can be.
The given function has a domain of all real numbers, which means it is defined for any value of x.
The function is increasing throughout its domain, which means that as x increases, the y-value of the function also increases.
Conversely, as x decreases, the y-value of the function decreases.
Since there is no restriction on the x-values in the domain, we can let x approach positive infinity to find the largest possible y-value, and negative infinity to find the smallest possible y-value.
As x approaches positive infinity, the y-value of the function keeps increasing without any upper limit, meaning that the function can take any arbitrarily large positive y-value.
Similarly, as x approaches negative infinity, the y-value of the function keeps decreasing without any lower limit, meaning that the function can take any arbitrarily large negative y-value.
Therefore, the range of the function must include all real numbers since the function is able to take any positive or negative y-value without restriction.
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Find the 27th term. -21, -14, −7, 0, 7, ... 27th term = [ ? ]
Answer: the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7)
Step-by-step explanation:
Given a1=38,a17=-74. a17=a1+(n-1)d. =38+(17-1)d. -74=38+16d. -74-38=16d. -112=16d. d= -7. the term 27 ; a27=a1+(n-1)d. a27=38+(27-1)(-7).
Answer: 7
Step-by-step explanation: number adds up by 7
helpp asapp will give brainliest!!!
Answer:
10.14 inches square
A garter snake is 22 inches long.if a python is 9 times as long as the garter snake,how much longer is the python?write and solve equaions
By answering the presented question, we may conclude that So, the equation python is 176 inches longer than the garter snake.
What is equation?In mathematics, an equation is a claim that two expressions are equivalent. Two sides that are separated by the algebraic symbol (=) make form an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is the goal of equation solving. Equations can include one or more parts and be straightforward or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. In many different branches of mathematics, including algebra, calculus, and geometry, lines are used.
Let's use "P" to represent the length of the python in inches.
P = 9(22):
P = 198
Therefore, the python is 198 inches long.
198 - 22 = 176
So, the python is 176 inches longer than the garter snake.
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PLS HELP WILl MARK BRAiNLIEST
Step-by-step explanation:
draw a triangle then label corners a and b. spread them 120 degrees apart and there you have it.
WXYZ is a trapezium . If WY//XY and M is the mid point of YZ then prove that:
Area of triangle WXM = 1/2 AREA OF TRAPEZIUM WXYZ
Therefore , the solution of the given problem of triangle comes out to be the desired outcome is demonstrated.
What precisely is a triangle?If a polygon has at least one additional segment, it is a hexagon. Its structure is a simple rectangle. Something like this can only be distinguished from a regular triangular form by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Area is equal to (sum of parallel edges) / 2 * (distance between them)
=> WXYZ area equals (WZ plus XY) / 2 * hS
=> (XM / XY)2 equals Area of WXM / Area of WXY
=> XM / XY = 1/2
=> WXM area divided by WXY area equals (1/2)2 = 1/4.
=> WXY plus WXM together make up the area of WXYZ.
=> WXY / 2 + WXM / 4 equals (WZ + XY) / 2 * h
=> WZ * h equals WXY * h plus 2 * WXM:
=> (WZ - WXY) / 2 * h equals WXM
=> WXYZ area equals (WZ plus XY) / 2 * h
=> (WZ+WXY+(WZ-WXY)) / 2 * h
=> (2WZ) / 2 * h
=> WZ * h
=> WXYZ Area equals 2 * WXM Area
Thus, the desired outcome is demonstrated.
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insert a monomial in the place of * so that the result is an identity:
(*-b^4)(b^4+*)=121a^10-b^8
100m^4-4n^6=(10m^2-*)(10m^2+*)
m^4-225c^10=(m^2-*)(*+m^2)
PLS PLS HURRY THANK YOU
a. There is no value of the missing monomial that will satisfy the equation.
b. The missing monomial is ±2
c. The missing monomial is ±15
What is monomial?
A polynomial with only one word is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have numerous variables and a greater degree.
The given equations can be solved by using the algebraic identity:
(a+b)(a-b) = a² - b²
Using this identity, we can determine the missing monomials in each equation:
1. (-b⁴)(b⁴+)=121a¹⁰-b⁸
Expanding the left-hand side of the equation, we get:
()b⁴ - b⁸ + b⁴() - b⁸() = b⁴() - b⁸(*)
Since the right-hand side of the equation is 121a¹⁰ - b⁸, we can equate the coefficients of b⁸ and a¹⁰ on both sides of the equation:
Coefficient of b⁸:
-1 = -1
Coefficient of a¹⁰:
0 = 121
The coefficient of a¹⁰ is not equal, which means that there is no value of the missing monomial that will satisfy the equation.
