Annabelle records the length, in inches, of a colored pencil over time. Review the table showing her data.

Which description best fits the regression model for the data?

The sum of the first n terms of an arithmetic sequence can be proven using the principle of induction. We assume the formula holds for n = k, and then show it holds for n = k+1, thus showing it holds for all values of n.

The sum of the first n terms of an arithmetic sequence can be determined using the formula S_n = (n/2)(a_1 + a_n), where a_1 is the first term and a_n is the nth term.

We can prove this formula using the principle of induction.

Base Case: Let n = 1. Then S_1 = (1/2)(a_1 + a_1), which simplifies to S_1 = a_1. This is the same result we would get if we added the first term of the sequence.

Inductive Step: Assume that the formula holds for n = k.

Then S_k = (k/2)(a_1 + a_k).

Now consider n = k+1.

S_k+1 = (k+1/2)(a_1 + a_k+1)

= (k/2)(a_1 + a_k) + (1/2)(a_1 + a_k+1)

= S_k + (1/2)(a_k+1 - a_1)

= S_k + (1/2)(a_k+1 - a_k) + (1/2)(a_k - a_1)

= S_k + (1/2)(a_k+1 - a_k) + [S_k - (k/2)(a_1 + a_k)]

= (k+1/2)(a_1 + a_k+1)

= S_k+1

Therefore, we have shown that if the formula holds for n = k, then it also holds for n = k+1. By the principle of induction, the formula holds for all n.

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On solving the provided question, we can say that the sample size would have to be multiple by 4  = 4048

The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.

the sample size would have to be multiple by 4

n = 1012

n X 4

= 1012 X 4

= 4048

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The numeric values of the function f(x) = -x - 2 are given as follows:

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = -x - 2.

The numeric values are found replacing the lone instance of x by the input value, hence they are given as follows:

The problem asks for the numeric values for the function f(x) = -x - 2, with inputs x = -5, x = -3 and x = -1.

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Using commutative property of addition, the expression 3T 1,892 lb + 1,325 lb is equal 4.5T, 217 lb

A mathematical procedure called adding expressions entails merging two or more expressions to create a new expression. A reduced version of the original expressions is produced by adding expressions, which works similarly to adding integers.

We merge similar phrases while adding expressions. When a variable is raised to the same power, terms are said to be like terms. Because they both have the same variable (x) raised to the same power, for instance, 2x and 3x are similar phrases (1).

It's crucial to remember that the commutative characteristic of addition ensures that the order of the terms has no impact on the outcome when adding or subtracting expressions.

In conclusion, adding expressions is a mathematical operation that combines two or more expressions to create a new expression; it is comparable to adding integers. We merge similar phrases while adding expressions. When a variable is raised to the same power, terms are said to be like terms. The commutative property of addition accounts for the fact that the outcome is unaffected by the order of the terms.

In this problem, we have two expressions which we need to add together.

NB;

So, in the given expression;

3T 1,892 lb + 1,325 lb = 3T 3217lb

But 1 pounds = 0.5 ton

3000 pounds = 1.5 ton

3T 1,892 lb + 1,325 lb = 4.5T, 217 lb

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The value of x is 7 from the given figure.

What is Triangle ?

Triangle can be defined in which three sides , three angles and the sum of three angles is always is 180 degrees.

From the given triangle ,

Let the triangle be ABC

where A = 60 and B = 30 and C = 90

CA = 7[tex]\sqrt{3}[/tex]

CB = x .

sin60 =  7[tex]\sqrt{3}[/tex]  /x

[tex]\sqrt{3}[/tex] / 2  =  7[tex]\sqrt{3}[/tex]  /x

1/7  = 2 * x

x = 7 * 2

x = 14

In triangle ABC ,

AC^2 + CB ^ 2  = AB ^2

7[tex]\sqrt{3}[/tex]  ^2 + CB^2 = 14*14

CB^2 = 196 - 149

CB^2 = 49

CB = 7

Hence, The value of x is 7  from the given figure.

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Considering the diagram of the bike path crosses the angle measures are calculated to be

x = 21 degrees

< KMH = 96 degrees

According to the diagram, the angle at the intersection of the road shows that

84 degrees = 4x

The angles are equal based on the vertical angle theorem

solving for x

84 degrees = 4x

4x = 84

x = 84 / 4 = 21

x = 21 degrees

solving for < KMH

< KMH and 84 are supplementary angles

< KMH + 84 = 180

< KMH = 180 - 84

< KMH = 96 degrees

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Answer:

Step-by-step explanation:

7.8, 7/29, 1234/21, 11.1212, 9.8, 76/1112

Integers can only be positive numbers, negative, non negative or 0.

Answer: 20 ( Choice A )

Step-by-step explanation: You can prove that triangle RTS and triangle RTU are the same using the Side-Angle-Side method, so ultimately, side RS should equal RU. Therefore, 8x = 6x + 5.

x should equal 2.5. The question is asking you how long side RU is, simply plug in 2.5 and you get 20.

