PLEASE ANSWER WILL GIVE POINTS AND VOTE YOU BRAINLIEST.

Select all stories that the tape diagram can represent.

A. Lin buys a pack of 87 pencils. She gives 39 to her teacher and shared the remaining pencils between herself and 3 friends.

B. Diego’s family spends $87 on 4 tickets to the fair and $39 for dinner.

C. There are 87 children and 39 adults at a show. The seating in the theatre is spilt into 4 equal sections.

D. Andre buys 4 packs of paper clips with 39 paper clips in each. Then he gives 87 paper clips to his teacher.

E. There are 87 first graders in after care. After 39 students are picked up, the teacher put the remaining students into 4 groups for an activity.

PLEASE ANSWER WILL GIVE POINTS AND VOTE YOU BRAINLIEST. Select All Stories That The Tape Diagram Can

Answers

Answer 1
I think B is the correct answer please forgive me if I’m wrong

Related Questions

Help ME ASAP

Zach solved the problem 124.8 / 24 = 5. Complete the following model with partial products to check Zach’s work with multiplication.

Part A
Drag values to the boxes to complete the partial products. Not all choices will be used.

{ 0.4 }
{ 0.8 }
{ 2 }
{ 4 }
{ 8 }
{ 10 }
{ 20 }
{ 100 }

The product for A=
The product for B =
The product for C =
The product for D =

Part B
Choose the words to complete the statement
Zach's work is ______
because the total of the partial products is _______ as the dividend.

Help ME ASAP Zach solved the problem 124.8 / 24 = 5. Complete the following model with partial products

Answers

The partial products in Zach's work are the result of multiplying each digit

in turn based on their place values.

The given problem is  \(\dfrac{124.8}{24} = 5\)

Part A

The values to be placed in the boxes are presented as follows;

\(\begin{array}{|c|c|c|}&5&0.2\\&&\\20&\underline{100}&\underline{4}\\&&\\4&\underline{20}&\underline{0.8}\end{array}\right]\)

The total of the partial product is 100 + 20 + 4 + 0.8 = 124.8 = The dividend

Part B

The completed statement is; Zach's work is correct because the total of

the partial product is the same as the dividend.

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Frank practised for 4 hours and 35 minutes. If he stopped practising at 9:17 p.m, what time did he start practising?

Answers

4:42 p.m

You start with 9:17 and you subtract 4 hours. That gives you 5:17. Now you have to subtract the remaining 35 minutes. To make things easy we can make 5:17, five o-clock. We can do this by subtracting 17 then you'll get five o-clock. Now you have another 28 minutes to subtract. 5:00 - 28 = 4:42. Then you add the p.m.

A directional test (>) one sample t test was conducted. The results was t (30) = 3.99. You will: O accept the null. O reject the null.
O cannot tell with the information provided.

Answers

A directional test (>) one sample t-test was conducted. The results was t (30) = 3.99. We can reject the null. The null hypothesis can be rejected based on the given information.

Based on the given information, the test statistic (t-value) is 3.99, which indicates a significant difference between the sample mean and the hypothesized population mean.

In a directional one-sample t-test, the null hypothesis states that the population mean is equal to a specific value. However, since the calculated t-value is large and falls in the rejection region, it provides evidence against the null hypothesis.

Therefore, the appropriate decision is to reject the null hypothesis and conclude that there is a significant difference between the sample mean and the hypothesized population mean.

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PLEASE ANSWER DUE IN 9 MINS WILL GIVE BRAINLIEST!!

PLEASE ANSWER DUE IN 9 MINS WILL GIVE BRAINLIEST!!

Answers

Answer:

176in^2

Step-by-step explanation:

Total Surface Area:

2*16+4*36=32+144=176in^2

Bobby has 4 shoes and sells 5 shoes. How many shoes does Bobby have left?

Answers

Answer:

Step-by-step explanation:

4-5 would be less than 1 so it would be -1

Bobby has -1 shoes because 5 - 4 is -1

Determine the domain of the following graph:

Determine the domain of the following graph:

Answers

Answer: [-11, 11)

Step-by-step explanation:

Because the point is closed and shaded in at x = -11, we know that the value is included in the domain. So, in interval notation, we will use a "[".

