fill in the numbers resulting from the indicated operation: 2 −1 −4 7 3 4 5 5 −1 2 1 −1 2 −1 −4 7

The solution for definite integral ∫2^x dx from [−1,1] is

 3/ 2 ln2

Definite Integral:

A definite integral is defined as the exact limit and summation examined in the previous section to find the net area between the function and the x axis. Also note that the definite integral notation is very similar to the indefinite integral notation. The reason for this will become clear in due course.

There are a few terms that should be left out along the way. The number "a" below the integral sign is called the lower integral limit, and the number "b" above the integral sign is called the upper integral limit. Even if the intervals a and b are specified, the lower bound is not necessarily less than the upper bound. Collectively, a and b are often referred to as the interval of integration.

Given a function :

f(x) that is continuous function on the interval [a , b]

we divide the interval into n subintervals of equal breadth, Δx, and from each interval choose a point, x i. Then the definite integral of f(x) from a to b is

[tex]\int\limits^b_a f(x) \, dx = \lim_{n \to \infty} f(xi)[/tex] Δx.

According to the question:

let's start by differentiating 2ˣ.

   y = 2ˣ

⇒ ln y = x ln 2

⇒ 1/y dy/dx = ln2

⇒ d /dx = y ln 2 = 2ˣ ln2

So remembering integration is the reverse of differentiating.

  y = 2ˣ

⇒ dy/dx = 2ˣ ln 2

⇒ ∫2ˣ dx = 2ˣ / ln 2 + C

2ˣ > 0, ∀ x ∈ R, there is no negative area so we can

Insert the limits and evaluate immediately.

= 1/ ln2 [2x][tex]\left \{ {{y= -1} \atop {x=1}} \right.[/tex]

= 1/ln 2  (2¹ - 2⁻¹)

= 3/ 2ln 2

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The average deviation from the mean is 0.19 that can be calculated from the mean.

An average is calculated for a set of numbers that are of the same value range.

Mean = (32.52+32.14+32.61+32.75)/4 = %32.50

Standard deviation =

|32.50-32.52| = 0.02

|32.50-32.14| = 0.36

|32.50-32.61| = 0.11

|32.50-32.75| = 0.25

(.02+.36+.11+.25)/4= 0.19

So the standard deviation is 0.19

Relative deviation = .19/32.50=0.0058 or %0.58

Yes, %32.14, because it deviates too far from the average.

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Answer:

first you need to write the given equation in a standard form

4x - 7y = 9

-7y = -4x + 9

y = 4/7x - 9/7

*parallel lines have equal gradient

m = 4/7

y - y1 = m(x - x1)

y - 3 = 4/7(x -7)

y - 3 = 4/7x - 4

y = 4/7x - 1

your equation is y = 4/7x - 1

Answer:

[tex]y = \frac{4}{7} + 5[/tex]

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, subtract 4x from both sides of the equation:

4x (-4x) - 7y = 9 (-4x)

-7y = -4x + 9

Next, divide -7 from both sides of the equation:

(-7y)/-7 = (-4x + 9)/-7

[tex]y = \frac{-4x}{-7} + \frac{9}{-7}[/tex]

[tex]y = \frac{4}{7}x - \frac{9}{7}[/tex]

Next, as long as your slope (4/7) is the same, you can adjust the b (-9/7 for original) to get a parallel line.

In this case, I will utilize 5

[tex]y = \frac{4}{7}x + 5[/tex]

See attached image for the result. The blue line is the adjusted parallel line, while the red line is the original line given by the question.

~

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Answer:

x = 6 units

Step-by-step explanation:

We know that, By pythagoras theorem,

Hypotenuse2 = base2 + perpendicular2

Given, Hypotenuse = 6.5

perpendicular = 2.5

base = x

So, by putting the values,

6.52 = 2.52 + x2

42.25 = 6.25 + x2

36 = x2  

Hence, x = 6 units

The number of party popper she bought is 32 and the number of balloons she bought is 18.

The first step is to form a system of equations using the information provided in the question.

0.20x + 0.50y = $20 equation 1

x + y = 52 equation 2

The solution using the elimination method :

Multiply equation 2 by 0.20

0.20x + 0.20y = 10.40 equation 3

Subtract equation 3 from equation 2 :

0.30y = 9.60

Divide both sides of the equation by 0.30

y = 9.60 / 0.30

y = 32

The solution using the substitution method:

Make x the subject of the formula in equation 2

x = 52 - y equation 3

Substitute for x in equation 1 :

0.20(52 - y) + 0.50y = $20

10.40 - 0.20y + 0.50y = $20

Combine similar terms together

0.50y - 0.20y = $20 - $10.40

0.30y = $9.60

y = 9.60 / 0.30

y = 32

x = 50 - 32

x = 18

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Taking into account the definition of a system of linear equations, the price of one order of chicken nuggets and one chicken sandwich is $2.98 and $4 respectively.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

