Required factor form is 2x³(3x + 4).
What is GCF?
GCF stands for Greatest Common Factor, also known as the Greatest Common Divisor (GCD). In mathematics, the GCF of two or more numbers is the largest positive integer that divides each of the numbers without a remainder. For example, the GCF of 12 and 18 is 6 because 6 is the largest integer that divides both 12 and 18 without a remainder. The concept of GCF is important in many areas of mathematics, including algebra, number theory, and calculus, and is used in various problem-solving applications.
Given form is 6x⁴+8x³.
Here is two term 6x⁴ and 8x³.
By factorisation,
6x⁴ = 2×3×x⁴ and 8x³ = 2×2×2×x³
The greatest common factor (GCF) of 6x⁴ and 8x³ is 2x³.
To factor it out, we can divide each term by 2x³:
Now,
6x⁴ ÷ 2x³ = 3x
8x³ ÷ 2x³ = 4
So, we can write:
6x⁴ + 8x³ = 2x³(3x + 4)
Therefore, the factored form of 6x⁴ + 8x³ is 2x³(3x + 4).
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The points P(1. -2) and Q(7, 1) lie on the circumference of a circle. Show that the centre of the circle lies on the line 4x + 2y = 15
Answer:
Sure, I can help you with that geometry problem! To find the center of a circle given two points on its circumference, we need to find the perpendicular bisector of the line segment connecting those two points. Let's first find the midpoint of line segment PQ. Midpoint M = ( (1+7)/2 , (-2+1)/2 ) M = (4, -1/2) The slope of the line PQ is: Slope of PQ = (1-(-2)) / (7-1) Slope of PQ = 3/2 The slope of the perpendicular bisector of PQ is the negative reciprocal of the slope of PQ. Slope of perpendicular bisector = -2/3 Now we can find the equation of the perpendicular bisector of PQ in point-slope form using the midpoint M:
Question 5(Multiple Choice Worth 2 points)
(Box Plots MC)
The box plot shows the times for sprinters on a track team.
L
40 41
H
Sprinters' Run Times
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Time in Seconds
Which of the following lists the range and IQR for this data?
O The range is 10, and the IQR is 14.
O The range is 10, and the IQR is 13.
O The range is 14, and the IQR is 13.
O The range is 14, and the IQR is 10.how do I figure this out help pls
19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
how can you describe range?The range in statistics is the distinction between the greatest and lowest values within a set of data. It is a gauge of variation that reveals the degree to which values within a dataset are dispersed.
You simply take the difference between the two values to determine the range. The range is given by: When the dataset, for instance, has the values 2, 3, 5, 8, et 10, the lowest value is 2, and the highest is 10.
Range = Highest value – Lowest value = 10 – 2 = 8 .The range in this instance is hence 8.
given
The range is the discrepancy between the data set's maximum and minimum values.
The box plot shows that the range is between 40 and 59, with 40 being the smallest value and 59 being the maximum.
Maximum value - Minimum value equals 59 - 40, which equals 19.
You may determine the values of Q1 and Q3 to be roughly 45 and 59, respectively, using the box plot.
IQR = Q3 - Q1 = 59 - 45 = 14
When the IQR is 14 and the range is 19, the answer is:
19 is the range and 14 is the IQR. So, "The range is 19, and the IQR is 14" is the appropriate response.
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Which equation is the inverse of y = 2x² - 8?
X+8
Oy=2
O y=
+√√√x+8
2
NIX
-8
Oy=+√√√2+8
y=±₁
O y-√x +4
An equation which is the inverse of y = 2x² - 8 include the following: B. [tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = y = 2x² - 8
x = 2y² - 8
2y² = x + 8
By dividing both sides of the equation by 2, we have the following:
y² = (x + 8)/2
By taking the square root of both sides of the equation, we have the following:
y = √[(x + 8)/2]
[tex]y= \pm \sqrt{\frac{x+8}{2} }[/tex]
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100 POINTS
Divide.
