Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y< 2x+3

The polynomial (x-a)(x-b)(x-c)....(x-z) has a coefficient of -351 for the x²⁵ term. Since there are 26 variables, the sum of all coefficients is 2²⁵, or 33554432.

The polynomial (x-a)(x-b)(x-c)....(x-z) can be written as

x²⁶ - (a+b+c+...+z)x²⁶ + (sum of products of pairs)x²⁴ - ... - abc...xyz

The coefficient of x²⁵ is the negative sum of the constants, which is -(a+b+c+...+z). Since there are 26 variables in total, the sum of the constants is just the sum of the first 26 letters of the alphabet, which is

(a+b+c+...+z) = 1 + 2 + 3 + ... + 26 = 351

So the coefficient of x²⁵ is -351.

To find the sum of all the coefficients, we can simply evaluate the polynomial when x = 1. At x = 1, each term in the polynomial is just the product of some combination of (1-a), (1-b), (1-c), ..., and (1-z). Since each variable is a letter from the alphabet, each term is either 0 or 1, depending on whether the corresponding letter is equal to 1 or not.

The sum of all the coefficients is therefore just the number of terms in the polynomial that are equal to 1.

Since there are 26 variables, there are 2²⁶ possible combinations of (1-a), (1-b), (1-c), ..., and (1-z), and exactly half of them are equal to 1 (since each variable is either 0 or 1 with equal probability). Therefore, the sum of all the coefficients is

2²⁵ = 33554432

So the sum of the coefficients of the polynomial (x-a)(x-b)(x-c)....(x-z) is 33554432.

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[tex]32^5[/tex] - [tex]16^5[/tex] + [tex]2^{19}[/tex] is divisible by 63.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]32^5[/tex] - [tex]16^5[/tex] + [tex]2^{19}[/tex]

= 33554432 - 1048576 + 524288

= 33030144

Now,

33030144 ÷ 63

= 524288

Thus,

It is divisible by 63.

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Answer:

it has an error of 15 more then the actual temperature

Step-by-step explanation:

to find the change all you have to do is just subtract 340 -325 that is 15 so if the oven was 100 it would show 115

The first term of an arithmetic progression is 5 and the 10th term is 95. The sum of the first 10 terms is 455.

The sum of the first 10 terms of an arithmetic progression (A.P.) can be found using the formula:

S_n = n/2 * (2a + (n-1)d)

where a is the first term, d is the common difference, and n is the number of terms.

Given that the first term is 5 and the 10th term is 95, we can find the common difference (d) using the formula:

a_n = a + (n-1)d

Plugging in n = 10 and a = 5, we get:

95 = 5 + (10 - 1)d

Solving for d, we get:

d = (95 - 5) / (10 - 1) = 9

Now that we know the common difference, we can find the sum of the first 10 terms:

S_10 = 10/2 * (2 * 5 + (10 - 1) * 9) = 10/2 * (10 + 81) = 10/2 * 91 = 455

So, the sum of the first 10 terms is 455.

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Answer:

Step-by-step explanation: Sure! Here's a step-by-step solution to find the amount of red icing Ashley needs for one cake:

Divide the total amount of red icing by the number of cakes: 10 1/2 ÷ 3 1/2 = 3.

Simplify the result from step 1: 3 = 3 ounces of red icing per cake.

So Ashley needs 3 ounces of red icing to write a message on one cake.

This linear model's rate of change is 0.7 minute per song. This may be computed by subtracting the y-values (166.6 - 96.6) from the x-values (238 - 138).

A continual dependent variable is described as a function of one or more predictor variables in a linear model. They can assist you in comprehending and forecasting the behavior of complicated systems, as well as analysing scientific, economic, and medical data. Linear regression is a statistical technique for developing a linear equation. Linear functions have a straight line as their graph. There is one independent variable and one dependent variable in a linear function. x is the independent factor, while y is the dependent variable.

A linear equation is so named because plotting the graph of a given linear model yields a straight line.

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Answer:

90°

Step-by-step explanation:

every inscribed triangle with the baseline (Hypotenuse) being a diameter of the circle is a right-angled triangle.

therefore, that angle x = 90°.

David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.

We are given that David biked [tex]12\frac{7}{8}[/tex] miles on Tuesday and [tex]5\frac{3}{8}[/tex] miles on Wednesday.