A solution to a system is an assignment of values to the unknowns that makes each of the equations true. Solving a system means finding all the solutions of the system.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

2x +3y= 17.96

4x + 2y= 19.92

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "y" from the first equation:

3y= 17.96 -2x

y= (17.96 -2x)÷3

y= 17.96÷3 - 2÷3x

y= 449/75 - 2/3x

Substituting the expression in the second equation:

4x + 2×(449/75 - 2/3x)= 19.92

Solving:

4x + 2×449/75 - 2×2/3x= 19.92

4x + 898/75 - 4/3x= 19.92

4x - 4/3x= 19.92 - 898/75

8/3x= 596/75

x= 596/75÷ 8/3

x= 2.98

Remembering that y= 449/75 - 2/3x, you get:

y= 449/75 - 2/3×2.98

y= 4

Finally, the price of one order of chicken nuggets is $2.98 and the price of one chicken sandwich is $4.

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The ratio represents the number of votes for hot dogs to chicken is 2/5 ,

What is ratio?

Given,

Number of members voted for pizza = 6

Number of members voted for chicken = 10

Number of members voted for hot dogs = 20 - (10 +6) = 4

Now we have to determine the ratio represents the number of votes for hot dogs to chicken.

Number of members voted for hot dogs / Number of members voted for chicken = 4/10

= 2/5

Thus, the ratio represents the number of votes for hot dogs to chicken is 2/5.

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Answer:

look at the y axis. :)

The four matches can be sequenced in 1350 different ways, ensuring that each player gets to play at least once.

A sequence is an enumerated collection of things in mathematics where repetitions are allowed and order is important. It includes members, much like a set (also called elements, or terms). A sequence can be formalized as a function from natural numbers (the positions of sequence elements) to the elements at each place. An indexed family, which is a function from any index set, can be thought of as a generalization of the concept of a sequence.

The final matches can be between any two players after we have made sure that every player has played at least one match (except those three matches played)

We can select any two players from a pool of six for the first game =[tex]6_{c_{2} }[/tex]

We can select either of the two players from a total of four for the second match is [tex]4_{c_{2} }[/tex]

We have a choice of two players for the third game.=[tex]2_{c_{2} }[/tex]

Any of the two players from the pool of six can be selected for the fourth match= [tex]6_{c_{2} }[/tex]

P(x) =[tex]6_{c_{2} }[/tex]×[tex]4_{c_{2} }[/tex] ×[tex]2_{c_{2} }[/tex] ×  [tex]6_{c_{2} }[/tex]

P(x) = 15 × 6 × 1 × 15

P(x) = 1350

Therefore, the four matches can be arranged in 1350 different ways, ensuring that each player gets to play at least once.

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Answer:

  $808.76

Step-by-step explanation:

You want the simple interest earned on $1975 at the rate of 9.1% per year for 4.5 years.

The amount of simple interest is given by the formula ...

  I = Prt

where principal P is invested at rate r for t years.

Using the given values, the amount of interest earned is ...

  I = $1975·0.091·4.5 = 808.7625 ≈ $808.76

The amount of simple interest is $808.76.

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There are 60 different ways could you choose a car and this can be determined by using arithmetic operations.

What are arithmetic operations?

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-") Multiplication ("×") Finding the quotient in division ("÷").

Given :

A car dealership has five exterior color choices.

A car dealership has six interior color choices.

A car dealership has two model choices.

The following steps can be used to determine the different ways could you choose a car:

Multiply 5 and 6 that is multiply five exterior color choices and six interior color choices.

= 5 * 6

Multiply the above expression by 2 which is with two model choices.

= 30 * 2

Further, simplify the above expression.

= 60

Hence, There are 60 different ways could you choose a car.

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f(-7) will be equal to (-13) using given function and conditions.

What are function?

Function is an expression rule, or law that defines relationship between one variable and another variable.

An example of this would be y = x^2. If you put in anything for x, you get one output for y.

In given function,

y is represented by f(x),

f(x) = -x-6  for x ≠ 0

f(x) = 2      for x = 0

We need to find for x = -7 i.e. not equal to 0

So, we will take F(x) = -x-6

So, f(-7) = -7-6

             = -13

So, the value of f(-7) = -13.

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The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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The value of the number will be;

⇒ x = - 11

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

''Three times the quantity of a number increased by 7 is equal to the same number decreased by 15''

Now,

Let the quantity of a number = x

So, We can formulate;

⇒ 3x + 7 = x - 15

Solve for x as;

⇒ 3x - x = - 15 - 7

⇒ 2x = - 22

⇒ x = - 11

Thus, The value of the number will be;

⇒ x = - 11

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The expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸)

What is the integer exponent property?