(4x^4-4x^2-x-3)/(2x^2-3)
We can use polynomial long division to divide (4x^4 - 4x^2 - x - 3) by (2x^2 - 3):
2x^2 + 0x - 1
---------------------
2x^2 - 3 | 4x^4 + 0x^3 - 4x^2 - x - 3
4x^4 - 6x^2
-----------
2x^2 - x
2x^2 - 3
-------
x - 3
Therefore,
(4x^4 - 4x^2 - x - 3)/(2x^2 - 3) = 2x^2 + 0x - 1 with a remainder of (x - 3)/(2x^2 - 3).
So the final answer is
2x^2 - 1 + (x - 3)/(2x^2 - 3)
Which of the following can be constructed by drawing an angle on tracing
paper and then folding the paper so that the rays forming the angle lie upon
each other?
A. Parallel lines
B. Perpendicular line segment
C. Angle bisector
D. Median of a line segment
C. Angle bisector can be constructed by drawing an angle on tracing paper and then folding the paper so that the rays forming the angle lie upon each other. When you fold the paper, the crease that is formed will be the angle bisector of the original angle.
what is the value of 13.72x5.77?
Assume all lines that appear parallel, are parallel. Solve for y.
The value of y is 10. we canget this answer by using fact ratios of the corresponding sides are equal. Using this fact, we can set up the proportion
what is corresponding sides?
In geometry, corresponding sides are sides in two or more figures that are in the same relative position or location. For example, if you have two triangles ABC and DEF, and AB is corresponding to DE, BC is corresponding to EF, and AC is corresponding to DF, then AB and DE are corresponding sides, BC and EF are corresponding sides, and AC and DF are corresponding sides.
In the given question,
To solve for y, we need to use the fact that line wt and line ye are parallel to each other. This means that the ratios of the corresponding sides are equal. Using this fact, we can set up the following proportion:
wt/ty = we/yc
Substituting the given values, we get:
(8 + x + 6)/16 = 10/y
Simplifying and solving for y, we get:
y = (160)/(14 + x)
Now we need to use the fact that the sum of the lengths of two sides of a triangle is always greater than the length of the third side. Using this fact for triangle ATY, we get:
AT + TY > AY
Substituting the given values, we get:
x + 6 + 16 > y
Simplifying and substituting y with its expression, we get:
x + 22 > (160)/(14 + x)
Multiplying both sides by (14 + x), we get:
x² + 22x + 14x + 352 > 160
Simplifying and rearranging, we get:
x² + 36x - 192 > 0
Now we can solve this quadratic inequality to get the range of possible values for x:
(x - 4)(x + 48) > 0
The solutions are x < -48 or x > 4. Since x represents a length, we can ignore the negative solution. Therefore, we have:
x > 4
Substituting this value into the expression we derived for y, we get:
y = (160)/(14 + x) = (160)/(14 + 4) = 10
Therefore, the value of y is 10.
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Fourth-grade students recorded the distance it takes to get from home to the nearest grocery store. The distance in miles is recorded on the line plot. Which is the most common distance from home to the grocery store?
Using the line plot graph, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
Define line plot?A line plot is a type of graph that shows the frequency of each value together with the data using symbols above a frequency number-line. It is used to organise the information simply and is very easy to comprehend.
In the given graph we can see that the distance values are given.
So, in the first instance the number of times the distance is used = 2.
The 2nd distance has been used = 3.
The 3rd distance has been used = 2.
The 4th distance has been used = 4.
The 5th distance has been used = 5.
The 6th distance has been used = 2.
The 7th distance has been used = 2.
The 8th distance has been used = 2.
Hence, we can conclude that the 5th distance that is 5/4 is the most common distance from home to the grocery store.
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(co 3) a puck company wants to sponsor the players with the 10% quickest goals in hockey games. the times of first goals are normally distributed with a mean of 12.56 minutes and a standard deviation of 4.91 minutes. how fast would a player need to make a goal to be sponsored by the puck company? g
A player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.
To determine how fast a player needs to make a goal to be sponsored by the puck company, we'll need to find the
time cutoff for the top 10% quickest goals.