In order to find the number of miles David biked farther on Tuesday than on Wednesday, we will subtract the miles biked by him on Wednesday from the miles biked by him on Tuesday as follows -

[tex]12\frac{7}{8} - 5\frac{3}{8}[/tex]

So, first, we will subtract the whole number of parts as follows -

12-5 = 7

Then, we will subtract the fractional parts as follows -

7/8 - 3/8 = 4/8 = 1/2

so we get,

[tex]12\frac{7}{8} - 5\frac{3}{8} = 7\frac{1}{2}[/tex]

Therefore, David biked [tex]7\frac{1}{2}[/tex] miles farther on Tuesday than on Wednesday.

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Answer:

(24) + (20) + (8) = 52 ft^2

Step-by-step explanation:

This figure is a compound of 3 rectangles that can be split up like in my attached picture.

The top, horizontal rectangle is 8x3 = 24 sq ft.

The bottom, almost square rectangle is 4x5 = 20 sq ft.

The middle rectangle has a height of 4 feet and a width of (8-6) = 2 feet.

So, its area is 4x2= 8 sq ft.

The compound figure is the sum of all of these areas:

24 + 20 + 8 = 52

The area of the compound figure is 52 sq ft.

Area of 1 = 8 * 3 = 24

Area of 2 = 4 * 2 = 8

Area of 3 = 5 * 4 = 20

Total area = 24 + 8 + 20 = 52

The value of the lettered sides of the triangle are n=4, m=3

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry

From the Triangles, <BAC = <DBC                         given

⇒ΔBAD ≅ ΔDBC       (SAS)

/BA/ =/BD/ = 3 units

Also, /BC/ = /AD/ = 4 units

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The expression for the given model will be 3÷2/5.

What exactly are expressions?

Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.

e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.

Now,

as shown in figure the model is shaded uptil 3

and in 1 unit there are 5 total boxes which are divided in 2 parts

Therefore, it will be represented by 3÷2/5.

Hence,

         The expression for the given model will be 3÷2/5.

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The quadratic equation whose roots are 3 and -3 is x² - 9 = 0.

Given the roots of the quadratic equation;

x = 3 and x = -3

The two real distinct solutions for the quadratic equation are x = 3 and x = -3.

Which means x - 3 and x + 3 are the factors of the equation.

Hence;

( x - 3 )( x + 3 ) = 0

Now, expand using FOIL method

x( x + 3 ) - 3( x + 3 ) = 0

x² + 3x - 3x - 9 = 0

x² - 9 = 0

Therefore, the equation is x² - 9 = 0.

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The measure of ∠1 is 114.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

∠7 = 114

From the figure,

Line a is parallel to line b.

So,

∠7 and ∠1 are alternate exterior angles.

And,

Alternate exterior angles are equal.

So,

∠7 = ∠1 = 114

Thus,

∠1 is 114.

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The standard form of the quadratic function that represents the area of the garden is: G(x) = - 2x² + 20x

Mrs Miller has 20 ft of fencing to put around three sides of the garden.

Let us assume that l represents the length of the garden.

Here x represents the width of the rectangular garden.

So, l = 20 - 2x

We know that the formula for the area of rectangle is:

A = length × width

Let G(x) be a function that represents the area of the garden.

Using above formula,

G(x) = x × l

G(x) = x(20 - 2x)

G(x) = 20x - 2x²

G(x) = - 2x² + 20x

Therefore, the required quadratic function is: G(x) = - 2x² + 20x

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Find dthe complete question below.

Answer:

1/237.12.

Step-by-step explanation:

The probability of winning the minimum award can be calculated by multiplying the probability of picking 4 numbers correctly from 1 to 51 and then multiplying by the probability of picking 1 number correctly from 1 to 42.

The probability of picking 4 numbers correctly from 1 to 51 is given by the formula:

(number of combinations of 4 numbers from 51) / (number of combinations of 5 numbers from 51)

= (51 choose 4) / (51 choose 5)

= 51! / (4! * 47!) / (51! / (5! * 46!))

= (51 * 50 * 49 * 48) / (5 * 4 * 47 * 46)

= 19600 / 10,946

= 1/5.6 approximately

The probability of picking 1 number correctly from 1 to 42 is given by the formula:

1/42

The final probability of winning the minimum award is given by multiplying the above two probabilities:

1/5.6 * 1/42 = 1/237.12

So, the probability of winning the minimum award is approximately 1/237.12.