Because the point is empty and not shaded in at x = 11, we know that values approaching x = 11 are included, but not x = 11 itself. So, in interval notation, we will use a ")".

What is the solution of this quadratic equation? x2 + 10 = 0

Answers

Answer:

-5

Step-by-step explanation:

put the 10 on the other side of the = wich will change it to -10 then do -10/2 and x2/2 to get x=-5

What to put in blank spaces including the y= and x+
Giving brainiest please help

What to put in blank spaces including the y= and x+ Giving brainiest please help

Answers

Answer:

Not answer but this'll help solve

Step-by-step explanation:

Divide each weight on Earth by 6 to find the weight on the moon

use corollary 2 of lagrange’s theorem (theorem 7.1) to prove that the order of u(n) is even when n . 2.

Answers

To prove that the order of u(n) is even when n > 2, we can use Corollary 2 of Lagrange's theorem (Theorem 7.1). Corollary 2 states that if G is a group and a is an element of G of finite order, then the order of a divides the order of G.

Let's consider the group G = U(n), the multiplicative group of integers modulo n, and let a = u(n), an element of G. We want to show that the order of a is even when n > 2.

By definition, the order of an element a in a group is the smallest positive integer k such that a^k = e, where e is the identity element of the group.

Since a = u(n), we have a^n ≡ 1 (mod n) by Euler's theorem. This implies that a^n - 1 is divisible by n.

Now, let's consider the order of a. Assume the order of a is odd, i.e., k is an odd positive integer such that a^k = e. This implies that a^(2k) = (a^k)^2 = e^2 = e.

Since k is odd, 2k is even. Therefore, we have found a positive integer (2k) such that a^(2k) = e, contradicting the assumption that k is the smallest positive integer satisfying a^k = e. Thus, the order of a cannot be odd.

By Corollary 2 of Lagrange's theorem, the order of a divides the order of G. Since n > 2, the order of G is even (it contains the identity element and at least one non-identity element). Therefore, the order of a (u(n)) must also be even.

Hence, we have proven that the order of u(n) is even when n > 2 using Corollary 2 of Lagrange's theorem.

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a bus drives for 3 and a half hours at an average speed of 56mph how far does the bus drive?

Answers

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

suppose you have a function of two variables, nand k; for instance h(n, k).if you are told that h(n, k)

Answers

Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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18 more than twice a number is 8

Answers

Answer:

-5

Step-by-step explanation:

-5 times 2 is -10 plus 18 is 8

HELP I WILL GIVE BRAINLIEST

Solve for x.

7x + 14 – 2x = −x + 12 – x − 19
A. x = −3
B. x = −1
C. x = 1
D. x = 3

Answers

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

X COULD BE 2 OR 7

Step-by-step explanation:

Answer:

A. x= -3

Step-by-step explanation:

firstly collect all the terms . then move the term so it'd look like 5x+14 = -2x - 7 then calculate it then it would look like this : 5x+2x = -7 -14 after you move the terms you again calculate it and then the finish product would look like this : 7x = -21 so after you get that you divide by both sides and the answer is -3 . (im sorry if that don't make sense) but the answer is A.

which of the following statements is most accurate? multiple choice question. examples of statistics include the population mean and the population proportion. a statistic is a random variable whose value depends on the chosen random sample. a statistic is a constant although its value may be unknown. we use a parameter to make inferences about the unknown sample statistic.

Answers

The most accurate statement is: "A statistic is a random variable whose value depends on a random sample chosen."

A statistic is a calculated value from a sample of data. It is a random variable as its value depends on the selected sample. For example, the sample mean is a statistic whose value depends on the specific value of each observation in the sample.

parameters are fixed values ​​that characterize the population. Usually unknown and estimated using sample data. For example, the population mean is a parameter that can be estimated using sample data.

In summary, a statistic is a value computed from sample data that is used to draw inferences about a population. Parameters are values ​​that characterize a population and are estimated from sample data.

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There's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters.

Which statement is true?

Question 6 options:

The correlation is most likely due to a lurking variable.