2. 100m⁴ - 4n⁶=(10m²-)(10m²+)
Using the algebraic identity, we can write:
(10m² - *)(10m² + ) = (10m²)² - ()²
= 100m⁴ - (*)²
Since the left-hand side of the equation is 100m⁴ - 4n⁶, we can equate the coefficients of m⁴ and n⁶ on both sides of the equation:
Coefficient of m⁴:
100 = 100
Coefficient of n⁶:
-4 = - (*)²
Solving for the missing monomial:
(*)² = 4
(*) = ±2
Therefore, the missing monomial is ±2, and the equation can be written as:
100m⁴ - 4n⁶ = (10m² - 2)(10m² + 2)
3. m⁴ - 225c¹⁰ = (m² - )( + m²)
Using the algebraic identity, we can write:
(m² - )( + m²) = (m²)² - (*)²
= m⁴ - (*)²
Since the left-hand side of the equation is m⁴ - 225c¹⁰, we can equate the coefficients of m⁴ and c¹⁰ on both sides of the equation:
Coefficient of m⁴:
1 = 1
Coefficient of c¹⁰:
-225 = - (*)²
Solving for the missing monomial:
(*)² = 225
(*) = ±15
Therefore, the missing monomial is ±15, and the equation can be written as:
m⁴ - 225c¹⁰ = (m² - 15)(15 + m²)
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Look at the picture and help me pass math it would be very nice
Answer:
[tex] \frac{1}{3} [/tex]
The answer is B
Step-by-step explanation:
There are six outcomes in total (numbers: 1; 2; 3; 4; 5 and 6)
The number she had spinned must be greater than 4 (that means there are two favorable outcomes: 5 and 6)
n = 6
m = 2
[tex]p = \frac{m}{n} = \frac{2}{6} = \frac{1}{3} [/tex]
The measure of an angle is 121.9°. What is the measure of its supplementary angle?
What would a monthly payment be on a purchase of a $10,000 car at 5.9% for
4 years?
A. $212.50
OB. $250.00
OC. $234.39
OD.
-$234.39
SUBMIT
The monthly payment on a purchase of a $10,000 car at 5.9% for 4 years is: C. $234.39.
How to find the monthly payment?To calculate the monthly payment for a car loan, we can use the formula:
M = P [ i(1 + i)^n / ((1 + i)^n – 1) ]
Where:
M = Monthly payment
P = Principal (he amount of the loan)
i = Monthly interest rate (annual interest rate divided by 12)
n = Number of months in the loan term
Using this formula with the given information, we get:
P = $10,000
i = 5.9% / 12 = 0.004917
n = 4 years x 12 months/year = 48 months
M = $10,000 [ 0.004917(1 + 0.004917)^48 / ((1 + 0.004917)^48 – 1) ]
M = $234.39 (rounded to the nearest cent)
Therefore, the answer is option C.
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Jordan compared 10 books at the school library. The following table shows the number of chapters and the total number of pages for each book.
Number of Chapters 3 4 5 8 10 12 13 14 16 20
Total Pages 18 38 45 85 76 145 138 160 180 220
Which of the following representations is most appropriate to show the relationship between the number of chapters and the total pages of a book?
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 20 and the y axis labeled total pages ranging from 0 to 275 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
scatter plot titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
line graph titled school library, with the x axis labeled number of chapters ranging from 0 to 38 and the y axis labeled total pages ranging from 0 to 450 with points at 3 comma 18, 4 comma 38, 5 comma 45, 8 comma 85, 10 comma 76, 12 comma 145, 13 comma 138, 14 comma 160, 16 comma 180, and 20 comma 220
The most appropriate representation to show the relationship between the number of chapters and the total pages of a book would be a scatter plot titled "School Library".
with the x-axis labeled "Number of Chapters" ranging from 0 to 20 and the y-axis labeled "Total Pages" ranging from 0 to 275 with points at (3, 18), (4, 38), (5, 45), (8, 85), (10, 76), (12, 145), (13, 138), (14, 160), (16, 180), and (20, 220).
A scatter plot is a graph used to display the relationship between two variables. In this case, the two variables are the number of chapters and the total number of pages in a book. The plot consists of dots, each representing a single data point. The x-axis represents the independent variable, which in this case is the number of chapters. The y-axis represents the dependent variable, which is the total number of pages. By plotting each data point on the graph, it is easier to visualize the relationship between the two variables.