Answer:

Step-by-step explanation:

Basically, because till x = 6, f(6) was less than 0.

They are asking the value of f(x), not x.

Thanks

From Quiana's perspective, the net change in the loan during the last 5 months is $1237.15.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.

Here,

15234.68-247.43*5=13997.53

Net change

= Initial loan amount - current balance

= $15,234.68 - $13,997.53

= $1237.15

The net change to the loan from Quiana’s perspective over the past 5 months is $1237.15.

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Answer:Your mom

Step-by-step explanation:big

Answer:

Look, I don't know how to tell the answers by looking at the squares but I can tell you how to do it.

a) Subtract the number on the left with the number on the top, pretty simple, i am sure u can do that.

b) After you have done that, count how many negative scores you got and divide that by 9.

c)Finally, count all the numbers more than 3 again and divide it by 9.

Note: 9 here is the total number of outcomes.

Thanks

At the highest level of discrete value two kinds of data which are  exists as quantitative and qualitative.

Quantitative data which deals with numbers and things that can be measure objectively that are dimensions such as height, width, and length. Temperature as well as  humidity. Prices. Area and volume. Qualitative data deals with characteristics and descriptors that can't be easily measured, but can also be observed subjectively such as smells, tastes, textures, attractiveness, and color. if we measure something and give it a number value, we create as  quantitative data. When we classify or judge something, we create qualitative data.  hence  the highest level of data are also different types of quantitative and qualitative data. There are two types of quantitative data, which is also said  as numeric data of continuous and discrete. in general rule, counts are discrete and measurements are continuous. Discrete data  count that can't be made as more precise. Typically it involves the number of  integers. For  at instance

Continuous data, on the other hand, of variable  could be divided and reduced to maximally of  finer and finer levels.

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As per the concept of probability that it takes three rolls until the player rolls doubles is 0.11574 and this can be determined by using the given data.

In math the term probability of an event is defined as nothing but a number between 0 and 1 where zero shows the impossibility and one shows the certainty.

Here we have given that a certain board game, here the player rolls two fair six-sided dice until the player rolls doubles.

And here we know that the probability of rolling doubles with one roll of two fair six-sided dice is 1/6.

Here first we need to determine the probability of rolls to obtain doubles in each roll.

That can be calculated as ,

=> 1 - 1/6 = 5/6

Then the fails in the second roll is calculated as,

=> 1 - 1/6 = 5/6

Then the third roll the player rolls doubles that is calculated as,

=> 1/6

So, the probability of requiring 3 rolls until getting doubles will be calculated as

=> 5/6 x 5/6 x 1/6

=> 25/216

When we simplify this one then we get,

=> 0.115

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The triangles ABC and CED are similar by none.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The figure in shown in image.

We know that;

Two triangles are similar if there corresponding sides are in proportion.

So, In triangles ABC and CED;

The ratio of corresponding sides are equal to each other.

Hence, By the options, we get;

The triangles ABC and CED are similar by none.

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Answer:

C. 8 : 1

Step-by-step explanation:

A unit rate is a ratio of a number to one.

To make both sides of the given ratio:

[tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex]

whole numbers (and make the right side 1), simply multiply both sides by the Least Common Multiple (LCM) of the denominators.

To find the LCM of two numbers, list out their prime factorizations and then multiply the highest power of each distinct prime number present.

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5 = 5

20 = 4 * 5

LCM(5, 20) = 4 * 5 = 20

The LCM of 5 and 20 is 20.

Next, we need to multiply 20 by both sides of the ratio.

[tex]20\left(\dfrac{2}{5}\right) : \left(\dfrac{1}{20}\right)20[/tex]

Then, simplify.

[tex]\dfrac{40}{5} : 1[/tex]

[tex]8 : 1[/tex]

So, the unit ratio of [tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex] is 8 : 1.

Answer:

17562 pounds

Step-by-step explanation:

16000*96%=15360. 15360*96%=14745.6. 14745.6*106%=15630.336. 15630.336*106%=16568.1562. 16568.1562*106%=17562.2456. 17562.2456 approximately equals 17562 pounds.

The solution of the linear inequality 2x + 8 > x + 10 > 3x + 9 is:

X>2 and X<1/2

When two mathematical expressions or two numbers are compared in an unequal way, it is called an inequality in mathematics. Inequalities can generally be classified as either numerical, algebraic, or a combination of the two. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, which is the case in a linear inequality, which is an inequality involving at least one linear algebraic expression.

step1:

2x + 8 > x + 10 > 3x + 9

2x+8>x+10 and  x+10>3x+9

2x + 8 > x + 10 :X>2

X+10>3X+9:X<1/2

Step2:

X>2 and X<1/2

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Answer: 1: x = 2y - 1 This equation shows that the value of x is always 2 times the value of y minus 1.

2: y = 3x + 3 This equation shows that the value of y is always 3 times the value of x plus 3.

3: y = (x/4) - 1 This equation shows that the value of y is always the value of x divided by 4 minus 1.

4: y = x-5 This equation shows that the value of y is always the value of x minus 5.

Answer: 45

Step-by-step explanation:

Answer:

34 successful free throws out of 120

Step-by-step explanation:

We can use the 28% free throw rate to predict Jai's success in shooting 120 free throws.  If the 28% was calculated from throws made under similar circumstances (e.g., during an actual game), then we can predict that he'll also hit 28% of the 120 attempts:

Likely free throw successes = (28%)*(120)

  (0.28)*(120) = 33.6 successful free throws out of 120.  We need to round 33.6 to the nearest whole number, which makes it 34 successful free throws out of 120.

Answer:

Step-by-step explanation:

It is difficult to determine the rule for the table without further context or information. However, based on the pattern in the table, it appears that the rule for generating the second number in each row is to add 2 to the first number in that row. The rule for generating the third number in each row is to add 6 to the second number in that row. The fourth number is the sum of the first and the third number in that row.

The best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24 are x = 43 and y = 22

From the information given, we have the expressions;

This is represented as;

x - y = -65

x + 3y = 24

Make 'x' the subject from equation 1

x = -65 + y

Now, substitute the expression into equation (2), we get;

-65 + y + 3y = 24

collect the like terms

4y = 24 + 65

Add the like terms

4y = 89

Divide the values by the coefficient of y

y = 89/4 = 22

Substitute the value in eqation3

x = -65 + 22

Add the values

x = 43

Hence, the values are 43 and 22

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The curve is concave upward for t values greater than zero, according to the assertion made.

Curve, An abstract phrase used to characterize the trajectory of a series of movements particle in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The IS curve displays combinations of borrowing costs and production levels where anticipated expenditure and income are equal. The many interest and income configurations along which is something the goods market is still in equilibrium are represented by the IS Curve.

dx/dt = e^t

dy/dt = -te^-t + e^-t

so dy/dt X dt/dx = dy/dx= -te^-t + e^-t /e^t = -t e^(-2t) + e^(-2t)

d2y/dx2 = -dt/dx e^(-2t) +2 t e^(-2t) dt/dx -2e^(-2t) dt/dx

= -e^(-3t) +2te^(-3t) -2e^(-3t)

-t e(-2t) + e(-2t) >0 for curved dy/dx >0

=> t<0 the curve is concave.

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Answer:

x=6

Step-by-step explanation:

Expand brackets:

2x-12=12

This is because 2 times x=2x and 2 times -6= -12

Add 12 to the right side to cancel out the -12 on the left.

2x-12+12=12

Simplify to get 2x=12

Divide by 2 to get x=6

Answer:

125 pounds = 2500 five pence

Answer:

Step-by-step explanation

£1.00=100p

Answer:

a) let 's' = number of bags of snacks

b) let 's+50' = number of bags of beverages

s + s+50 = 400

Step-by-step explanation:

a) let 's' = number of bags of snacks

b) let 's+50' = number of bags of beverages

s + s+50 = 400

solve:

2s + 50 = 400

2s = 350

snacks = 175

beverages = 175+50 or 225

total = 400

Therefore , as a result, the answer to the provided median problem is that the median will range from 38.

The median value is the number that exactly lies in the middle of a dataset that has been arranged. The gap between the minimum and maximum 50% of the data is a maximum likelihood measure or average. Depending on whether you have an odd or possibly even amount of data points, different formulas are used to calculate the median and mode.

Here,

Given the values:

50,42,32,35,41,44,24,46,31,47,36,32,30,44,22,47,31,56,28,37,49,28.42,38 and 45

The following is what we have: => (50+42+32+35+41+44+24+46+31+47+36+32+30+44+22+47+31+56+28+37+49+28.42+38 + 45) /25 = 37.88

The median will reach around 38.

As a result, the answer to the provided median problem is that the median will range from 38.

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The complete question is "A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given: 50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 The following histogram is a representation of the data. Calculate the median ages"

Amy can use a one-sample z-interval to estimate the true proportion of lids in the population of 1,000,000 that have the defect.

Sample can refer to an example of a particular item or type of thing. It can also refer to a section of a population that is chosen in order to represent the whole group. When used in research, samples are used to make conclusions about a population as a whole. Samples are also often used to test products or services in order to assess their quality or performance.

First, she will calculate the sample proportion of lids with the defect by dividing the number of lids in the sample with the defect (555) by the total number of lids in the sample (100,000). This sample proportion is 0.00555.

Next, Amy will calculate the standard error of the sample proportion. This is calculated by taking the square root of the sample proportion multiplied by (1 - sample proportion) divided by the sample size. The standard error for this sample is 0.00023.

Finally, Amy can calculate the one-sample z-interval. This is done by subtracting the standard error from the sample proportion and adding it to the sample proportion. This gives a one-sample z-interval of 0.0053 to 0.0058.

This one-sample z-interval tells Amy that she can be 95% confident that the true proportion of lids with the defect in the population of 1,000,000 is between 0.0053 and 0.0058.

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