Step 1: Determine the z-score for the 90th percentile (since we want the top 10%).
We can use a standard normal distribution table (or a calculator) to find that the z-score for the 90th percentile is
approximately 1.28.
Step 2: Use the z-score formula to find the time cutoff.
The formula is: Z = (X - μ) / σ
Where Z is the z-score, X is the time cutoff we're looking for, μ is the mean (12.56 minutes), and σ is the standard
deviation (4.91 minutes).
Step 3: Solve for X.
Rearrange the formula to solve for X: X = Z × σ + μ
Plug in the values: X = 1.28 × 4.91 + 12.56
X ≈ 6.29 + 12.56
X ≈ 18.85
So, a player would need to make a goal in approximately 18.85 minutes or faster to be sponsored by the puck company.
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The large dairy farm produced 936 eggs last year. How many dozen eggs did this
farm produce?
A
B
C
D
78
79
83
88
Answer: A=78
Step-by-step explanation: 936/12=78
936 eggs were produced last year by the sizable dairy farm. 78 dozen eggs are produced by this farm. The answer is option (A).
What is Algebra?The study of symbols for math and the procedures for using them to solve equations and comprehend the relationships between variables is the subject of the branch of mathematics known as algebra. When representing quantities and their relationships using letters and symbols, algebra uses graphs, functions, and expression manipulation in addition to equation and inequalities solving.
Numerous branches of science, technology, economics, and other disciplines make considerable use of algebraic concepts and methods. It is a fundamental area of mathematics that is frequently studied as a pre-requisite for more difficult maths and science courses.
Algebraic concepts that are important to know include:
Addition, subtraction, multiplication, and division are operations using numbers and variables.
Using variables to solve equations and inequalities
Algebraic expressions manipulation and simplification
Knowing how to graph both linear and nonlinear functions
Utilising matrices and vectors
studying trigonometric, rational, and polynomial functions
We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.
936/12 = 78
We must divide the total number of eggs by 12 to determine the number of dozen eggs produced.
The answer is A) 78.
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for the previous example, which statements are accurate conclusions? group of answer choices the proportion of drinkers in the population of ca college students is not 0.60. there is a statistically significant difference between the proportion of drinkers in the american adult population (0.60) and the proportion of drinkers in the population of ca college students. a larger proportion of ca college students drink alcohol compared to the adults nationwide. when we compare the american adult population to the population of ca college students, there is a 0.06 difference in the proportion of drinkers.
The following statements are accurate conclusions:
The proportion of drinkers in the population of California college students is not 0.60.There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinkers in the population of California college students.A larger proportion of California college students drink alcohol compared to adults nationwide.The null hypothesis is: The proportion of California college students who currently drink alcohol is the same as the proportion nationwide (p = 0.60).
The alternative hypothesis is: The proportion of California college students who currently drink alcohol is different from the proportion nationwide (p ≠ 0.60).
p in the hypotheses represents the proportion of college students who currently drink alcohol.
The Z-score is calculated as:
Z = (0.66 - 0.60) / 0.023 = 2.61
The P value can be obtained from a standard normal distribution table or calculator:
P = 0.0045 (for a two-tailed test)
We reject the null hypothesis and come to the conclusion that there is a statistically significant difference between the proportion of drinkers in the population of California college students and the proportion of drinkers in the American adult population because the P value (0.0045) is less than the significance level (which is not stated in the question) (0.66).
For the given question:
The following statements are accurate conclusions:
The proportion of drinkers in the population of California college students is not 0.60.There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinkers in the population of California college students.A larger proportion of California college students drink alcohol compared to adults nationwide.The result that "There is a 0.06 difference in the proportion of drinkers when we compare the US adult population to the population of CA college students" is untrue since the hypothesis test is not concerned with proportional differences.