The correlation is most likely a causation.


The correlation is most likely a coincidence.

Answers

Note that where there's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters, then the statement that is TRUE is: "The correlation is most likely due to a lurking variable." (Option B).

What is a lurking variable?

A correlation does not imply causation, and a moderate positive correlation is not enough to establish a causal relationship between two variables.

It is possible that the correlation is due to an underlying factor (lurking variable) that affects both the length of the child's hair and the time it takes for the child to run 100 meters. To establish causality, other methods such as experimental design and statistical analysis are necessary.

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Please help me with this PLEASE!!!

Please help me with this PLEASE!!!
Please help me with this PLEASE!!!
Please help me with this PLEASE!!!
Please help me with this PLEASE!!!

Answers

Answer:  1.5

Step-by-step explanation: 4.05x3=12.15

                                             2.75x4.5=12.375  

4.5-3=1.5

                                           

Let V be the vector space of all 3 x 3 matrices with real number entries. Let Hį be the subset of V that contains all 3 x 3 triangular matrices and H2 be the subset of V that contains all 3 x 3 matrices whose traces are integers. Choose all statements that are correct. - H2 is closed under scalar multiplication. - H2 is NOT a subspace of V. - H1 is closed under scalar multiplication. - H2 is closed under matrix addition. - H is a subspace of V. - H is closed under matrix addition.

Answers

the correct statements are: H1 is closed under scalar multiplication and matrix addition, H2 is closed under scalar multiplication but is NOT a subspace of V, and H2 is NOT closed under matrix addition.

First, let's examine the properties of the two subsets, H1 and H2, in relation to the vector space V. H1 is the subset of V that contains all 3 x 3 triangular matrices, and we can see that it is closed under scalar multiplication because multiplying a triangular matrix by a scalar will still result in a triangular matrix.

Additionally, H1 is closed under matrix addition because adding two triangular matrices will result in another triangular matrix.

On the other hand, H2 is the subset of V that contains all 3 x 3 matrices whose traces are integers. We can see that H2 is closed under scalar multiplication because multiplying any matrix by a scalar will not affect the trace, so the resulting matrix will still have an integer trace.

However, H2 is not a subspace of V because it is not closed under matrix addition. Adding two matrices with integer traces may result in a matrix with a non-integer trace.

Therefore, the correct statements are: the correct statements are: H1 is closed under scalar multiplication and matrix addition, H2 is closed under scalar multiplication but is NOT a subspace of V, and H2 is NOT closed under matrix addition.

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A box of fruit candy contains 50 candy pieces in five different colors: red, orange, yellow, green, and purple. willy opened the box and found that 22% , percent of the candy pieces are purple. if the box willy opened is representative of that particular brand of fruit candy, what best estimates the total number of non-purple candy pieces in 36 boxes of the same candy?

Answers

Answer: 1,404 Non-Purple Candies

Step-by-step explanation:

First, you must figure out how many are non-purple in the box of 50:

50*0.22=11

Then, you must figure out how many are NOT purple:

50-11=39

Next, since you are trying to calculate how many non-purples are in 36 boxes of that candy, you must multiply the number of non-purple found in 1 box by 36:

39*36= 1404

So, there are 1,404 Purple Candies in 36 Boxes of Candy (approximately)

The best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

If 22% of the candy pieces in one box of fruit candy are purple, then 78% (100% - 22%) of the candy pieces are non-purple. To find the best estimate of the total number of non-purple candy pieces in 36 boxes of the same candy, we need to use proportions.

Let x be the total number of candy pieces in one box of fruit candy. Then, the number of non-purple candy pieces in one box is 0.78x. Therefore, the total number of non-purple candy pieces in 36 boxes is:

36 boxes x 0.78x non-purple candy pieces per box = 28.08x non-purple candy pieces

To find the value of x, we can use the fact that the box contains 50 candy pieces in total. Therefore:

22% of x = 0.22x purple candy pieces
78% of x = 0.78x non-purple candy pieces
Total number of candy pieces = 50

Using these equations, we can solve for x:

0.22x + 0.78x = 50
1x = 50 / 0.78
x = 64.1 (rounded to one decimal place)

Therefore, each box contains approximately 64 candy pieces. And the total number of non-purple candy pieces in 36 boxes is:

28.08x non-purple candy pieces = 28.08 x 64.1 = 1802.728 non-purple candy pieces

So the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1803 (rounded to the nearest whole number).