Exponents that are integers are known as integer exponents. Exponents with positive integer values tell us how many times to multiply the base by itself. We are instructed by negative integer exponents to first flip the numerator and denominator before multiplying the result by the specified number of times.

Here, we have

Given expression:  (ab⁷)⁴

We have to find the expression that is equivalent to this expression.

Using integer exponent property:

= (ab⁷)⁴

= (a⁴b²⁸)

Hence, the expression that is equivalent to (ab⁷)⁴ is (a⁴b²⁸).

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The simplification of [tex](16)^{1/2}[/tex] is 4.

To simplify [tex](16)^{1/2}[/tex] , you can use the property of exponents that says that [tex]{(a^b)}^c = a^{(b*c)[/tex]. Therefore, [tex](16)^{1/2}[/tex] can be rewritten as [tex]16^{(1/2)}[/tex].

The square root of 16 is 4, so [tex]16^{(1/2)}[/tex] = 4. Therefore, [tex](16)^{1/2}[/tex] = 4.

You can also simplify [tex](16)^{1/2}[/tex]  by writing 16 as a product of its prime factors: 16 = [tex]2^4[/tex]. The square root of 16 is the same as the square root of 2^4[tex]2^4[/tex], which is [tex]2^{(4/2) = 2^2} = 4[/tex]. Therefore, [tex](16)^{1/2}[/tex] = 4.

Simplification is a process of making something simpler or easier to understand. This can be done by reducing the complexity of a system, removing unnecessary components, or making the language more concise.

Simplification complexity is the process of reducing the complexity of a problem, system, or process. This can involve breaking down a complex problem into smaller, more manageable parts, or reorganizing the system or process to make it simpler and easier to understand and use. Simplifying complexity can make a system or process more efficient and easier to maintain.

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The area of the triangle formed by the birdbath, bird feeder and the birdhouse is 15 squared units

Given: the birdbath is at (2,2), the bird feeder is at (8,2), and the birdhouse is at (5,7)

(Consider the image attached)

The distance between the points can be calculated using the formula:

d=√((x2 – x1)² + (y2 – y1)²)

birdbath (5,7) and birdhouse (2,2)

d=√((2 – 5)² + (2 – 7)²) = √34

bird feeder (8, 2) and birdhouse (2,2)

d=√((2 – 8)² + (2 – 2)²) = 6

birdbath (5,7) and bird feeder (8,2)

d=√((8 – 5)² + (2 – 7)²) = √34

The height of the triangle is:

h = √((√34)²-3²) = 5

Area of triangle = 1/2 × base × h

Area of triangle = 1/2 × 6 × 5 = 15 squared units

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The integration of 1/ln(x) is not possible as We permit y = lnx, we then recognize that x = ey.

By differentiating each aspects of this equation with admire to y we get:dx/dy = ey, because the exponential characteristic differentiates to itself whilst differentiated with admire to its power.

In mathematics, the logarithmic quintessential characteristic or quintessential logarithm li(x) is a unique characteristic. It is applicable in issues of physics and has variety theoretic significance. In particular, in keeping with the high variety theorem, it's far a excellent approximation to the high-counting characteristic, that is described because the variety of high numbers much less than or same to a given value x.

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The correct decimal number for 17/22 will be equal to 0.7(727)bar.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. Decimal refers to the base-10 number system, which is perhaps the most widely used number system. The term "decimal number" refers to a number that has a decimal point followed by digits with values less than one.

Here,

17/22=0.772727.....

For 17/22, the proper decimal number is 0.7(727)bar.

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By adding up all the possible ways to distribute the coupon and subtracting it from the possible ways to distribute the 10 coupons to the 15 men, we can determine the total number of ways at least a woman can receive a coupon.

- The entire number of options for dividing the coupons among the 20 customers is the same as the total number of ways to choose a subset of 10 items from a set of 20.

In other terms, 20/10 = 20!/ 10!10 is the combinatorial number of 20 and 10.

- We must use the same calculation as above, but with a set of 15 items rather than 20, to get the total number of alternatives for distributing the coupons among the 15 males.

We now have 15/10, which is 15!/10!5! possibilities.

To ensure that at least one woman receives a coupon, we have 20/10 - 15/10 distribution options.

A combination is made up of r items chosen without replacement from a set of n items, where the order is irrelevant.

The amount of circular permutations of n other objects, taken r at a time, is nPr 2r if clockwise and anti-clockwise configurations are not considered to be distinct. Combinations are various groups or choices made from a variety of items, either all or some of them.

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The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.

In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.

One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.

The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.

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Complete Question:

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?

Answer:0.038

Step-by-step explanation:

The ordinary number equivalent of 3.8x10⁻² is expressed as 0.038.

