Which graph represents the solution set of the system of inequalities?
y < -3x-2
y ≤ x-2

Answer: t is the dependent variable  and x the independent variable

Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.

x is the independent variable as we can use whatever values we want for x it is not affected by t

By using the division algorithm to divide 116 by 3 will be 38.

The given integers a and b are 116 and 3 respectively.

Let q be the counter variable and r be the variable to store the new dividend after each loop.

Division algorithm,

If a<b

return 0;

else

q = 0;

r = a;

repeat

q = q+1;

r = r-b;

until r<b;

return q, r;

Working:

116 is not less than 3, implies

r = 116 -3 = 113

q = 0+1=1

Repeating until we get q = 38, r = 2 = a

2<3, hence returns q = 38, r =2

The question is incomplete, the complete question is:

use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.

(a) q = 39   (b) q =32   (c) q = 38

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In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.

What is an Agreement?

This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.

Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.

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Answer:

one 2

one 3

two 4's

one 5

one 6

Step-by-step explanation:

We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.

[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:

[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]

[tex]_4C_2=\dfrac{24}{2(2)}[/tex]

[tex]_4C_2 = 6[/tex]

So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:

(1, 3)     (3, 5)     (5, 7)

(1, 5)     (3, 7)

(1, 7)

Then, we can calculate the mean, or average, of each.

2           4           6

3           5

4

Finally, we can conclude that the distribution of the means for each possible set of number pairs is:

one 2

one 3

two 4's

one 5

one 6

The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

What is an equation of a circle?

A circle can be characterized by its centre's location and its radius's length.

Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

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The probability that the mean height x is between 68 and 70 inches is found as 37.28%.

The z-score is written as follows:

z = (x - μ)/σ

In which,

x =  between 68 and 70 inches.

μ = mean 69 inches

σ = standard deviation 6 inches

Put the values in the formula,

Probability that the mean height x is between 68 and 70 inches

P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)

P(68 < x < 70) = (-0.16) < z < (0.16)

P(68 < x < 70) = 0.4364 - 0.0636

P(68 < x < 70) = 0.3728

P(68 < x < 70) = 37.28%

Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.

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a. You would expect 3.5 of those in the sample to name chocolate.

b. The probability exactly four of those in the sample name chocolate is 0.2438.

c. The probability four or more name chocolate is 0.5829..

a. If 35% of people in the general population indicate that chocolate is their favorite flavor of ice cream, then we would expect 35% × 10 = 3.5 people in a sample of 10 to name chocolate as their favorite flavor. Since we cannot have a fractional number of people, we can round this down to 3 people.

b. The probability that exactly 4 people in a sample of 10 name chocolate as their favorite flavor can be calculated using the binomial distribution. The probability of each individual event (i.e., a person naming chocolate as their favorite flavor) is 0.35, and there are 10 total events. The probability of exactly 4 successes (people naming chocolate as their favorite flavor) is given by the formula:

(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])

Where "choose" denotes the binomial coefficient, and the exponent indicates the number of times each event occurs. Plugging in the values, we get:

(210) × (0.0036125) × (0.274625) = 0.2438

So the probability that exactly 4 people in the sample name chocolate as their favorite flavor is approximately 0.2438.

c. To calculate the probability that 4 or more people in the sample name chocolate as their favorite flavor, we can use the same formula as above, but sum the probabilities for each possible number of successes greater than or equal to 4. For example, the probability of 4 successes is given by:

(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])

The probability of 5 successes is given by:

(10 choose 5) × ([tex]0.35^5[/tex]) × ([tex]0.65^5[/tex])

And so on. Summing the probabilities for each possible number of successes greater than or equal to 4, we get:

0.2438 + 0.1933 + 0.1047 + 0.0380 + 0.0081 = 0.5829

So the probability that 4 or more people in the sample name chocolate as their favorite flavor is approximately 0.5829.

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The second term of the series will be 27.

Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.

Sum to infinity = a/1-r

where s = 300

r = 0.1

a = 300 (1 - 0.1)

a = 300 (0.9)

a = 270

The second term of the progression will be = ar

Second term = 270 x 0.1

Second term = 27

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The perimeter of the checker board  118.4 cm

Area of each square = 14 sq. cm.

What is the length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.

The square root of area is the length of one side

[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]

[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]

[tex]P=4 a[/tex]

[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]

[tex]\text { Perimeterofthecheckerboard }[/tex]

Therefor we get the perimeter of the checker board  118.4 cm

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Answer:

Read explanation :)

Step-by-step explanation:

Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.

Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.

Your Welcome Hope This Helps You.

The distance the ride will go for birr 1350 is 130 kilometres.

The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;

Let's use equation to represent the total amount spent on the distance covered.

Therefore,

let

Hence,

y = 50 + 10x

Therefore,

where

y = 1350

y = 50 + 10x

1350 = 50 + 10x

1350 - 50 = 10x

1300 = 10x

divide both sides by 10

x = 1300 / 10

x = 130 km

Therefore, the ride will go 130 km.

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Answer:

Below

Step-by-step explanation:

Only the middle three are tri -nomials  ( three terms)

the third one reduces to  (x+ 2)^2

Answer:

3

Step-by-step explanation:

(x+2)^2

The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n

And n = 24.1

Option (C) is correct.