A line graph is not appropriate for this situation because it suggests a continuous relationship between the two variables, which is not the case here. The number of chapters and total pages are discrete variables, and there is no natural order to the data points that would justify connecting them with a line.
The first scatter plot option is not appropriate because it shows the y-axis ranging up to 450, which is much higher than the maximum value of 275 for the total pages in this data set. This exaggerates the differences between the data points and can be misleading.
The chosen scatter plot is appropriate because it clearly shows the relationship between the number of chapters and the total pages of a book. It is easy to see that as the number of chapters increases, the total pages also tend to increase. The scatter plot also helps to identify any outliers or patterns in the data that may not be apparent from just looking at the numbers. It is a visual tool that helps to quickly understand the data and draw conclusions from it.
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16 A family of equations can be represented by other pronumerals (sometimes called parameters). For
4+ a
example, the solution to the family of equations 2x - a= 4 is x =
2
Find the solution for x in these equation families.
a x+a=5
Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.
how to solve an equation?A simple formula is a declaration that two forms are equal. It has two sides, the lower half (LHS) and the right-hand side (RHS), which are divided by the equal sign (=). In order to prove that an equation is correct, one or more uncertain variables may exist.
For instance, the solution 3x + 5 = 14 has a single unknowable variable, x. We must rearrange the equation to find the value of x by carrying out actions that preserve equality, such as deducting 5 from both sides of the equation:
given
We must isolate x on one side of the problem in order to solve the x + a = 5 equation family. By taking an away from both sides, we may accomplish this:
x + a - a = 5 - a
By condensing the left side, we obtain:
x = 5 - a
Hence, x = 5 - an is the answer to the equation x + a = 5 for any value of a as the problem in order to solve the x + a = 5 equation family.
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What is the percent of change from 8,000 to 6,000?
Answer:
here you go
Step-by-step explanation:
The percent of change from 8,000 to 6,000 can be calculated using the formula:
�������;�ℎ����=���;�����−���;��������;�����×100Percent;change=Old;ValueNew;Value−Old;Value×100
Substituting the given values, we get:
�������;�ℎ����=6,000−8,0008,000×100Percent;change=8,0006,000−8,000×100
Therefore, there is a decrease of 20% from 8,000 to 6,000.
Answer: decreases 6000 to 8000 = 33.33
x-
6000−50005000×100 = 20%
Step-by-step explanation:hope that helps have a great day and stay safe (;
Mr. Kelly Is a librarlan at Central Library. In examining a random sample of the library's book collection, he found the following.
936 books had no damage,
63 books had minor damage, and
41 books had major damage.
Based on this sample, how many of the 24,000 books in the collection should Mr. Kelly expect to have no damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches
Answer please mark as brainliest:
Allstars typically have the tallest players.
Step-by-step explanation:
To determine which team typically has the tallest players, we can compare the measures of center for each team. The measures of center we can use are the mean and median.
Using a calculator or a spreadsheet, we can calculate the mean and median for each team:
Allstars mean: (73+62+60+63+72+65+69+68+71+66+70+67+60+70+71)/15 = 67.1 inches
Allstars median: arrange the heights in order from smallest to largest: 60, 60, 62, 63, 65, 66, 67, 68, 69, 70, 70, 71, 71, 72, 73. The median is the middle value, which is 68 inches.
Champs mean: (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)/15 = 66.4 inches
Champs median: arrange the heights in order from smallest to largest: 58, 60, 60, 62, 65, 67, 67, 68, 69, 69, 70, 70, 70, 75. The median is the middle value, which is 67 inches.
Based on the measures of center, we can see that the Allstars have a higher mean and median height than the Champs. Therefore, we can conclude that the Allstars typically have the tallest players.
one bar of candy a and two bars of candy b have 779 calories. two bars of candy a and one bar of candy b contain 793 calories. find the caloric content of each candy bar.
The caloric content in candy A is 269 and that of candy B is 255.
The caloric content is the quantity of energy required to increase the temperature of one liter of water by one degree. A calorimeter was initially used to determine a food's calorie count.
Let us consider:
Caloric content of Candy A = x
Caloric content of Candy B = y
We can thereby make two equations:
Eqn 1: 1x + 2y = 779
Eqn 2: 2x + 1y = 793
By elimination method, we have
2x + 4y = 1558
Solving for x by subtracting with Eqn 2, we have,
3y = 765
y = 765 ÷ 3
y = 255.
Now substituting the value of y in Eqn 2, we have:
2x + 1y = 793
2x + 1 × 255 = 793
2x + 255 = 793
2x = 793 - 255
2x = 538
x = 538 ÷ 2
x = 269.
Hence caloric content in candy A is 269 and that of candy B is 255.
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please help with this geometry hmw
5x² - 25x - 30 has a common factor with 4x² - 25x + 6, which is (x - 6).
option C.
Which polynomial shares a common factor with 4x² - 25x + 6?
To find the common factor of two polynomials, we can use the method of polynomial factorization.
First, let's factor the polynomial 4x² - 25x + 6:
4x² - 25x + 6 = (4x - 1)(x - 6)
Now, let's factor each of the answer choices:
A. 3x² - 15x + 18 = 3(x² - 5x + 6) = 3(x - 2)(x - 3)B. 4x² + 20x + 24 = 4(x² + 5x + 6) = 4(x + 2)(x + 3)C. 5x² - 25x - 30 = 5(x² - 5x - 6) = 5(x - 6)(x + 1)D. 2x² + 8x - 24 = 2(x² + 4x - 12) = 2(x + 6)(x - 2)We can see that only choice C has a common factor with 4x² - 25x + 6, which is (x - 6). Therefore, the answer is C.
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Evaluate each expression for the given value.
a. a2 when a= 3/4
b. b3 when b = 1.1
Answer:
a. 9/16 or 0.5625
b. 1.331 or 1331/1000
Step-by-step explanation:
I’m assuming you meant a^2 and b^3
Create a real life example that includes function composition in it and solve it?
how can you multiply binomial with a trinomial? Give an example about it and solve it.
Function composition is a mathematical concept that involves combining two or more functions to create a new function. A real-life example of function composition might involve a company that uses a software program to calculate payroll. The program might use one function to calculate an employee's hourly rate based on their salary, and another function to calculate their total hours worked based on their timecard data. These two functions could be combined using function composition to create a new function that calculates the employee's total pay.
As for multiplying a binomial with a trinomial, here's an example:
(2x + 3)(4x² + 5x - 6)
To solve this, we use the distributive property of multiplication, which involves multiplying each term in one set of parentheses by each term in the other set of parentheses. We can break this down into three separate multiplications:
2x (4x² + 5x - 6) = 8x³ + 10x² - 12x
3 (4x^2 + 5x - 6) = 12x² + 15x - 18
Adding these two results together, we get:
(2x + 3)(4x² + 5x - 6) = 8x³ + 22x² + 3x - 18
Therefore, the product of the binomial (2x + 3) and the trinomial (4x² + 5x - 6) is 8x³ + 22x² + 3x - 18.
[tex] \: [/tex]
Given two polygons, you perform the following transformations:
1) Translate (x+1, y-7)
2) Rotation 180°
3) Dilate by a scale factor of ½
The final image will be...
a
Congruent to the original image
b
Similar to the original image
c
Not congruent and Not similar
Recall the definitions for congruence and similarity.
similar - the shapes are the same shape but are different sizes
congruent - the shapes are identical
Now if you have two polygons, assuming that they are identical to start out with (If not you won't be able to solve the problem. Do you see why?) and you perform the operations to one of them, the translation and the rotation will not change anything. But the dilation will make one shape 1/2 as big as the other. So in this case the two polygons are similar but not congruent.
5-|p+6|=-8 pls wut is answer
Answer:
+ or - (7)
Step-by-step explanation:
5-|p+6|= -8
-|p+6|=-8-5
|p+6|= 13
p+6 = + or - (13)
so case 1
p+6 = 13
p = 7
case 2
p+6 = -13
p+ -7
11. FINANCIAL LITERACY Jerome is buying paint for a mural. The cost of the paints can be
modeled by f(p) = 6.99p, where p is the number of paints he buys. He has a coupon for
15% off his purchase at the paint store.
a. Write a function n(p) that represents the costs of the paints with the 15% discount.
b. Find the cost of purchasing 5 paints before and after the discount.
a. The function n(p) that represents the cost of the paints with the 15% discount is n(p) = 6.99p - 0.15(6.99p).
b. The 15% discount reduces the cost of the paints from 34.95 to 29.70.
What is discount?Discount is term used for reduction in the original price of a good or service. It is a common practice used by retailers and businesses to attract customers.
a. The function n(p) that represents the cost of the paints with the 15% discount is given by:
n(p) = 6.99p - 0.15(6.99p)
= 5.94p
b. The cost of purchasing 5 paints before the discount is 6.99 x 5 = 34.95.