The value of the expression is 5.

What is order of operations?

The order of operations is a rule that specifies the correct sequence of steps to be taken when evaluating a mathematical equation.

To simplify this expression, we need to follow the order of operations, which is:

Exponents (powers, roots)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

So, we start with the exponents:

[tex]3^0+4^{-1} \\= 1 + 1/4 \\= 5/4[/tex]

Now we substitute this value back into the original expression:

[tex](3^0+4^{-1} )*2^2\\ = (5/4) * 2^2 \\= (5/4) * 4 \\= 5[/tex]

Therefore, the value of the expression is 5.

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After solving the expression from the given data we get that the cost of the book is £5.90.

Let's assume the cost of the book is "b" in pounds. From the information given, we can set up the following system of equations:

6x = 12.30 (Andy pays £12.30 for 6 sketch pads)

2x + b = 10 (Jo pays £10 for 2 sketch pads and 1 book). where x is the cost of one sketch pad in pounds. Solving the first equation for x, we get: x = 12.30/6 = 2.05

Substituting this value of x into the second equation, we get: 2(2.05) + b = 10

Simplifying this equation, we get: 4.10 + b = 10

Solving for b, we get: b = 5.90

Therefore, the cost of the book is £5.90.

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Answer:

Step-by-step explanation:

First, we need to evaluate the expression inside the parenthesis: 4(12) = 4 * 12 = 48.

Next, we can simplify the expression: 42 - 6 * 48 = 42 - 288 = -246.

Finally, we raise the result to the third power: (-246)^3 = (-246) * (-246) * (-246) = -158,048.

So, the result is -158,048.

For the two given graphs, the value for vector equation is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

What is a vector?

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

From first graph it is seen that -

[tex]\vec{u}= < 1,1 >[/tex] and [tex]\vec{v}= < -1,2 >[/tex]

From second graph it is seen that -

[tex]\vec{w}= < 1,4 >[/tex]

So, it is obtained that -

[tex]a\vec{v}+b\vec{u}=\vec{w}[/tex]

Substitute all the values in the equation -

a<-1,2> + b<1,1> = <1,4>

<-a,2a> + <b,b> = <1,4>

<-a+b,2a+b> = <1,4>

The two equation obtained are -

-a + b = 1

2a + b = 4

Subtracting the equation 1 from 2 -

2a + b - (-a + b) = 4 - 1

2a + b + a - b = 3

3a = 3

a = 1

Substitute the value of a in equation 1 -

-1 + b = 1

b = 1 + 1

b = 2

So, the equation [tex]a\vec{v}+b\vec{u}=\vec{w}[/tex] becomes -

[tex]\vec{v} + 2\vec{u} = \vec{w}[/tex]

Therefore, the vector is obtained as [tex]\vec{w} = 2\vec{u} + \vec{v}[/tex].

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The slope of the line is 9.75 and the y-intercept is -25.

Two distinct but related concepts are referred tο by the phrase "linear function": A polynomial function of degree zero οr one that has a straight line as its graph is referred tο as a linear function in calculus and related fields.

Given: Yvette is saving mοney to buy holiday gifts. She will save the money she makes at her part-time job. Hοwever, she borrowed $25 from her sister which she has to pay back befοre she can start saving.

Let the linear functiοn that models the given situation be y = ax + b. Here, a and b are constants.  We can use this infοrmation to find the values of a and b.

We put x = 0 & y = -25 into y = ax + b

b = -25

Substitute the value of b intο y = ax + b

y = ax -25...(1)

Nοw we put x = 4 and y = 14 in equatiοn(1) and we get

14 = 4a - 25

4a = 39

a = 9.75

Substitute the value of a in equatiοn (1):

y = 9.75x - 25

Cοmpare the above function with the slοpe-intercept form of a line y = mx + c

m = 9.75, c = -25

Hence, the slοpe οf the line is 9.75 and the y-intercept is -25.

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Mr. Steiner will need to pay $18774 in total and he paid $4774 more than the actual price of the car.

we know that the amount of money earned, in compound interest after t years is showed as, A(t) = P (1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]

here, we know that A(t) is the amount of money after t years.

