An example of a function that models a linear relationship between two quantities, x and y is y = mx + b
How to explain the functionWe need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:
y = mx + b
In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.
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4Construct a function to model a linear relationship between two quantities.
The following histogram shows the exam scores for a Prealgebra class. Use this histogram to answer the questions.Prealgebra Exam ScoresScores 70.5, 75.5, 80.5, 85.5, 90.5, 95.5, 100.5Frequency 0, 4, 8, 12, 16, 20, 24Step 1 of 5:Find the number of the class containing the largest number of exam scores (1, 2, 3, 4, 5, or 6).Step 2 of 5:Find the upper class limit of the third class.Step 3 of 5:Find the class width for this histogram.Step 4 of 5:Find the number of students that took this exam.Step 5 of 5:Find the percentage of students that scored higher than 95.595.5. Round your answer to the nearest percent.
Answer:
The number of the class containing the largest score can be found in frequency 24 and the class is 98 - 103
For the third class 78 - 83 ; the upper limit = 83
The class width for this histogram 5
The number of students that took the exam simply refers to the frequency is 84
The percentage of students that scored higher than 95.5 is 53%
Step-by-step explanation:
The objective of this question is to use the following histogram that shows the exam scores for a Pre-algebra class to answer the question given:
NOW;
The table given in the question can be illustrated as follows:
S/N Class Score Frequency
1 68 - 73 70.5 0
2 73 - 78 75.5 4
3 78 - 83 80.5 8
4 83 - 88 85.5 12
5 88 - 93 90.5 16
6 93 - 98 95.5 20
7 98 - 103 100.5 24
TOTAL: 84
a) The number of the class containing the largest score can be found in frequency 24 and the class is 98 - 103
b) For the third class 78 - 83 ; the upper limit = 83 ( since the upper limit is derived by addition of 5 to the last number showing in the highest value specified by the number in the class interval which is 78 ( i.e 78 + 5 = 83))
c) The class width for this histogram 5 ; since it is the difference between the upper and lower boundaries limit of the given class.
So , from above the difference in any of the class will definitely result into 5
d) The number of students that took the exam simply refers to the frequency ; which is (0+4+8+12+16+20+24) = 84
e) Lastly; the percentage of students that scored higher than 95.5 is ;
⇒\(\dfrac{20+24}{84} *100\)
= 0.5238095 × 100
= 52.83
To the nearest percentage ;the percentage of students that scored higher than 95.5 is 53%
Answer:
1. 98-103 (6th class)
2. 88
3. 5
4. 84
5. 52%
Step-by-step explanation:
Find attached the frequency table.
The class of exam scores falls between (1, 2, 3, 4, 5, or 6).
The exam score ranged from 68-103
1) The largest number of exam scores = 24
The largest number of exam scores is in the 6th class = 98 -103
Step 2 of 5:
The upper class limit is the higher number in an interval. Third class interval is 83-88
The upper class limit of the third class 88.
Step 3 of 5:
Class width = upper class limit - lower class limit
We can use any of the class interval to find this as the answer will be the same. Using the interval between 73-78
Class width = 78 - 73
Class width for the histogram = 5
Step 4 of 5:
The total of students that took the test = sum of all the frequency
= 0+4+8+12+16+20+24 = 84
The total of students that took the test = 84
Step 5 of 5:Find the percentage of students that scored higher than 95.5
Number of student that scored higher than 95.5 = 20 + 24 = 44
Percentage of students that scored higher than 95.5 = [(Number of student that scored higher than 95.5)/(total number of students that took the test)] × 100
= (44/84) × 100 = 0.5238 × 100 = 52.38%
Percentage of students that scored higher than 95.5 = 52% (nearest percent)
Iris has 120 songs on her playlist. Each week, she downloads 4 new songs. How do I write an expression to show the total number of songs on Iris's playlist after w weeks
The expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Iris has 120 songs on her playlist. Each week, she downloads 4 new songs.
We can write the expression to show the total number of songs on Iris's playlist after {w} weeks as -
y = 120 + 4w
Therefore, the expression to show the total number of songs on Iris's playlist after {w} weeks is → y = 120 + 4w.
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1. What does this quote mean to you?