To express the number 3.8x10⁻² as an ordinary number, we need to understand scientific notation. In scientific notation, numbers are written in the form of a coefficient (a decimal number greater than or equal to 1 but less than 10) multiplied by 10 raised to a certain power (positive or negative). This notation is commonly used to represent very large or very small numbers in a concise and standardized way.

Let's break down 3.8x10⁻² step by step:

The coefficient: 3.8

The coefficient is the decimal part of the number, which should be greater than or equal to 1 but less than 10. In this case, the coefficient is 3.8.

The exponent: -2

The exponent indicates the power of 10 to which the coefficient is raised. If the exponent is negative, it means the number is less than 1. In this case, the exponent is -2, which means we are dividing the coefficient by 100 (10 raised to the power of -2 is 1/100).

Now, to express 3.8x10⁻² as an ordinary number, we simply perform the calculation:

3.8 × 10⁻² = 3.8 ÷ 100 = 0.038

So, the ordinary number equivalent of 3.8x10⁻² is 0.038.

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A proportion of 0.455 and 0.505 contain the true portion of the total population of 10,000 with 95%confidence.

A sampling technique called random sampling, also known as probability sampling, enables the randomization of sample selection, meaning that each sample has the same chance of being chosen to reflect the entire population.

Every subject in your target demographic must have an equal probability of being chosen for your sample in order for it to be considered truly random. This assumption might be broken, for instance, by performing a survey to determine how much time college students spend working out each week at your campus.

If 95% of all the samples, then we expect between 45.5% and 50.5% of the total samples contain the true proportion of the population.

If we repeatedly make new samples, taking samples of size 10,000, approximately with 95% confidence of those samples would have between 45.5% and 50.5% containing true portion of population.

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The symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign, so 16 ÷ 4 + 12 = 4 + 24 ÷ 2.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given expression:

16 ÷ 4 + 12 □ 4 + 24 ÷ 2

Here calculate the first term

16 ÷ 4 + 12 = 4 + 12 = 16

Calculate the second term

4 + 24 ÷ 2 = 4 + 12 = 16

Thus, the equal sign will replace the box,

Therefore, the symbol replaces the box to make the statement true that 16 ÷ 4 + 12 □ 4 + 24 ÷ 2 is an equal sign.

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Answer:

-25.77200

Step-by-step explanation:

Answer:

[tex]\dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Step-by-step explanation:

Given equation:

[tex]-4x^2 + 9y^2 + 32x + 36y - 64 = 0[/tex]

Collect like terms:

[tex]\implies 9y^2 + 36y -4x^2+ 32x - 64 = 0[/tex]

Move the constant to the right side of the equation:

[tex]\implies 9y^2 + 36y -4x^2+ 32x =64[/tex]

Factor out 9 from the terms in y, and 4 from the terms in x:

[tex]\implies 9(y^2 + 4y) -4(x^2-8x)=64[/tex]

Add the square of half the coefficient of the term in y and x inside the parentheses on the LHS, and the distributed values on the RHS:

[tex]\implies 9\left(y^2 + 4y+\left(\dfrac{4}{2}\right)^2 \right) -4\left(x^2-8x+\left(\dfrac{-8}{2}\right)^2 \right)=64+9\left(\dfrac{4}{2}\right)^2 \right+4\left(\dfrac{-8}{2}\right)^2 \right[/tex]

Simplify:

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=64+36-64[/tex]

[tex]\implies 9(y^2 + 4y+4) -4(x^2-8x+16)=36[/tex]

Factor the perfect trinomials:

[tex]\implies 9(y+2)^2 -4(x-4)^2=36[/tex]

Divide both sides by 36:

[tex]\implies \dfrac{9(y+2)^2}{36} -\dfrac{4(x-4)^2}{36}=\dfrac{36}{36}[/tex]

Simplify:

[tex]\implies \dfrac{\diagup\!\!\!\!9(y+2)^2}{\diagup\!\!\!\! 9\cdot 4} -\dfrac{\diagup\!\!\!\!4(x-4)^2}{9 \cdot \diagup\!\!\!\!4}=1[/tex]

[tex]\implies \dfrac{(y+2)^2}{4} -\dfrac{(x-4)^2}{9}=1[/tex]

Therefore, the function is a hyperbola with:

If we reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the null hypothesis is true.

In hypothesis testing, the researcher makes a claim about the population and then uses a sample of the population to determine whether or not the claim is accurate. Before the sample is drawn, the degree of significance—or the predicted error—must be determined. The validity of a claim is determined by the value of a test statistic.

The researcher rejects the provided null hypothesis if the test statistic's value is significant. When the null hypothesis is rejected, there is no discernible difference between the hypothesized value and the sampled observations. If the null hypothesis is rejected, it is determined that there is insufficient statistical support to draw the conclusion that it is true.

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Answer:

50

Step-by-step explanation:

Answer: False

Step-by-step explanation:

Answer:

84

Step-by-Step Explanation: