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The sum of first five or twelve term in the A.P given the value 60.

The term AP refers a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value.

Here we have given that  A. P. 16,14,12,.

And we need to find the number of term to get the value of 60.

While we looking into the given question we have identified that the  common difference d of the A.P. is − 2

Here we also know that the terms of the A.P. are in descending order.

Now, we have to take n = 5  then then first 5 terms are 16,14,12,10,8.

Here we have identified that the sum is 60.

Similarly, here by taking n = 12 , then the last 7 terms ( 12 − 5 ) (12-5) are 6 , 4 , 2 , 0 , − 2 , − 4 , − 5 6,4,2,0,-2,-4,-5

Here we have identified that the sum of these seven terms is 0.

Therefore, sum of first 12 terms is also 60.

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The direct proportion means that two numbers increase or decrease together and in the same ratio and the inverse proportion means that if one number increases the other decreases and vice versa.

Direct Proportion: Two numbers or quantities are said to be in direct proportion if they increase or decrease together in the same ratio.

If a and b are in direct proportion, they can be written as

a ∝ b

Inverse Proportion: Two numbers or quantities are said to be in inverse proportion if one increases when the other decreases and vice versa.

If a and b are in inverse proportion, they can be written as

a ∝ 1 / b

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chi-square test statistic is statistically significant.

What is Test Statistic?

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

To determine whether the amount of television a person watches is related to their liking for bourbon whisky, the researcher could use a chi-square test of independence.

The chi-square test is a statistical test that is used to determine whether there is a significant association between two categorical variables.

In this case, the two variables of interest are television watching (more or less than 2 hours per day) and liking for bourbon whisky (measured using a Likert scale).

The chi-square test statistic is calculated based on the observed frequencies of each combination of television watching and liking for bourbon whisky, and it is used to determine whether the observed frequencies are significantly different from the frequencies that would be expected if the two variables were independent.

If the chi-square test statistic is statistically significant, it indicates that there is a significant association between the two variables, and the researcher can conclude that television watching is related to liking for bourbon whisky.

Hence, chi-square test statistic is statistically significant.

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Answer:

c is the closest

Step-by-step explanation:

it should take about 2 years

The value of 3 √ 4 √ x is 48

A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root. Squares and square roots are hence related concepts.

Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.

As per the question, 3 √ 4 √ x when x =4096

first we need to calculate square root of 4096 by  prime factorisation method

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)

√4096 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))

√4096 = 2 × 2 × 2 × 2 × 2 × 2

√4096 = 64

Therefore the square root of 4096 = 64.

x=64

now putting the value of x in  3 √ 4 √ x

= 3 √ 4 √ 64

= 3 √  256

=3×16

=48

so the value of 3 √ 4 √ x  is 48

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Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.

4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

4096 = (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2)

√4096 = √((2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2) × (2 × 2))

√4096 = 64

x=64

= 3 as 4 as 64

= 3 as  256

=3×16

=48

The expression 2x² + 7x + 3 can be factored as (2x + 3)(x + 1).So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).

To factor this expression, we can use the method of grouping. First, we rewrite the expression as:

2x² + 7x + 3

Then, we group the first and last terms and the middle term:

(2x² + 3) + (7x)

Next, we try to factor in the first group. Since 2x² + 3 can be rewritten as (2x + 1)(x + 3), we can factor the entire expression as:

(2x + 1)(x + 3) + (7x)

Finally, we can rearrange the terms to get the factored form:

(2x + 7x) + (1)(3)

This simplifies to:

(2x + 7x)(1) + (3)

Which is equal to:

(2x + 7x + 3)

And finally:

(2x + 7x + 3) = (2x + 3)(x + 1)

So, the factored form of 2x² + 7x + 3 is (2x + 3)(x + 1).

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The sum of the interior angle measures of the given polygon will be equal to  360°.

A polygon is described in geometry as a compact, two-dimensional shape having three or more straight lines.

Poly, which means "many," and gon, which means "angle," make up the Greek word "Polygon." Polygons of several kinds can be seen all around us.

As per the given information in the question,

Use the formula of the sum of an interior angle of the polygon,

180(n - 2)     (i)

Here, n is the number of sides.

As per the given figure, n = 4

Put n = 4 in equation (i)

180 (4 - 2)

180 (2)

= 360°

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An example of geometric term is ar².

When a set of numbers follow a particular order, they are said to be in sequence.

A set of numbers are said to be in geometric sequence if the ratio between second and first term is same as the ratio between third and second term and so on. The geometric sequence is presented as

Geometric Sequence = a, ar, ar², ar³,  ......, arⁿ⁻¹, arⁿ.

where,

The first term is a.