The complete question is:-
Normal Distribution Calculator Drag the orange flag left or right to change the Z-score Alternatively, enter a Z-score into the textbox and click enter. Enter 8 -1 Z-score: -1.000 0 Z-score The area to the left of the Z value is 0.1587 The area to the right of the Z value is 0.9413 Question 1 6 pts California College Students Who Drink According to the Centers for Disease Control and Prevention, 60% of all American adults ages 18 to 24 currently drink alcohol. Is the proportion of California college students who currently drink alcohol different from the proportion nationwide? A survey of 450 California college students indicates that 66% currently drink alcohol. The null hypothesis is (Select] The alternative hypothesis is Select] p in the hypotheses represents [Select) The standard error is 0.60(1-0.60) 450 = 0.023 The Z-score is (Select] The P value is Select) The conclusion is Select Question 2 4 pts For the previous example, which statements are accurate conclusions? The proportion of drinkers in the population of CA college students is not 0.60. There is a statistically significant difference between the proportion of drinkers in the American adult population (0.60) and the proportion of drinknes in the population of CA college students A larger proportion of CA college students drink alcohol compared to the adults nationwide When we compare the American adult population to the population of CA college students, there is a 0.06 difference in the proportion of drinkers
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A principal wants to know if students at a particular high school are in favor of a new dress code at their school. The principal is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students to represent the high school.
Select which sample of students the principal should choose.
The principal should then survey the selected students to gather their opinions on the new dress code.
To answer your question, the principal should choose a sample of students that is both representative and random. This will ensure that the opinions gathered are an accurate reflection of the entire high school population.
How the principal can achieve this:
Determine the sample size:
The principal should decide on a suitable sample size based on the total number of students in the high school.
A larger sample size will yield more accurate results, but it may not be feasible to survey too many students.
To ensure representativeness, the principal should divide the high school population into different strata, such as grade levels or other relevant demographic categories.
This will help ensure that the sample includes a balanced mix of students from different backgrounds and groups.
Select a random sample:
Within each stratum, the principal should choose a random sample of students.
The principal should then survey the selected students to gather their opinions on the new dress code.
By following these steps, the principal can select an appropriate sample of students that will provide an accurate representation of the high school's overall opinion on the new dress code.
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Which statement is true for the absolute values of points P and Q on the number line? Responses A |−8| ≤ 6|−8| ≤ 6 B |6| > |−8||6| > |−8| C |−8| > |6||−8| > |6| D |−8| < |6||−8| < |6| Question 2 Which absolute value statement is TRUE? Responses A |−6| > |−8||−6| > |−8| B |−10| < |−5||−10| < |−5| C |−8| < |3||−8| < |3| D |−9| > |−8||−9| > |−8|
For the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
What is statement?
In mathematics, a statement is a declarative sentence that is either true or false, but not both. Statements are often expressed using variables, symbols, or mathematical notation, and they can describe mathematical objects, relationships, properties, or operations.
For the first question, the correct response is:
B |6| > |−8|
This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line. So, the absolute value of 6 is greater than the absolute value of -8, because 6 is further away from zero than -8 on the number line.
For the second question, the correct response is:
C |−8| < |3|
This is true because the absolute value of -8 is greater than the absolute value of 3. Absolute values tell us the distance from zero on the number line, and the distance between -8 and 0 is greater than the distance between 3 and 0.
Therefore for the given statements the correct answer is B |6| > |−8| and C |−8| < |3|.
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Send Halp What is the interest rate if the investment is $1,000 at 16% simple interest for 20 yrs?
Answer:
The interest rate is already given as 16%. If you want to calculate the total interest earned on the investment, you can use the formula:
Simple Interest = (Principal x Rate x Time)/100
Where:
Principal = $1,000
Rate = 16%
Time = 20 years
Substituting the values, we get:
Simple Interest = (1000 x 16 x 20)/100 = $3,200
Therefore, the total interest earned on the investment is $3,200.
Step-by-step explanation:
Ally needs 90 meters of tape for a project. Tape comes in different size rolls. If she bought 50 meters, 22.86 meters, and an 18.288-meter roll, how much tape will she have in all? ___________ meters
Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.