2. How can you apply it to your life?
"You exist only in what you do." ~ Federico Fellini
***Must answer with a pharagraph, minimum 5 sentences, just give me your opinion.
Answer:
My opinion is that you can exist any many things as you navigate through life. This quote is very wrong because you can exist in doing things for other people and not just yourself! You can not be selfish your entire life! I think that you should be for other people! I think that doing stuff for yourself is okay to a certain extent!
Step-by-step explanation:
THIS IS SOOO WRONG( idk tho)
This quote is telling us that you can't exist unless you are doing something worth being remembered for. Through out our lives we all listen to what the world tells us, but not many of us actually do what we want to. We live our lives for someone else, but I plan to change that. Instead of letting the public decide how I should live my life I will live for me. I will work harder in school, become smarter than my parents and grow as a person. I want to be remembered for stepping out of my comfort zone and being different. This is the year that I exist, and show people that I exist for a purpose.
Step-by-step explanation:
Went really deep with this one.
Solve for X.
X-3 - 2(6 - 2x) = 2(2x - 5)
A)
3
B)
5
C)
9
D)
11
☁️ Answer ☁️
annyeonghaseyo!
The answer is:
B - x = 5
Hope it helps!
Have a nice day hyung/noona!!~  ̄▽ ̄❤️
What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
Work out the volume
A school bus requires 40 liters of fuel per week. If your school district runs 5,000 school buses, how many liters of fuel will the buses consume in 52 weeks? A. 15 million liters B. 10 million liters C. 10.4 million liters D. 200 million liters
Answer:
C. 10.4 million liters.
Step-by-step explanation:
1. First, you want to create an equation to help you solve this. You know that there are 5,000 school buses and they use 40 liters of fuel per week. So, you know that 5,000 · 40x would be the amount of fuel for x weeks (where x is the number of weeks).
2. To figure out how many liters would be used in 52 weeks, simply put 52 in for x. So, the expression is 5,000·40(52).
3. Multiply 40(52) to get 2,080. Your expression now looks like this: 5,000·2,080
4. Multiply 5,000(2,080) to get your answer of 10,400,000 liters.
Hope this helps! :) If you could give me Brainliest that would be super helpful!
At a sale this week, a desk is being sold for $536. This is 67% of the original price.
What is the original price?
Answer:
884.4
Step-by-step explanation:
Answer:
The original price is 895.12$
I haven't done percent in ages, lmk if you get it right
kudos to any other answer besides this
Step-by-step explanation:
A town had six flower shops their one year sales figures are compared in the chart find the ratio of sales of Winnie the florist to those of at flowers of distinction
The one-year sales of Winnie the forest were $300 thousand
The one-year sales of Flowers of distinction were 675 thousand.
Now, we need to find the ratio:
Winnie the forest/ Flowers of distinction = 300/675
Simplify the expression:
300/675 = 4/9
Make the ratio in order that the question gives you:
Winnie the forest:4
Flowers of distinction:9
The ratio would be 4:9 = 4/9
What is the probability that a smart phone buyer did not also own either a tablet/ laptop or a music player?
Answer: 78% of buyers didn't own both a music player or tablet/laptop at once
Step-by-step explanation:
36% didn't own a tablet/laptop, 72% didn't own a iPod/music player and 78% didn't own both at once
I put the question in the photo but it’s basically a contingency table I just can’t find which like formula to us
a) The probability that exactly one of them will be a girl = 0.3407
b) The probability that at least one of them will like the football = 0.7672
a) If we select three students then the probability that exactly one of them will be a girl
From the attached two way table we can observe that the total number of girls = 22
the total number of boys = 18
and the total number of students = 40
The possible outcomes for selecting 3 students from 40 would be,
⁴⁰C₃
Using combination formula,
⁴⁰C₃ = 40! / (3! × (40 - 3)!)
= 9880
If there is exactly one girl then other two must be boys in the set of 3 selected students.
So, the required probability would be,
P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃
P = (22 × 153)/9880
P = 0.3407
b) The number of students like the football = 15
and the number of students who don't like the football are 40 - 15 = 25
The probability that at least one of them will like the football would be,
P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃
P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880
P = 0.7672
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The width of a rectangle is 7in less than the length. The area of the painting is 98in squared. Find the length and width
Answer:
Length = 14 in.
Width = 7 in.
Step-by-step explanation:
The formula for the area of a rectangle is given by:
A = lw, where
A is the area in units squared,l is the length,and w is the width.Since the width is 7 in. less than the length, we can show this with the following equation:
w = l - 7
Now we can substitute l - 7 for w in the area formula and 98 for A to find l, the length of the rectangle:
Step 1: Distribute the l:
98 = l(l - 7)
98 = l^2 - 7l
Step 2: Subtract l^2 from both sides:
We have a quadratic and in order to solve, we'll need to put it in standard form, whose general equation is given by:
ax^2 + bx + c = 0
Thus, we'll need to move l^2 and -7l to the left-hand side of the equation by first subtracting l^2 from both sides:
(98 = l^2 - 7l) - l^2
-l^2 + 98 = -7l
Step 3: Add 7l to both sides to put the quadratic in standard form:
Now we can add 7l to both sides to put the quadratic in standard form:
(-l^2 + 98 = -7l) + 7l
-l^2 + 7l + 98 = 0
Step 4: Factor the quadratic:
Since the quadratic is in standard form, -1 is our a value, 7 is our b value, and 98 is our c value. We can factor the quadratic by finding two numbers whose product equals a * c (-1 * 98) and whose sum is b (7).-7 and 14 meets these two requirements as -7 * 14 = 98 and -7 + 14 = 7.When putting the quadratic in factored form, we use the opposite sign of -7 and 14.Thus, the quadratic in factored form is (l + 7)(l - 14) = 0
Step 5: Solve the quadratic by setting each term equal to 0:
Since our variable is l, solving the quadratic will give us the length of the rectangle.We can solve the quadratic by setting (l + 7) and (l - 14) equal to 0:
Setting (l + 7) equal to 0:
(l + 7 = 0) - 7
l = -7
Setting (l - 14) equal to 0:
(l - 14 = 0) + 14
l = 14
Because we can't have a negative side length, the length is 14 in.
Step 6: Identify the width:
The only number which you can multiply with 14 to get 98 is 7.Thus, the width is 7 in.
Simplify:
9x/2 - 4x - 3 = ?
Answer: Um, I think is \(\frac{x}{2-3}\).
Step-by-step explanation:
An investment of $1,000 earns an annual interest rate of 2%. How much more interest is earned in Year 5 with compound interest than with simple interest?
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method.
How to determine money gain by simple interest
Simple interest (C) is the amount of money gained and solely related to the initial capital (\(C_{o}\)), in monetary units. The money earned by simple interest is determined by the following formula:
\(C = \frac{C_{o}\cdot r\cdot t}{100}\) (1)
Where:
r - Interest rate, in percentaget - Time, in yearsCompound interest (C) takes into account the capital throughout time and its formula is presented below:
\(C = C_{o}\cdot \left[\left(1+\frac{r}{100} \right)^{t}-1\right]\)
Now we proceed to determine the simple and compound interest: (\(C_{o} = 1000\), r = 2, t = 5)
Simple interestC = [(1000) · (2) · (5)]/100
C = $ 100
Compound interestC = (1000) · {[1+(2/100)]⁵-1}
C = $ 104.08
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method. \(\blacksquare\)
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Which of these expressions can be used to calculate the monthly payment for
a 20-year loan for $170,000 at 12.6% interest, compounded monthly?
O A.
О в.
O C.
O D.
$170 000 0.0105(1+0.0105) 240
(1+0.0105) 240 - 1
$170 000 0.0105(1-0.0105) 240
(1-0.0105) 240 +1
240
$170 p000 0.0105(1 – 0.0105)²
(1-0.0105) 240-1
$170 000 0.0105(1+0.0105) 240
(1+0.0105) 240 +1
The monthly payment for a 20-year loan for $170000 at 12.6% interest, compounded monthly is \(708.33(1+0.0105)^{20}\).
What are the formula for calculating the compound interest and the amount?For the principal \(P\), the annual rate of interest \(r\%\) compounded monthly, the amount after \(t\) years can be given by the following formula:
\(A=P(1+\frac{r}{12\times 100})^t\).
The compound interest is given by: \(CI=A-P\).
Here, in the given problem, \(P=\$170000, r=12.6, t=20\).
So, the amount will be \(A=170000(1+\frac{12.6}{12\times 100})^{20}=170000(1+0.0105)^{20}\).
Now, \(20\hspace{1mm}\text{years}=20\times 12=240\hspace{1mm}\text{months}\).
Hence, the monthly payment will be: \(\frac{A}{240}=\frac{170000(1+0.0105)^{20}}{240}=708.33(1+0.0105)^{20}\).
Therefore, the monthly payment for a 20-year loan for $170000 at 12.6% interest, compounded monthly is \(708.33(1+0.0105)^{20}\).
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$170 000 0.0105(1+0.0105) 240
(1+0.0105) 240 - 1
Step-by-step explanation:
The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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Consider the radical equation √(x+3)=4. Solve this equation by squaring both sides and then solving for x. Now, replace 4 by -4 and solve for x again. Is the value you found for x still a solution? Explain your reasoning.
Given the radical eqaution
\(\sqrt[]{(x+3)}=4\)To find the value of x
Square both sides of the equation
\(\mleft\lbrace\sqrt[]{(x+3)}\mright\rbrace^2=(4)^2\)Solve the brackets
\(\begin{gathered} x+3=16 \\ \text{Collect like terms} \\ x=16-3=13 \\ x=13 \end{gathered}\)Replacing 4 by -4 in the given radical equation
\(\sqrt[]{(x+3)}=-4\)To find the value of x
Square both sides of the equation
\(\lbrace\sqrt[]{(x+3)}\rbrace^2=(-4)^2\)Solve the brackets
\(\begin{gathered} x+3=16 \\ x=16-3 \\ x=13 \end{gathered}\)To check:
Substitute 13 for x into both radical equations
For the first equation
\(\sqrt[]{(x+3)}=4\)Substituting the value of x into the above equation
\(\begin{gathered} x=13 \\ \sqrt[]{(x+3)}=4 \\ \sqrt[]{(13+3)}=4 \\ \sqrt[]{16}=4 \\ 4=4 \end{gathered}\)For the second equation
\(\sqrt[]{(x+3)}=-4\)Substituting the value of x into the above equation
\(\begin{gathered} \sqrt[]{(x+3)}=-4 \\ \sqrt[]{(13+3)}=-4 \\ \sqrt[]{16}=-4 \\ 4\ne-4 \end{gathered}\)Hence,
\(\begin{gathered} x=13\text{ is a solution to }\sqrt[]{(x+3)}=4\text{ (i.e 4 }=4) \\ x=13\text{ is not a solution to }\sqrt[]{(x+3)}=-4\text{ (i.e 4 }\ne-4) \end{gathered}\)How many 11-card hands are possible with a 20-card deck?
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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Which comparison is correct?
0.298 < 0.289
0.420 > 0.42
1.32 < 1.319
d) 3.544 > 3.455
Step-by-step explanation:
Option D is the correct answer because 3.544 is greater than 3.455
Option D is true in given comparison.
Here,
We have to find the correct comparison.
What is Decimal expansion?
The decimal expansion terminates or ends after finite numbers of steps. Such types of decimal expansion are called terminating decimals.
Now,
In option D;
The one tenth of 3.544 is 5 and place value of one tenth number in 3.455 is 4.
Clearly, 5 > 4
So, 3.544 > 3.455
Hence, option D; 3.544 > 3.455 is true.
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solve by square root\((3x - 2) ^{2} = - 12\)
Solve by square root;
\((3x-2)^2=-12\)We start by taking the square root of both sides, and we'll have;
\(\sqrt[]{(3x-2)^2}=\pm\sqrt[]{-12}\)Note that the square root sign cancels out the square sign on the left side.
\(3x-2=\pm\sqrt[]{-12}\)The square root of negative 12 can be splitup into the following;
\(undefined\)Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 23.5 for a sample of size 775 and standard deviation 12.2. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 95% confidence level). Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:
\(22.6 < \mu < 24.4\)
How to obtain the confidence interval?The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:
\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)
Looking at the z-table, the critical value for a 95% confidence interval is given as follows:
z = 1.96.
The lower bound of the interval is then given as follows:
\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)
The upper bound of the interval is then given as follows:
\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)
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prove that there exist only five regular polyhedron
To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.
Proving there exist Five Regular PolyhedronThe five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.
The five regular polyhedra are:
1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.
2. Cube: It has six square faces, and three squares meet at each vertex.
3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.
4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.
5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.
To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:
"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".
For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:
V - E + F = 2
=> kV/2 - kE/2 + F = 2
=> k(V/2 - E/2) + F = 2
Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:
k(V/2 - (nF)/2) + F = 2
=> (kV - knF + 2F)/2 = 2
=> kV - knF + 2F = 4
Now, we need to consider the conditions for a valid polyhedron:
1. The number of faces (F), edges (E), and vertices (V) must be positive integers.
2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.
Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:
(n, k) pairs:
(3, 3) - Tetrahedron
(4, 3) - Cube
(3, 4) - Octahedron
(5, 3) - Dodecahedron
(3, 5) - Icosahedron
Therefore, there exist only five regular polyhedra.
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In the diagram below, side PQ has a length of 26.86 cm and side PR has a length of 40.00 cm.
Determine the measure of angle Q in degrees to one decimal place.
Goodness gracious! The diagram cannot be rendered!
Step-by-step explanation:
what is the answer to 100001/9
A rectangular garden is 35m long and 25m broad. find the perimeter of the rectangular garden. find the length of wire required to fence with 2 round.
Answer:
The perimeter is the distance all round,
Step-by-step explanation:
perimeter of a rectangle is gotten by the formula
P=2(L+W)
2(35+25)=120m
The wire covers the distance all round
so we use 120m×2=240m
100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
626.71 cm^2
Step-by-step explanation:
Area of figure = area of half circle + Area of half circle + area of a rectangle
here, diameter=15 cm
radius = 15/2=7.5 cm
length=30cm
breadth=15cm
Now
Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth
=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15
=626.71 cm^2
HELPP PLEASE !!!!!!
Answer:
-9
Step-by-step explanation:
The in the first expression, y is to the -9'th degree, which means n is -9.
(If there are numbers of similar term multiplied together, the exponents are to be added.)
Man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and she wants to order between 15% and 20% extra of the material
The order for the extra materials that are ordered by the man will be between 17.31 ft² and 23.08 ft².
How to calculate the value?From the information, the man is ordering new tile for her kitchen floor the area of the floor is 115.4 ft.² and wants to order between 15% and 20% extra of the material.
It should be noted that 15% of the material will be:
= 15% × 115.4
= 17.31 ft²
It should be noted that 20% of the material will be:
= 20% × 115.4
= 23.08 ft²
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1. Introduction to frequency distributions Which of the following phrases correctly complete the sentence “A frequency distribution....”? Check all that apply. is a graphical presentation of original data in a histogram. is a distribution in which the values of the variable are tabled or plotted against their frequency of occurrence. is used to display summary statistics such as means and standard deviations. is often a first step of organizing the data into a logical order. You are assigned to a study group of eight students. As a “getting to know you” exercise, you each identify the season of your birth. The following are the responses of the students in your group: fall winter spring summer fall winter spring fall Organize the responses by completing the following frequency distribution table: Frequency Distribution Table for Birth Season Birth Season Number of Students Spring Summer Fall Winter
A frequency distribution is a distribution in which the values of the variable are tabled or plotted against their frequency of occurrence and is often a first step of organizing the data into a logical order. .
How to determine the correct definition of the frequency distribution?As a general rule:
A frequency distribution is in form of a tableIt is used to organize data in logical order or in groupsAn example of a frequency table is
Commute time Frequency
1 - 15 10
16 - 30 18
31 - 45 11
46 - 60 5
61 - 75 0
76 - 90 1
By comparing the above highlights to the given definitions, we have the correct options to be:
A distribution in which the values of the variable are tabled or plotted against their frequency of occurrenceIt is often a first step of organizing the data into a logical order.Read more about frequency distribution at
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Please use the following for the next 6 questions. Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the population standard deviation for the earnings for such employees is $50. A sample of 100 such employees is selected at random.
1) What is the probability distribution of the average weekly earnings for employees in general automotive repair shops?
2) Find the probability that the average weekly earnings is less than $445.
3) Find the probability that the average weekly earnings is exactly equal to $445.
4) Find the probability that the average weekly earnings is between $445 and $455.
5) In answering the previous 3 questions, did you have to make any assumptions about the population distribution?
6) Now assume that the weekly earnings for employees in all general automotive repair shops is normally distributed, obtain the probability that a given employee will earn more than $480 in a given week.
1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.
3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.
4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.
5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.
6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.