Every two consecutive terms, r is the common ratio.

The number of terms is n.

Let us take an example.

The numbers 2, 6, 18, 54 are in geometric sequence because 6:2 = 18:6 = 54:18 and when we will write it as 2 + 6 + 18 + 54, it will become a geometric series and 2, 6, 18, 54 are geometric terms.

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An example of inequality is 3 < 5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.

They are denoted by the symbols ≥ < > ≤. An example of inequality is 3 < 5. This simply means that 3 is less than 5.

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Answer:

m = -3

Step-by-step explanation:

The slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 30 and the x decrease by 10, so the slope is

-30/10 = -3

So, m = -3

Answer:

Slope = -3

Step-by-step explanation:

Formula of slope,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Now the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (11 -(-19))/(-12 -(-2))

→ m = (11 + 19)/(-12 + 2)

→ m = 30/-10

→ m = -(30/10)

→ [ m = -3 ]

Hence, the slope is -3.

Answer:

PROPORTION:

13:6 = x/27

6x = 27(13)

6x = 351

x = 58.5

Therefore, cucumber salad need 58.5 cups of tomatoes to make 27 servings.

Step-by-step explanation:

Yes, the expression represented as negative 1 is a number

From the question, we have the following parameters that can be used in our computation:

Is negative 1 a number?

As a general rule

Numbers are expressions, words and representations that have an arithmetic value

Using the above as a guide, we have the following:

negative 1

Mathematically, this can be represented as

-1

-1 is an integer

Hence, negative 1 is a number

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Answer:

-4, 0.046, 1/10, 0.46, 4/6

Step-by-step explanation:

First, we know that -4 is the least because it is a negative number.

Next, we need to convert the fractions to decimals. 1/10 is 0.1, and 4/6 is 0.66.

Then, we order the decimals.

0.046 is the next smallest, because it is a hundredth, and the remaining decimals are tenths and therefore greater.

We compare the remaining decimals, which are 0.10, 0.46, and 0.66. These are easy to compare and order.

Now, we've compared and ordered all the numbers. We can convert the fractions back into their original form.

The total number of books Lori owns is 45.

Let x be the total number of books.

Mark owns 1/4 of x

Kevin own 1/3 of x

Kevin owns 9 more than Mark, so;

1/4x - 1/3x = 9

Multiplying both sides by 12

4x - 3x = 108

x = 108

The total number of books is 108

but;

Mark owns 1/4 of x = 1/4 x 108

Mark = 27

while Kevin owns 1/3 x 108

Kevin = 36

Therefore, Lori would own

108 - 36 - 27 = 45

Lori's number of books will be 45.

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The work out fraction that is halfway between 0 and 3/4 is 1/2

In math, what are fractions?

A fraction is a part of the whole. In a quotient, where the numerator and denominator are divided, the number is mathematically expressed. In a straightforward fraction, both are integers. A complicated fraction has a fraction in either the numerator or denominator. In a correct fraction, the numerator is smaller than the denominator.

What seven types of fractions are there?

Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.

A midway fraction is defined.

Halfway of Two Fractions is what? Exactly halfway between 2/3 and 3/4, a fraction cannot be smaller than 2/3 or larger than 3/4. Nothing is halfway but the average of two fractions.

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To find holes, look for places where the function is undefined. To find asymptotes, look for where the function approaches infinity or negative infinity. Additionally, look for places where the function has a vertical or horizontal line, as these are also potential asymptotes.

To find holes in a function, look for places where the function is undefined. This can occur when the denominator of a fraction is equal to zero, as the fraction becomes undefined. Additionally, look for places where the function is not continuous, as this can indicate a hole in the graph. To find asymptotes, look for places where the function approaches infinity or negative infinity. This can occur when the denominator of a fraction is equal to zero and the numerator is not. Additionally, look for places where the function has a vertical or horizontal line, as these can also indicate potential asymptotes. Asymptotes are also present when the degree of the numerator is higher than the degree of the denominator. By looking for these areas, you can identify potential holes and asymptotes in a function.

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Answer:

Step-by-step explanation:

New houses in a neighborhood are selling for $175,000. A down payment of $18,000 is

required and a 25-year mortgage at an annual interest rate of 8% is available. Find the

monthly mortgage payment.

Selling price = 175000

down payment = 18000

interest rate = 8% = 0.08

time = 25 years = 300 months (25 * 12)

First, we will compute the total interest for the loan

I = P * R * T

I = (175000 - 18000)(0.08)(25)

I = (157000)(0.08)(25)

I = 314000

The value of x is 31 mm, which  makes given prisms similar.

Similarity of a triangle is the ratio of their corresponding sides or angles which are equal.

In the given prisms,

The length of the large prism = 29 mm,

And width = x mm.

In small prism, the length =  14.5 mm,

And width = 15.5 mm.

According to given condition,

Both the prisms are similar.

By property of similarity,

The in similar figure, the ratio of corresponding sides are equal.

For the given prisms,

29 / x = 14.5 / 15.5

x = 2 × 15.5

x = 31

The required value of x is 31 mm.

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The triangles are congruent if there are two pairs of corresponding angles and one pair of corresponding sides.

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Answer:

Step-by-step explanation:

Answer:

  A = 14

  B = 4

Step-by-step explanation:

You want to know the values of A and B consistent with ∆EFG being congruent to ∆HJI, given that EF=14B-15, FG=9A-28, HJ=7B+13, JI=7A.

Corresponding sides of congruent triangles have the same measure, so we have ...

  FG = JI

  9A -28 = 7A

  2A = 28 . . . . . . add 28-7A

  A = 14 . . . . . divide by 2

and ...

  FE = JH

  14B -15 = 7B +13

  7B = 28 . . . . . . . . add 15-7B

  B = 4 . . . . . . divide by 7

The values of A and B are 14 and 4, respectively.

The figure's circumference, as seen in the diagram, is 60.84 m.

What are some instances of perimeters?

The perimeter of an object is the space surrounding it. For instance, your house has a fenced-in yard. The perimeter is the length of the fence. If the yard is 50 feet by 50 feet, your fence is 200 feet long.

The formula below is used to determine the figure's perimeter.

Formula:

Equation 1: P = 2L + W + W / Equation 1:

P = The figure's perimeter

L is the figure's length.

W is the figure's width.

Considering the query,

Given:

L = 15 m\sW = 12 m\sπ = 3.14

Replace the values in equation 1 with these ones.

P = (15×2)+12+(12×3.14/2)

P = 30+12+18.84

P = 60.84 m

As a result, the figure's perimeter is 60.84 meters.

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Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary  when calculated using discriminant.

In mathematics, the number that results in the original number when it is multiplied by itself is called the root.

We can find nature of root using discriminant.

B² - 4AC = 0 ----> Roots are equal ,real & rational

B² - 4AC > 0 , and also a perfect square --> Roots are real , distinct & rational

B² - 4AC >0 ,but not a perfect square -----> Roots are real, distinct & irrational

B² - 4AC <0 , ---> Roots are imaginary

B² - 4AC >= 0 ---> Roots are real

Given 2x² - 4x + 3 = 0

Now, Calculate Discriminant,

Here

B = -4

A = 2

C = 3

==> B² - 4AC

= (-4)² - 4 * 2 * 3

= 16 - 24

= -8 < 0

Discriminant is negative

Nature of roots of equation, 2x² - 4x + 3 = 0 be imaginary .

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Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

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Answer:

i think 2.oo or 7.51 not sure

Answer:

the answer to this is a.

Step-by-step explanation:

Interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

Higher Placement The College Board's Advanced Placement Program makes a college-level course and exam in United States Government and Politics available to high school students.

By organizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues, interest groups enable citizen participation in governance.

a group of individuals united by a shared interest or objective and working to sway public policy. group leaders. As adolescents gain knowledge, they frequently form their own groups. government.

Therefore, interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

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Observing the polynomial and the coefficient provided, The leading coefficient of the polynomial function is the coefficient of the highest degree term.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

polynomial of the form [tex]ax^{2}+bx+c[/tex].

Since, The degree is 2 and the coefficient of [tex]x^{2}[/tex] is a.

The leading coefficient is 'a'.

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According to the value of scale factor, we have to prove that the two shapes are similar.

The term shape in math is defined as the object that the form of an object or its outline, outer boundary or outer surface.

Here we have to find the way to prove two shapes are similar.

Here we have given that there are two shapes are given, in order to prove that those two shapes are similar, we must consider that the two shapes are considered to be "similar figures" if they have the same shape, congruent corresponding angles which means the angles in the same places of each shape are the same and equal scale factors.

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The examples of SAS (Statistical Analysis System) are Mathematical Programming

SAS is a statistical software suite developed by the SAS Institute for data management, advanced analytics, multivariate analysis, business intelligence, criminal investigations, and predictive analytics. It is used for

Examples of SAS are :

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