What is a linear equation?

A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.

To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:

8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories

We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:

193.5 + 12 n = 288.5 + 8 n

Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:

n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75

Therefore, the number of calories in each chicken nugget is 24.1 calories.

Hence, option (C) is correct.

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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.

1 dozen of Rose costs = $30.96

1 dozen of chrysanthemums costs = $17.80

1 dozen of of tulips costs = $ 21.10

Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips

                         = 16 * 30.96 + 40 * 17.80 + 20 *21.10

                         = $1629.36

There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76

Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.

What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
                        = 16 * 30.96 + 40 * 17.80 + 20 *21.10
                        = $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 =  $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.

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An expression that shows number of cookies each friend got is c/5.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.

Total number of cookies =c

Sharing among 5 friends

Number of cookies each friend got =Total number of cookies/5

= c/5

Therefore, an expression that shows number of cookies each friend got is c/5.

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The general anti derivative or indefinite integral of the function

cos2x - sec²x is 1/2 sin2x + tan x + C .

The given function is of the form : cos2x - sec²x

Now we will use the indefinite integral on the above expression:

∫cos2x - sec²x

This can be broken into :

∫cos2x -  ∫sec²x

Now we will integrate them separately:

∫cos2x, we will use u-substitution.

Let 2x = u

Differentiation both sides we get:

2 dx = du

or, dx = 1/2 du

Hence we will use this value:

∫cos2x

= ∫cos u · 1/2du

= 1/2 ∫ cos u du

=1/2 sin u + C , where C is a constant.

Again we will do the second part of the integral:

∫sec²x

= tan x + C

Hence the required integral will be:

1/2 sin2x + tan x + C .

Now we will use differentiation to check the integral

d/dx (1/2 sin2x + tan x + C )

= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)

= cos 2x + sec² x

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The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.

It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.

On this note, since the given expression is;

2log2 + 2log4

It follows from factorisation that we have;

2 ( log 2 + log 4 )

Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;

= 2 ( log ( 2 × 4 ) )

= 2 log 8.

Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.

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The inverse of the function shown is (x + 5).

What is the inverse of the function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Coordinates of the given line are (8,3) and (-2,-7)

The function of the given graph for two points form is

[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]

or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]

or, y - 3 = x - 8

or, y = x -8 + 3 = x - 5

y = x - 5

To find the inverse, replace x with y and y with x then, we get

x = y - 5

y = x + 5

[tex]f^{-1}[/tex] = x + 5

Hence, the inverse of the function shown is (x + 5).

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From the given Isosceles trapezoid ABCD, the three correct statements are:

∠ADC ≅ ∠BCD

AD ≅ BC

AC ≅ BD

An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.

Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.

Thus, three correct statements are -

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Answer:

1st {-6, -3, 0, 3, 6}

Step-by-step explanation:

range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient

Let f:R⇒S be a surjective homomorphism of rings with identity.

We have to find if R is a PID, prove that every ideal in S is principal.

We know that,

Let I be the ideal of S

Since f is sufficient homomorphism.

So, f⁻¹(I) is an ideal of R.

Since R is PID so ∈ r ∈ R such that

f⁻¹(I) = <r>

I = <f(r)>

Therefore,

Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.

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Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by

f(x) = Σ[∞], n=1 cnyn(x)

To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).

cn = (f,yn) = ∫[0,4]f(x)yn(x)dx

Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by

cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx

Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.

cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx

= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx

= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx

= 1/2 ∫[0,2] (x+2)yn(x) dx

Therefore, the coefficient Cn is given by

Cn = 1/2 ∫[0,2] (x+2)yn(x) dx

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The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = |x| - 2 and g(x) = 2 f(x)

The function g(x) is rewritten as,

g(x) = 2 (|x| - 2)

g(x) = 2|x| - 4

The function f(x) is an absolute function and the function g(x) will be twice the function f(x).

x           f(x) = |x| - 2               g(x) = 2f(x)

-2                0                               0

-1                -1                               -2

0                -2                              -4

 1                -1                               -2

2                0                                0

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Answer:

Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)

Good luck;)

Step-by-step explanation:

4% is  the percentage rate of increase or decrease in exponential function.

What exactly makes a function exponential?

A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.

                    The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.

We have,

y = 420( 1.04)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is

y(x)= a(1-r)^x such that r is the growth percent.

    1 + r = 1.04

      r = 0.04 ⇒  4%

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The n expressed in terms of r and p is n=r/p.

How to solve the word problems?

Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:

You must frequently create two distinct linear equations in two variables in order to solve these issues.

So, it is expressed as:

r=pn

n=r/p

Hence, The n expressed in terms of r and p is n=r/p.

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The final function  after the transformations are applied to the graph of y =√x is y = 2√(x - 5) +1.

What is transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Rule of transformation:

g(x) = c f(x+a) + b

If c > 1, then f(x) vertically starched by c factor. If 0< c < 1, then f(x) vertically compressed by c factor.

If a>0, then f(x) is shifted horizontally a unit right side. If a<0, then f(x) is shifted horizontally a unit left side.

If b>0, then f(x) is shifted vertically b unit upward. If a<0, then f(x) is shifted vertically b unit downward.

Putting c = 2, a = -5, b = 1, and f(x) = √x

y = 2√(x - 5) +1

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