Let's use the terms you've provided to solve the problem step-by-step.

Step 1: Determine the number of purple candies in one box.
22% of the 50 fruit candy pieces are purple. To find this, multiply 50 by 0.22 (the decimal equivalent of 22%):
50 * 0.22 = 11 purple candy pieces

Step 2: Determine the number of non-purple candies in one box.
There are 50 fruit candy pieces in total. Subtract the 11 purple candies to find the number of non-purple candies:
50 - 11 = 39 non-purple candy pieces

Step 3: Estimate the total number of non-purple candies in 36 boxes.
To find this, multiply the number of non-purple candies in one box (39) by the number of boxes (36):
39 * 36 = 1,404

So, the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.

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Heavy children: Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in the United States was 49.3 pounds. Another NHANES survey, published in 2008, reported that a sample of 196 six-year-old girls weighed between 2003 and 2006 had an average weight of 48.8 pounds. Assume the population standard deviation is σ=15.2 pounds. Can you condude that the mean weight of six-year-old giris is lower in 2006 than in 2002 ? Use the α=0.10 ievel of significance and the p-value method with the T1-84 calculator. Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses. Compute the P-value. Round your answer to at least four decimal places. P. value =

Answers

The task is to determine if there is evidence to conclude that the mean weight of six-year-old girls in the United States was lower in 2006 than in 2002. Data from the NHANES surveys conducted

To test the hypothesis, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean weight of six-year-old girls in 2006 is not lower than the mean weight in 2002.

Alternative Hypothesis (H1): The mean weight of six-year-old girls in 2006 is lower than the mean weight in 2002.

Next, we can compute the p-value using the T1-84 calculator or statistical software. The p-value is the probability of obtaining a sample mean as extreme or more extreme than the observed sample mean, assuming the null hypothesis is true.

Using the provided data, the sample mean in 2002 is 49.3 pounds, the sample mean in 2006 is 48.8 pounds, and the population standard deviation is 15.2 pounds. We can calculate the p-value by performing a one-sample t-test, comparing the sample mean of 48.8 pounds to the hypothesized population mean of 49.3 pounds.

After calculating the p-value, we compare it to the significance level of 0.10. If the p-value is less than 0.10, we can reject the null hypothesis and conclude that the mean weight of six-year-old girls in 2006 is lower than in 2002. If the p-value is greater than or equal to 0.10, we fail to reject the null hypothesis and do not have sufficient evidence to conclude that the mean weight is lower.

Note: Since the specific p-value calculation requires detailed statistical calculations, I am unable to generate the exact value without access to a calculator or statistical software.

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Twice during the assembly, a student is chosen at random to assist with the presentation. after the first student has finished assisting, the student returns to the group and can be chosen a second time. what is the probability that the first student chosen is a senior and the second student chosen is a sophomore?.

Answers

Using it's concept, it is found that the probability that the first student chosen is a senior and the second student chosen is a sophomore is given by:

\(p = \frac{11}{320}\)

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, we have that there are:

31 juniors, 10 sophomores, 17 juniors, 22 seniors.

Then:

Out of 31 + 10 + 17 + 22 = 80 students, 22 are seniors, hence the probability that the first student is a senior is given by \(p_1 = \frac{22}{80} = \frac{11}{40}\).All students can be chosen again, hence the probability that the second student is a sophomore is given by \(p_2 = \frac{10}{80} = \frac{1}{8}\).

The events are independent, hence the probability of both is given by:

\(p = p_1p_2 = \frac{11}{40} \times \frac{1}{8} = \frac{11}{320}\)

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there are 12 students on the academic team. the team advisor randomly chooses 4 students for the next competition. what is the probability that marcus, adam, brittany, and luisa are chosen in any order?

Answers

The probability that Marcus, Adam, Brittany, and Luisa are chosen in any order can be calculated using the concept of combinations, resulting in a probability of 1/495.