Adding the length of the first two rolls, we get:
50 meters + 22.86 meters = 72.86 meters
Then adding the length of the third roll to the sum above, we get:
72.86 meters + 18.288 meters = 91.148 meters
Therefore, Ally will have 91.148 meters of tape in all.
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HELPPP! WHOEVER GETS THE ANSWER GET POINT PLS!
7. Alonzo and Mandy are selling raffle tickets at school for a fundraiser. Alonzo sells 5 tickets less than three times what Mandy sells. Together they sell a total of 43 tickets. Let n equal the number of tickets Mandy sells. Use an equation to determine the number of tickets Alonzo sells. Show how you arrived at your answer.
That we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells: a = 3n - 5 = 3(12) - 5 = 31
Alonzo sells 31 tickets.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
Let's use algebra to solve the problem:
Let's start by defining some variables:
Let n be the number of tickets Mandy sells.
Let a be the number of tickets Alonzo sells.
We know that:
Alonzo sells 5 tickets less than three times what Mandy sells. So we can write:
a = 3n - 5
Together they sell a total of 43 tickets. So we can write:
a + n = 43
We have two equations with two variables, so we can solve for a by substituting the first equation into the second equation:
(3n - 5) + n = 43
4n - 5 = 43
4n = 48
n = 12
Now that we know that Mandy sells 12 tickets, we can use the first equation to find out how many tickets Alonzo sells:
a = 3n - 5 = 3(12) - 5 = 31
Therefore, Alonzo sells 31 tickets.
So the answer is: Alonzo sells 31 tickets.
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Please help me find the surface area.
Answer:
Step-by-step explanation:
From midnight to 2:00 am, the temperature dropped 1.15°C each hour. If the temperature at 2:00 am was 3.7°C, what was the temperature at midnight?
Answer:
6 degrees Celsius
Step-by-step explanation:
The temperature at 2am was 3.7 degrees C.
Since the temp dropped 1.15 degrees each hour, at 1am the temp was 3.7+1.15 = 4.85 degrees
So at midnight, 12am, the temp was 4.85+1.15 = 6 degrees Celsius
Please Help Me Answer These
Answer:
1) 100m^2 3) 96cm^2 4) 36 inches
Step-by-step explanation:
1) 10*10=100[tex]m^{2}[/tex]
2)
3) 12*8=96[tex]cm^{2}[/tex]
4)9*4=36 inches
select all the expressions equivalent to 80-20x
Answer:
where is the pic
Step-by-step explanation:
potassium 42 has a decay rate of 5.5% per hour. in how many hours will the original quantity be halved?
The half-life of Potassium-42 can be calculated using the following formula:
t1/2 = (ln 2) / λ
where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.
Substituting the values given, we get:
t1/2 = (ln 2) / 0.055
t1/2 ≈ 12.6 hours
Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.
It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.
How we can understand about how many hours will the original quantity be halved?To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:
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help pls it's not too hard I'm just bad
Answer:
x=21
Step-by-step explanation:
i tried everything and it was wrong
Answer:
A = 28π meters or 87.92 meters
Step-by-step explanation:
A = 2πrh
Find radius
Diagonal = 14 so radius 14 : 2 = 7
A = 2πrh
A = 2π×7×2
A = 2π x 14
A = 28π meters or 87.92 meters
Find the volume of the pyramid
The volume of the given pyramid is 86 in³ respectively.
What is a pyramid?A three-dimensional shape is a pyramid.
A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base.
The bases are joined to the peak to create a pyramid.
The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
A three-dimensional figure is a pyramid.
Its base is a flat polygon.
The remaining faces are all triangles and are referred to as lateral faces.
So, the formula for the volume of the pyramid is:
V = lwh/3
Now, insert values as follows:
V = lwh/3
V = 7.4*7*5/3
V = 86.33333
Rounding off: 86 in³
Therefore, the volume of the given pyramid is 86 in³ respectively.
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the height h (in feet) above the water of a cliff diver is modeled by h=-16t^2+10t+26 where t is time (in seconds). how long is the diver in the air?
Step-by-step explanation:
When the diver hits the water at Height = 0 , the diver is no longer in the air .
0 -16t^2 + 10t + 26 Use Quadratic Formula
a = -16 b = 10 c= 26
to find the positive value of t = 1.625 s
The number of toy trucks in Mike's toy collection is 2/5 of the number of toy cars a,Express the number of toy cars as a fraction of the number of toy trucks. b,What is the ratio of the number of toy trucks to the total number of toy trucks and toy cars? c,What fraction of the total number of toy trucks and toy cars is the number of toy cars?
The number of toy cars to the number of trucks is 5/2,the number of toy trucks is 2/7 of the total number of toy cars and toy trucks and the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
EquationsLet's represent the number of toy cars as 'c' and the number of toy trucks as 't'.
From the problem, we know that:
t = 2/5c
Express the number of toy cars as a fraction of the number of toy trucks:
c = 5/2t
c/t = (5/2t)/t = 5/2
Therefore, the number of toy cars is 5/2 times the number of toy trucks.
The total number of toy cars and toy trucks is:
c + t
Substituting t = 2/5c, we get:
c + (2/5)c = 7/5c
So the ratio of the number of toy trucks to the total number of toy cars and toy trucks is:
t/(c + t) = (2/5c) / (7/5c) = 2/7
Therefore, the number of toy trucks is 2/7 of the total number of toy cars and toy trucks.
The fraction of the total number of toy cars and toy trucks that is the number of toy cars is:
c / (c + t)
Substituting t = 2/5c, we get:
c / (c + 2/5c) = c / (7/5c) = 5/7
Therefore, the number of toy cars is 5/7 of the total number of toy cars and toy trucks.
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The math club is planning a meeting. They are planning to serve cookies and brownie bites and want to have one dessert per person. They expect an attendance of a total of 75 people. Cookies (c), come in packs of 12 each, and the brownie bites (b) come in packages of 15. What is the equation for the total number of packages of each dessert that the club treasurer needs to purchase in order to have a dessert for each person who attends? b+ 12 15 75 C= If the treasurer buys 1 package of brownie bites, how many packages of cookies are needed according to this equation? packages of cookies Is this value a reasonable value in this
Equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites; 5 packages of brownie bites and 15 packages of cookies needed to serve one dessert per person for a total of 75 attendees.
What is the equation for the total number of dessert packages needed for a math club meeting with cookies and brownie bites?We can use the following equation to calculate the total number of packages of each dessert that the club treasurer must purchase:
Total packages of brownie bites (b) + Total packages of cookies (c) = Total number of attendees (75)
We know that brownie bites come in packages of 15, so the total number of packages of brownie bites the treasurer needs to purchase would be:
b = ceil(75/15) = 5
where "ceil" refers to the ceiling function, which rounds to the nearest integer. In this case, we need at least 5 packages of brownie bites to have one dessert per person.
To find the number of packages of cookies needed, we can substitute the value of b into the equation:
c + 12b = 75
c + 12(5) = 75
c + 60 = 75
c = 15
However, this value is not reasonable since 15 packages of cookies would provide 180 cookies, which is more than 2 cookies per person. Therefore, the treasurer would need to adjust the number of packages of cookies based on the actual number of cookies in each package to ensure that they have exactly one dessert per person.
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assume that 11% of people are left-handed. if we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
The required probability of randomly selected people among 11% of left handed are,
Having some lefties (≥1) among the 5 people is 0.4416.
Having exactly 3 lefties in the group of 5 people is 0.01054.
Percentage of people left handed = 11%
Number of people selected at random = 5
Probability that there are some lefties (≥1) among the 5 people,
Probability of the complement event, which is that there are no lefties in the group.
Probability of selecting a right-handed person is
=1-0.11
=0.89.
Probability that all 5 people are right-handed is,
P(all right-handed)
= (0.89)^5
= 0.5584
Probability of there being some lefties (≥1) is the complement of this,
P(some lefties)
= 1 - P(all right-handed)
= 1 - 0.5584
= 0.4416
Probability of there being some lefties (≥1) among the 5 people is 0.4416.
Probability that there are exactly 3 lefties in the group of 5 people,
Use the binomial distribution formula,
P(X=3) = (⁵C₃) × (0.11)^3 × (1-0.11)^2
where X is the number of lefties in the group.
Using the binomial coefficient formula
ⁿCₐ= n! / (a! * (n-a)!)
P(X=3)
= (5!/(3!*(5-3)!)) × (0.11)^3×(0.89)^2
= 0.01054
Probability of there being exactly 3 lefties in the group of 5 people is 0.01054
Therefore, the probability of having some lefties ( ≥ 1) among the 5 people and exactly 3 lefties in the group is equal to 0.4416 and 0.01054 respectively.
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The above question is incomplete, the complete question is:
Assume that 11% of people are left-handed. if we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
a. There are some lefties ( ≥ 1) among the 5 people.
b. There are exactly 3 lefties in the group.
A fair dice is thrown n times.
Find an expression for the probability of getting at least one six in the n throws.
The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.
The complement rule of Probability:The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.
In this problem, we use the complement rule to find the probability of getting at least one six in n throws of a fair dice by subtracting the probability of not getting any sixes in n throws from 1.
Here we have
A fair dice is thrown n times.
The probability of getting at least one six in n throws of a fair dice is equal to 1 minus the probability of not getting any sixes in n throws.
The probability of not getting a six on any one throw = 5/6
[ Since there are 5 possible outcomes that are not six and 6 possible outcomes in total ]
Therefore,
The probability of not getting any sixes in n throws is (5/6)ⁿ.
So, the probability of getting at least one six in n throws is:
P(at least one six) = 1 - P(no sixes) = 1 - (5/6)ⁿ
Therefore,
The expression for the probability of getting at least one six in n throws of fair dice is 1 - (5/6)ⁿ.
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Jordan wants a collapsible puppy pen that gives his puppy at least 35 square feet of area and at Least 10 feet of diagonal length. Should Jordan buy the pen shown? Explain.
Using area formula, we can find that the diagonal length is not 10ft. So, Jordan should not buy the pen.
Define area of square?A square's area is a measurement of the volume or surface that it takes up. It is equivalent to the two sides' combined lengths. Since the product of a square's two sides determines its size, the area is expressed in square units.
Here in the question,
Jordan wants an area that is of 35 ft² and 10ft diagonal length.
Now in the figure,
Dimensions of the pen are:
Length, l = 6ft.
Width, w = 6ft.
Height, h = 6ft.
So, it's a square.
Area that the puppy pen will provide = l × w
= 6 × 6
=36ft².
Diagonal of the pen is: (As per Pythagoras theorem)
√ (6² + 6²)
= √ (36+36)
= √ 72
= 8.48
The pen does provide 35ft² of area as it has 36ft², but it does not have a diagonal length of 10ft.
Therefore, Jordan should not buy the puppy pen.
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The complete question is:
Jordan wants a collapsible puppy pen that gives his puppy at least 35 square feet of area and at Least 10 feet of diagonal length. Should Jordan buy the pen shown? Explain.
We may determine that the diagonal length is not 10 feet using the area formula. Jordan shouldn't buy the pen.
Define area of square?The volume or area that a square occupies is determined by its area. It is equal to the sum of the lengths of the two sides. The area is given in square units since a square's size is determined by the product of its two sides.
Jordan requests a 35ft² square foot area with a 10-foot diagonal.
Now look at the figure.
The pen is the following size:
Length, l = 6ft.
Width, w = 6ft.
Height, h = 6ft.
So, it's a square.
The area that the puppy kennel will offer
= 6 × 6
=36ft².
Diagonal of the pen is:
= √ (6² + 6²)
= √ (36+36)
= √ 72
= 8.48
The pen has 36ft² square feet, so it does offer 35ft² square feet, but it lacks a 10 foot diagonal.
Jordan shouldn't purchase the Puppy pen as a result.
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The complete question is attached below,