P is the initial sum of money, know as principal,

r is the interest rate as a decimal value,

n is the number of times that interest is compounded per year,

and

t is the time in years for which the money is invested or borrowed.

now here we know,

P = 14000, r = 0.049, n = 12, t = 6

when we have all values we can find,

A(t) = P(1+[tex]\frac{r}{n}[/tex])ⁿ[tex]^{t}[/tex]

A(6) = 14000 (1+[tex]\frac{0.049}{12}[/tex])¹²ˣ⁶

A(6) = 18774

therefore we know that Mr. Steiner needs to pay $18774 in total.

now,

18774 - 14000 = 4774

therefore we get to know that Mr. Steiner paid $4774 more than the actual price of the car.

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Answer:

I got 20 when calculating this

The rule for the given geometric sequence as required to be determined is; a (n) = 64 (-1/2)^(n-1).

By observation, the first term of the sequence is; 64.

Also, the common ratio of each successive terms is as follows;

-32 / 64 = 16 / -31, -8 / 16 = -1/2.

On this note, the ratio is; -1/2.

Consequently, it follows that the answer choice which correctly represents the rule for the geometric sequence is; an = 64(-1/2)^n-1.

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The six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

The six trigonometric functions of an angle θ are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ), and cosecant (csc θ). These functions can be used to calculate the coordinates of a point on the terminal side of θ when the angle and one coordinate are known.

For example, if you know the angle θ and one coordinate (in this case, -4) of a point on the terminal side of θ, you can use the six trigonometric functions to calculate the remaining coordinate. In this case, the point is (-4, -1). The sine of θ is equal to the y-coordinate (-1) divided by the hypotenuse (distance from the origin). Therefore, sin θ = -1/5. The cosine of θ is equal to the x-coordinate (-4) divided by the hypotenuse. Therefore, cos θ = -4/5. The tangent of θ is equal to the y-coordinate (-1) divided by the x-coordinate (-4). Therefore, tanθ = -1/-4 = 1/4. The cotangent of θ is equal to the x-coordinate (-4) divided by the y-coordinate (-1). Therefore, cot θ = -4/-1 = -4. The secant of θ is equal to the hypotenuse (distance from the origin) divided by the x-coordinate (-4). Therefore, sec θ = 5/-4 = -5/4. The cosecant of θ is equal to the hypotenuse divided by the y-coordinate (-1). Therefore, csc θ = 5/-1 = -5.So, the six trigonometric functions of the angle θ for the given point (-4, -1) are sin θ = -1/5, cos θ = -4/5, tan θ = 1/4, cot θ = -4, sec θ = -5/4, and csc θ = -5.

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Answer:

I believe Edgar payed $84 for the tickets.

Step-by-step explanation:

12(4)=48

6(6)=36

48+36=84

The surcharge weight should be set at 12.25 lb, since 99% of all packages are at least 1.0 lb under this weight.

In this problem, we are given that the weight distribution of packages sent in a certain manner is normal, with a mean value of 12 lb and a standard deviation of 3.5 lb. The standard deviation is a measure of how much the data varies from the mean.

Now, the package service wishes to establish a weight value c, beyond which there will be a surcharge. We want to find the value of c such that 99% of all packages are at least 1.0 lb under the surcharge weight. This means that we are looking for a weight value that is exceeded by only 1% of all packages.

To find this weight value, we can use the properties of the normal distribution. We know that the area under the normal curve represents the probability of an event occurring. In this case, we want to find the weight value c that corresponds to the 1% probability.

To do this, we first need to standardize our normal distribution by converting it to the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by subtracting the mean (12 lb) from our target weight value c, and then dividing by the standard deviation (3.5 lb). This gives us a z-score, which represents the number of standard deviations away from the mean our target weight value is.

Next, we can use a standard normal distribution table or calculator to find the z-score that corresponds to the 1% probability. This is approximately -2.33.

Finally, we can solve for c by reversing the standardization process. We multiply the z-score (-2.33) by the standard deviation (3.5 lb) and add the mean (12 lb) to get our target weight value c.

Therefore, c = -2.33 x 3.5 + 12 ≈ 0.25 lb.

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Answer:

Remainder:

Step-by-step explanation:

Step 1: Divide 5843 by 11.

5843/11 = 530.272727

Step 2: Find the quotient.

Quotient = 530

Step 3: Find the remainder.

Remainder = 3

The possible rational roots of the equation 3x³ + 9x - 6 = 0 are given as follows:

± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible roots are given as follows:

± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.

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