Your friend was bored one day and started making patterns using Cheerios from a new box he had opened. He laid the Cheerios on the table as such:
Based on the two images above and the information about the box, answer the following questions.
A) Identify and label the variable
B) Make a table for up to 8-figure patterns
C) Write an equation to represent the nth term of the sequence.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
E) Is it reasonable to think this pattern would continue forever? If not, explain.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?
PLS ANSWER ALL OF THE QUESTIONSSS I REALLY NEED THE ANSWERS ASAPPPPPPP PLEASE AND THANK YOU
Answers
A) The variable is n, which represents the number of the figure in the pattern.
B) Here is a table for up to 8-figure patterns:
Figure Number of Cheerios
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
C) The equation to represent the nth term of the sequence is n(n+1)/2.
D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.
E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.
F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.
Here is a more detailed explanation of how to answer each question:
A) Identify and label the variable
The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.
B) Make a table for up to 8-figure patterns
Here is a table for up to 8-figure patterns:
Figure Number of Cheerios
1 1
2 3
3 6
4 10
5 15
6 21
7 28
8 36
C) Write an equation to represent the nth term of the sequence
The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.
D) If the pattern continues, what figure number will have 20 whole Cheerios in it?
If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.
E) Is it reasonable to think this pattern would continue forever? If not, explain.
It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.
F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?
Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.
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Related Questions
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 216x + 3, [−4, 5]
Answers
Answer:
absolute minimum = -749 and
absolute maximum = 467
Step-by-step explanation:
To get the absolute maximum and minimum of the function, the following steps must be followed.
First, we need to find the values of the function at the given interval [-4, 5].
Given the function f(x) = 6x³ − 9x² − 216x + 3
at x = -4;
f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3
f(-4) = 6(-64) - 9(16)+864+3
f(-4) = -256- 144+864+3
f(-4) = 467
at x = 5;
f(5) = 6(5)³ − 9(5)² − 216(5) + 3
f(5) = 6(125) - 9(25)-1080+3
f(5) = 750- 225-1080+3
f(5) = -552
Then we will get the values of the function at the crirical points.
The critical points are the value of x when df/dx = 0
df/dx = 18x²-18x-216 = 0
18x²-18x-216 = 0
Dividing through by 18 will give;
x²-x-12 = 0
On factorizing the resulting quadratic equation;
(x²-4x)+(3x-12) = 0
x(x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x+3 = 0 and x-4 = 0
x = -3 and x = 4 (critical points)
at x = -3;
f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3
f(-3) = 6(-27) - 9(9)+648+3
f(-3) = -162-81+648+3
f(-3) = 408
at x = 4
f(4) = 6(4)³ − 9(4)² − 216(4) + 3
f(4) = 6(64) - 9(16)-864+3
f(4) = 256- 144-864+3
f(4) = -749
Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively
Camila has 6 bags of candy. She can pour 1/3 of a bag of candy into a bowl. How many bowls of candy can Camila make in all?
Answers
Answer:
18 Bowls of Candy
Step-by-step explanation:
Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.
Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.
Now, we can calculate the total number of bowls of candy:
Total bowls of candy = (Number of bags) x (Bowls per bag)
Total bowls of candy = 6 bags x 3 bowls per bag
Total bowls of candy = 18 bowls
Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.
What is the answer too 509+35+12
Answers
Answer:
556
Step-by-step explanation:
the answer to your question
How many servings in 3/4 of a cookie when each serving is 1/2 cookie
Answers
Suppose that a and b are integers with a < b How many numbers are in the list a, a+1, a+2.... b?
So I thought about doing a-(a-1) to get the first number to one so the list becomes 1,2,3 but i soon realized that does not work
Answers
The count of numbers in the list a, a+1, a+2.... b is b - a + 1
How to determine the count of numbers in the list a, a+1, a+2.... b?The list of numbers is given as:
a, a+1, a+2.... b
From the above list, we can see that the numbers are consecutive numbers.
This means that, the count of numbers in the list is
Count = Highest - Least + 1
Where
Highest = b
Least = a
Substitute the known values in the above equation
Count = b - a + 1
Hence, the count of numbers in the list a, a+1, a+2.... b is b - a + 1
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y+1-x when x=4 and y=5
Answers
Answer:
2
Step-by-step explanation:
Y = 5
x = 4
Substitute
5 + 1 - 4
6 - 4
2
Answer:
Given that x = 4 and y = 5,
\(\sf 5 + 1 - 4\\(5 + 1) - 4\\5 + 1\\= 6\\= 6 - 4\\= 2\)
Therefore, the answer is 2.
Mathhh helppp meeee fast
Answers
the answer shoulldd be 136°
Answer:
136 degrees
Step-by-step explanation:
I'm guessing you have to find the red line angle so umm, let's start I guess.
We see that m<AGF and m<GJE are corresponding and therefore, they are equal. Let's put that in an equation
6x+34=8x
subtract 6x on both sides
34=2x
x=17
WOOH, WE GOT WHAT X EQUALS!!!