To determine the probability of Marcus, Adam, Brittany, and Luisa being chosen in any order, we need to consider the total number of possible outcomes and the number of favorable outcomes. The total number of ways to choose 4 students out of 12 can be calculated using the combination formula: 12C4 = 12! / (4!(12-4)!).

To find the number of favorable outcomes, we need to consider that Marcus, Adam, Brittany, and Luisa can be chosen in any order. Since there are 4 students, there are 4! = 4 * 3 * 2 * 1 = 24 possible permutations of their selection.

Thus, the probability of choosing Marcus, Adam, Brittany, and Luisa in any order is given by: 24 / (12! / (4!(12-4)!)) = 1 / 495.

Therefore, the probability that Marcus, Adam, Brittany, and Luisa are chosen in any order is 1/495. This means that out of all the possible combinations of 4 students, only one combination will include Marcus, Adam, Brittany, and Luisa in any order.

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The fraction of area model A is 4 12 . The fraction of area model B is 3 9 . Compare the two fractions and write an equation or inequality to show how the two fractions are related. Use <, >, or =. Two rectangles are shown. The left rectangle is divided into 12 equal parts and arranged in 3 rows of 4 cells each. 4 of these cells are colored yellow. The right rectangle is divided into 9 equal parts and arranged in 3 rows of 3 cells each. 3 of these cells are colored yellow.

Answers

The two fractions are related by the substitution property of equality.

How to compare fractions?

Model A = 4/12

= 1/3

Model B = 3/9

= 1/3

So,

4/12 = 3/9

Each area model shows 3 rows of cells.

In each model, one of those three rows is colored yellow. That is, each model represents the fraction is equivalent to 1/3

It can be concluded that the relation between the given fractions is an application of the substitution property of equality.

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Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 and deposits $66 per month into his account. Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 and deposits $66 per month into his account

Answers

it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit amount at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

To solve this problem, we can start by finding the monthly difference in their deposits:

Muhammad: $59/month

Connor: $66/month

Since Muhammad's monthly deposit is lower than Connor's, we need to find out how many months it will take for Muhammad's balance to catch up to and surpass Connor's. We can set up an equation to represent this situation:

$158 + $59x = $74 + $66x

where x is the number of months elapsed.

We can simplify and solve for x:

$158 + $59x - $74 - $66x = 0

$84 - $7x = 0

$7x = $84

x = 12

Therefore, it will take 12 months for Muhammad's account balance to surpass Connor's, assuming they continue to deposit money at the same rate. After 12 months, Muhammad's balance will be $950 ($158 + $59x) and Connor's balance will be $896 ($74 + $66x).

the complete question is :

Muhammad has $158 in his bank account and deposits $59 per month into his account. Connor has $74 in his bank account and deposits $66 per month into his account. If Muhammad and Connor continue to deposit money into their accounts at the same rate, how long will it take for Muhammad's account balance to surpass Connor's?

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4 square miles of land is separated into sections that each have an area of 1/2 square mile

Answers

The number of sections that each have an area of 1/2 square mile will be 8.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

4 square miles of land are separated into sections that each have an area of 1/2 square mile.

Then the number of the equal section is given as,

⇒ 4 / (1/2)

⇒ 8 section

The number of sections that each have an area of 1/2 square mile will be 8.

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$2.98 for 15.5 ounces of oreos

Answers

Answer:

$46.19

Step-by-step explanation:

the measure of an angle in standard position is given. find two positive angles and two negative angles that are coterminal with the given angle.

Answers

To find coterminal angles, you have to either add or subtract 2π. In this case, you would use 8π/4 so there is a common denominator.

Positives:

-3π/4+8π/4 = 5π/4

5π/4+8π/4 = 13π/4

Negative:

-3π/4-8π/4 = -11π/4

-11π/4-8π/4 = -19π/4

What is the measure of an angle?

In geometry, an angle measure is the length of the angle formed by two rays or arms intersecting at a common vertex.

Using a protractor, angles are measured in degrees (°). Joseph Huddart created the protractor in 1801. It was a more sophisticated protractor.