The cost of purchasing 5 paints after the discount is 5.94 x 5 = 29.70.
Therefore, the 15% discount reduces the cost of the paints from 34.95 to 29.70.
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x^2+x factorised in full answer
This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
To factorize an expression means to write it as a product of factors. In this case, we want to write [tex]x^{2}[/tex] + x as a product of factors. One way to do this is to look for common factors that we can take out of both terms in the expression.
In this case, the only common factor in both [tex]x^{2}[/tex] and x is x itself. Therefore, we can take out an x from both terms to get:
x(x + 1)
This is the fully factorized form of the expression [tex]x^{2}[/tex] + x. It shows that [tex]x^{2}[/tex] + x can be written as a product of two factors: x and (x + 1).
We can verify that this is correct by multiplying out the two factors:
x(x + 1) = [tex]x^{2}[/tex] + x
Therefore, This is the original expression x(x + 1) = [tex]x^{2}[/tex] + x that we started with, so we can be confident that our factorization is correct.
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Find the angle measure indicated. Assume that lines which appear tangent are tangent.
A. 110 degrees B. 175 degrees C. 155 degrees D. 120 degrees
The value of the angle QSR in the given circle containing lines and tangents is 120 degrees.
What is a circle?A circle is a two-dimensional geometric object made up of all points on a plane that are equally spaced from a central fixed point. The radius of a circle is the distance from the centre to any point on the circle. One of the most fundamental and significant geometric forms, the circle has many uses in mathematics, science, and engineering, including the study of trigonometry, coordinate geometry, and calculus. Moreover, circles are utilised in numerous practical contexts, including the creation of wheels, gears, and lenses as well as the simulation of physical phenomena like the motion of planets and electrons.
The measure of angle QSR is determined using the formula:
angle QSR = arc a + arc b / 2
Here, arc a = 150 and arc b = 90 thus:
angle QSR = 150 + 90 / 2
angle QSR = 240 / 2 = 120 degrees.
Hence, the value of the angle QSR in the given circle containing lines and tangents is 120 degrees.
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Please please help i'm trying to get an A
The area of the triangle is: 24 unit²
What is an area ?
Area is a measurement of the amount of space inside a two-dimensional figure or shape. It is typically measured in square units, such as square meters or square feet. The area of a shape is calculated by multiplying its length by its width, or by using a specific formula for the shape.
We can find the area of the triangle by using the formula:
Area = 1/2 * base * height
where the base is the distance between points A and B, and the height is the distance from point C to the line containing AB.
The distance between points A and B is 4 units (since they have the same x-coordinate). To find the height, we can use the equation of the line containing AB, which is:
y = 4x - 3
Substituting x = 4 (the x-coordinate of point C) gives us:
y = 4(4) - 3 = 13
So the height is 13 - 1 = 12 units.
Therefore, the area of the triangle is:
Area = 1/2 * base * height
= 1/2 * 4 * 12
= 24
So the answer is not one of the given choices. The correct answer is 24.
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In the diagram below, fg is parallel to CD, if CE = 32, FE = 20 and CD = 16 find the length of FG . Figures are not necessarily drawn to scale.
The length of FG is 40 units.
What are parallel lines?
Two or more lines that are consistently parallel to one another and that are located on the same plane are referred to as parallel lines. No matter how far apart parallel lines are, they never cross. The relationship between parallel and intersecting lines is the reverse. The lines that never meet or have any possibility of meeting are known as parallel lines.
Since FG is parallel to CD, triangles CDE and FGE are similar. Thus, we can set up the following proportion:
CE/CD = FG/FE
Substituting the given values, we get:
32/16 = FG/20
Simplifying the left side, we get:
2 = FG/20
Multiplying both sides by 20, we get:
FG = 40
Therefore, the length of FG is 40 units.
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Parallel lines r and s are cut by two transversals, parallel lines t and u
10 points
Angles corresponding with ∠8 are ∠4 and ∠12.
Define corresponding angleIn geometry, corresponding angles are angles that are in the same relative position at the intersection of two lines when a third line crosses them. When two lines are intersected by a third line, they form pairs of corresponding angles that are congruent, meaning they have the same measure.
In the given figure;
Lines r,s,t and u are parallel lines.
Angles ∠8 and ∠12 are in corresponding angle ( line t and u are parallel ands line intersect it)
Angle ∠4 and ∠8 are corresponding angle (line r and s are parallel and t line intersect it)
Hence, Angles corresponding with ∠8 are ∠4 and ∠12.
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