Ok now, we do 8*17 which is 136
that means that m<GJE= 136
Let me know if you have any questions
A cone has a volume of 2560 Pi cm cubed and a height of 30cm. Find the radius
Answers
•A volume of 2560 pi cm cube
•A height of 30 centimeters
The the required one
•The radius of the cone
Then find the solution
Using the formula
V=πr squared * h/3
Solving for
r=3V 3·2560
π·30≈9.02703
πh=
What is angle
Enter your answer in the box
Answers
Answer:
CAB is 37 degrees
Step-by-step explanation:
90 + 53 = 143
180 - 143 = 37
Alijah had a taxable income of $8450 and filed his federal income tax return with the Single filing status. Using the table below, find the amount he has to pay in taxes.
Single
Taxable income is over
8.350
33 950
82.750
171.550
372,950
But nat over
8,350
33.950
82,250
171.550
372.550
The tax is
Plus
50.00
835.00
4 675.00
16.750.00
41,754.00
108,216.00
10%
15%
25%
20%
33%
35%
Of the
amount over
50
8.350
33.950
82,250
171.550
372,850
O A. $835.00
• B. $850.00
O c. $2087.50
O D. $1252.50
Answers
Answer:
Step-by-step explanation:
67
Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.
Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.
This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.
He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.
Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.
Thus, looking at the provided options, option B ($850.00) would be the correct answer.
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The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation? A. The number of breakdowns on a randomly selected day is expected to be 0.28. B. The number of breakdowns on a randomly selected day will be 0.28 away from the mean. C. The average number of breakdowns per day for a random sample of days is expected to be 0.28 D. On average, the number of breakdowns per day varies from the mean by about 0.28. E. The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.
Answers
The correct option is (D). On average, the number of breakdowns per day varies from the mean by about 0.28.
Because standard deviation represents the typical distance between each data point and the mean.
The variability in a dataset is condensed into a single value called the standard deviation (SD). It shows the typical separation between the mean and each data point. Smaller values show that the data points are more evenly distributed around the mean, indicating that the dataset's values are generally stable.The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.
A discrete random variable's variance and standard deviation can be seen as measurements of the variability of the values the random variable assumes throughout the course of an experiment's multiple trials.So, the correct answer is On average, the number of breakdowns per day varies from the mean by about 0.28.
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The rule c=6.3r gives the approximate circumference c of a circle as a function of its radius r. Identify the independent and dependent variables in this relationship
Answers
The circumference (c) is the dependent variable.
The radius (r) is the independent variable.
How to identify the independent and dependent variables in a relationship?
An independent variable is a variable that does not depend on any other variable for its value
A dependent variable is a variable depend on any other variable for its value.
In the rule c = 6.3r, the circumference (c) of a circle depends on the radius for its value while the radius (r) does not depend on the circumference for its value.
Thus, the circumference (c) is the dependent variable while the radius (r) is the independent variable
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The graph below shows a line of best fit for data collected on the distance drivers traveled as a function of time. Which of the following is the equation of the line of best fit? A. B. C. D.
Answers
The equation for the line of best fit is given as follows:
y = 50x/3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b.
The parameters of the definition of the linear function are given as follows:
m represents the slope of the function, which is by how much the dependent variable y increases(positive) or decreases(negative) when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On the case of the graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.From the graph, when x = 0, y = 0, hence the intercept b is given as follows:
b = 0.
Hence:
y = mx.
When x = 3, y = 50, hence the slope m is given as follows:
3m = 50
m = 50/3.
Hence the equation is:
y = 50x/3.
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if you answer this correctly, i’ll give you brainliest!
-
-
find the value of x to make the following expression true:
6x = 216
Answers
Answer:
Original equation: 6x=216
Divide by 6: x=36
Let me know if this helps!
Answer:
If 216 = 6x then x = 216/6
216/6 = 36
x = 36
Step-by-step explanation:
(2)^-2Homework, thank you so much
Answers
Using the property of negative exponents, we know that:
\(2^{-2}=\frac{1}{2^2}\)Now, we only have to solve the power:
\(\frac{1}{2^2}=\frac{1}{4}=0.25\)It means that the answer is 1/4 or 0.25.
Segments RA and NY are best described as which of the following?
A. Parallel segments
B. Perpendicular lines
C. Perpendicular segments
D. Perpendicular rays
Answers
Which ratio is equivalent to the ratio 13:15
Answers
Answer:
26:30
Step-by-step explanation:
a deli employee can make a sandwhich in 6 minutes.she works for 84 minutes.how many sandwhiches can she make
Answers
Answer:
14
Step-by-step explanation:
84/6
Explanation: all you have to do is divide 84 by 6
Rewrite the expression without parentheses.
13m−(−9m−4)
Answers
Answer:
22m+4
Step-by-step explanation:
Let's break it down:
13m+-1(-9m-4)
13m+(9m+4)
22m+4
Answer:
22m+4
Step-by-step explanation:
Use the Distributive Property to expand the expression.
0.4(35m - 15n)
Answers
=14-6
=8
boom
Tickets to the museum cost $7.50 each. Students receive a 15% discount on admission
What is the cost of a student ticket?
Answers
Answer:
$ 6.375
Step-by-step explanation:
Cost of ticket = $7.50
Discount = 15%
Discount price = 15/100 x 7.50 = 1.125
Cost of student ticket = $7.50 - 1.125 = $ 6.375
I hope im right!!
Pls Answer this Right and Professionally I’m begging you I will mark a brainless too
Answers
Answer:
3. x=110 y=110 t=70
4. a=105 b=105 c=75 d=75 e=105 g=75 f=75
Step-by-step explanation:
Should be the answer to the 1st question. 110+70=180
Three pizza are shared equally among 12 people.what fraction of a pizza will each person get?
A
4/1
B
3/1
Answers
Answer:
d) 1/12
Step-by-step explanation:
The probability that = randomly selected person has high blood pressure (the event H) is P(H) = 0.2 and the probability that randomly selected person Is runner (the event R) is P(R) 0.4. The probability that a randomly selected person has high blood pressure and is runner 0.1. Find the probability that randomly ected person either has high blcod pressure or is runner or both0.6 0.4 0.8 None of the above
Answers
The probability that randomly selected person either has high blood pressure or is runner or both is 0.5.
Given:
P(H) = 0.2
P(R) = 0.4
P(H and R) = 0.1
The number of favorable outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.
Favorable Results/Total Results = x/n, where Probability(Event)
P(H or R) = P(H+P(r)-P(H and R)
= 0.2+0.4-0.1
= 0.5
Hence we get the probability as 0.5
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1. Kilometers and inches are some units used to measure length. What are some other
units used to measure length?
2. Tablespoons and liters are some units used to measure volume. What are some
other units used to measure volume?
100 point please helppp
Answers
Answer:
length- inches, meters, millameters
Volume- gallon, quart, cups, teaspoons
Step-by-step explanation:
Answer:
ength- inches, meters, millameters
Volume- gallon, quart, cups, teaspoons
Step-by-step explanation:
Draw a quick picture to find the product of 3×800
Answers
Answer:
daymn
it's gonna be okay
3) John and Kamira are playing a game. John's score (J) and Kamira's score 1 point
(K) after round 1 are shown on the number line. (MGSE7.NS.1.b) The score
recorded at the end of the first round is 6. What could this score
represent? *
K
3
5
4
-8-7-6
S
6
-109
2
8 9 10
The absolute value of the difference of John's score and Kamira's score.
The sum of John's score and Kamira's score.
The difference between John's score and Kamira's score.
The sum of the absolute value of John's score and the absolute value of Kamira's
score
Answers
Since the score recorded at the end of the first round is 6, this score could represent the following: B. The difference between John's score and Kamira's score.
What is a number line?In Geometry and Mathematics, a number line refers to a type of graph that is usually composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
Assuming the variable J represent John's score and the variable K represent Kamira's score on the number line. In this scenario and exercise, we would determine the solution for the given scenario by solving as follows;
J + K = 1 + 7 = 8
K - J = 7 - 1 = 6
|K - J| = |7 - 1| = |6| = -6
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
After adding the two equations to eliminate x you are left with 4y=-8. Solve for y: y =
Answers
Answer: -2
Step-by-step explanation:
4y/4 = -8/4
y = -2
Answer:
Step-by-step explanation:
Answer is -2
Select the graph of the solution. Click until the correct graph appears. |x| + 1 < 3
Answers
The solution to the given inequality is x<2. Therefore, option C is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is |x|+1<3.
Here, subtract 1 on both the sides of an inequality, we get
x<2
Therefore, option C is the correct answer.
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Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3000 grams and a standard deviation of 430 grams. If a 32-week gestation period baby weighs 2900 grams and a 41-week gestation period baby weighs 3200 grams, find the corresponding z-scores. Which baby weighs more relative to the gestation period?
Find the corresponding z-scores. Which baby weighs relatively more? Select the correct choice below and fill in the answer boxes to complete your choice.
(Round to two decimal places as needed.)
A. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 32.
B. The baby born in week 41 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 32.
C. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is larger than the z-score of enter your response here for the baby born in week 41.
D. The baby born in week 32 weighs relatively more since its z-score, enter your response here, is smaller than the z-score of enter your response here for the baby born in week 41.
Answers
Answer:
The 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
The 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
The 41 week gestation's period baby weighs relatively less.
Step-by-step explanation:
Normal model problems can be solved by the zscore formula.
On a normaly distributed set with mean and standard deviation , the z-score of a value X is given by:
The zscore represents how many standard deviations the value of X is above or below the mean .
Find the corresponding z-scores.
Babies born after a gestation period of 32 to 35 weeks have a mean weight of 2700 grams and a standard deviation of 800 grams. A 32-week gestation period baby weighs 2450.
Here, we have .
So
A negative z-score indicates that the value is below the mean.
So, the 32 week gestation's period baby weighs 0.31 standard deviations below the mean.
Babies born after a gestations period of 40 weeks have a mean weight of 2900 grams and a standard deviation of 385 grams. A 41 week gestation period baby weights 2650 grams.
Here, we have
So, the 41 week gestation's period baby weighs 0.65 standard deviations below the mean.
Which baby weighs relatively less?
The 41 week gestation's period baby has a lesser z-score, so this means that he weighs relatively less.