The angle created at the center of a circle is measured in radians, the unit of angular measurement. It is described as an angle that subtends from a circle's center and intercepts at an arc with a radius equal to the circle's radius. 57.3° is equal to one radian.

Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.

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Let a, b, and c be distinct points. If Pr({a, b}) = Pr({a, c}) = Pr({b, c}) and Pr({a, b, c}) = 1 what is Pr({a})
1/6
1/3
1/2
2/3
It cannot be determined from the information given.

Answers

If Probability of ({a, b}) = Pr({a, c}) = Pr({b, c}) and Pr({a, b, c}) = 1 .

Pr({a}) = 1/3

What is probability?

The  probability of an event is described as  a number that indicates how likely the event is to occur which  is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.

a, b, and c are different and we have that

Pr({a, b}) = Pr({a, c}) = Pr({b, c}) = 1/3,

Pr({a, b, c}) = 1.

We now Substitute these values and get the following:

Pr({a}) = 1 - 2Pr({a, b}) - 2Pr({a, c}) + 2Pr({a, b, c})

Pr({a} = 1 - 2/3 - 2/3 + 2 = 1/3

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Two less than the quotient of a number and 8 is 1/4.Find the number

Answers

For the given problem:

Let the number = x

Two less than the quotient of a number and 8 is 1/4

so, we can write the following expression:

\(\frac{x}{8}-2=\frac{1}{4}\)

Now, solve the equation to find (x)

Multiplying by (8) to eliminate the denominators:

\(\begin{gathered} 8\cdot(\frac{x}{8}-2)=8\cdot\frac{1}{4} \\ \\ 8\cdot\frac{x}{8}-8\cdot2=\frac{8}{4} \\ x-16=2 \end{gathered}\)

Add (6) to both sides:

\(\begin{gathered} x-16+16=2+16 \\ x=18 \end{gathered}\)

So, the answer will be the number is 18

Write an equation for the nth term of each arithmetic sequence. Then find the 12th term of the sequence.
as = 14, d = -3

Answers

We need to know about arithmetic sequence to solve this problem. The equation for the nth term of each arithmetic sequence is a+(n-1)d and the 12th term of the sequence is -19.

An arithmetic sequence is a sequence of numbers where the difference between consecutive numbers is constant. If a,b and c are in arithmetic sequence then we can say that 2b=a+c. If the starting value of an arithmetic sequence is a and the difference between every consecutive number is d, then we can write the second number as a+d, the third as a+2d and so on. So for the nth term of an arithmetic sequence the equation is

nth term=a+(n-1)d where a is the starting value, d is the constant difference

We have been given the value of a and d, a=14 and d=-3, we need to find the value of the 12th term of the sequence.

12th term= a+(n-1)d= 14+(12-1)x(-3)=14-33=-19

Therefore we found out using the concept of arithmetic sequence that the equation for the nth term is a+(n-1)d and the 12th term of the sequence is -19.

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write the equation of the parabola that has its x-intercepts at (-1.6, 0) and (-3.2, 0) and its y-intercept at (0, 25.6)

Answers

The equation of the parabola that has its x-intercepts at (-1.6, 0) and (-3.2, 0) and its y-intercept at (0, 25.6) is  5x² + 8x - 25.6

How to write the equation of the parabola with the x intercepts at (-1.6, 0) and (-3.2, 0)

The x intercept refers to the value of x when y = 0 this otherwise known as the roots of the polynomial equation.

The intercept form of parabolic equation is

y = a(x - p)(x - q)

where

p and q are roots

a = constant

writing the equation at (-1.6, 0), (-3.2, 0)

y  = a( x + 1.6 ) ( x + 3.2 )

passing through point (0, 25.6)

25.6  = a( 0 + 1.6 ) ( 0 + 3.2 )

25.6 = 5.12a

a = 5

substituting into the equating gives

y = a(x - p)(x - q)

y = 5( x + 1.6 ) ( x + 3.2 )

expanding the equation gives

= 5(x² + 3.2x - 1.6x - 5.12)

= 5(x² + 1.6x - 5.12)

= 5x² + 8x - 25.6

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