(for 100 points)

Multiply (3.84 x 10−9)(7.6 x 1015). Write the final answer in scientific notation.

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Answer:

Slope is -48, y-intercept is 432

[tex]y = - 48x + 432[/tex]

Step-by-step explanation:

[tex]m = \frac{432 - 288}{0 - 3} = \frac{144}{ - 3} = - 48[/tex]

[tex]432 = - 48(0) + b[/tex]

[tex]432 = 0 + b[/tex]

[tex]b = 432[/tex]

[tex]y = - 48x + 432[/tex]

The smallest possible value of the sum of the eight integers is given by:

116.

The eight integers in the problem are given as follows:

n, ..., n + 7.

Hence:

The smallest integer is more than 3/5 of the largest integer, hence the following inequality is built to relate them:

n > 3/5(n + 7)

Applying the distributive property on the right side, we have that:

n > 0.6n + 4.2.

0.4n > 4.2

n > 4.2/0.4

n > 10.5.

Hence the integers are:

11, 12, 13, 14, 15, 16, 17, 18.

(as 11 is the smallest integer possible).

Then the value of the sum is obtained as follows:

11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 = 116.

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The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5. 50 + 20. 50x  , the correct option is (a) .

In the question ,

it is given that ,

the total cost for 5 tickets = $108

the service fees for the tickets to a basketball game = $5.50

we need to find the cost function for 5 tickets .

we substitute , the value of x = 5 in each option and check which option gives the cost as $108 .

Option (a)

c(x) = 5.50 + 20.50x

= 5.50 + 20.50(5)

= 108

Option(b)

c(x) = 5. 50x + 20. 50

= 5.50(5) + 20.50

= 48

Option(c)

c(x) = 5. 50 + 21. 60x

= 5.50 + 21.60(5)

= 113.5

Option(d)

c(x) = 5. 50x + 21. 60

= 5.50(5) + 21.60

= 49.1

So, from the answers above we can conclude that the cost function representing the cost for 5 tickets is c(x) = 5. 50 + 20. 50x   .

Therefore , The Linear function representing the total cost , where x is the number of tickets is  c(x) = 5.50 + 20.50x  .

The given question is incomplete , the complete question is

Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108 . Which linear function represents c, the total cost, when x tickets are ordered ?

(a) c(x) = 5.50 + 20.50x

(b) c(x) = 5.50x + 20.50

(c) c(x) = 5.50 + 21.60x

(d) c(x) = 5.50x + 21.60.

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The simplified expression using the commutative property is in the first option :  1/3 + 2/3 + 3/5   = 1 + 3/5 = 1 3/5 .

now the given expression is 1/3 + 2/3 + 3/5 .

Therefore this expression can be simplified using the commutative property where we put the like terms together.

1/3 + 3/5  + 2/3

= 1/3 + 2/3 + 3/5 (here we use commutative property on the second and third terms of the expression)

= 1 + 3/5 (we know that 1/3 +2/3 = 1)

=1 3/5

Hence by using the commutative property we calculate the sum easily.

The commutative property applies to the arithmetic operations of addition and multiplication. This suggests that no matter how the numbers are arranged or placed, the result of adding or multiplying them remains the same.

As an illustration, 1 + 5 = 6 and 5 + 1 = 6. No matter how two numbers are added, the sum is unaffected. Multiplication uses the same principle. The commutative property does not hold for division and subtraction because the results are completely different when the numbers are rearranged.

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Answer:

60

Step-by-step explanation:

I believe two angles should add up to 180 in a parallelogram

No there will be no relay exchange in any of the 0.25-mile markers

the exchanges are

In a 4 mile race the exchanges are made equal by the number of the team members

therefore the exchanges will be at interval of 4/9 and repetitive addition give other points and the list are

4/9, 8/9, 4/3, 16/9, 20/9, 8/3, 20/9, 32/9, and 4

In decimal form this will be listed in four decimal place

0.4444

0.8889

1.3333

1.7778

2.2222

2.6667

3.1111

3.5556

4

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Step-by-step explanation:

628x50/100 = 314

Answer: 314 students have a pet

Step-by-step explanation: 628 divided by 2 = 314

Answer:

B. [tex]y=6x+12[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{36-12}{4-0}=6[/tex].

The [tex]y[/tex] intercept is 12, so the equation is [tex]y=6x+12[/tex].

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{5}}} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-2=2x-10\implies {\Large \begin{array}{llll} y=2x-8 \end{array}}[/tex]

The tons of waste recycled in 2021 was 619.4286 tons.

According to the question,

We have the following information:

In 2021: There were 2341 people living in the town. Each person in the town recycled an average of 264.6kg of waste. Aleks knows that 1 ton = 1000kg.

Now, the total waste recycled in 2021 can be found using multiplication:

Number of people*waste recycled by each person

2341*264.6

619428.6 kg

Now, we will convert this from kilogram to tons.

1 ton = 1000 kg

1 kg = 1/1000 ton

So, we will divide the waste in kilogram by 1000:

Total waste recycled = 619428.6/1000

Total waste recycled = 619.4286 tons

Hence, the tons of waste recycled in 2021 was 619.4286 tons.

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Answer:

X is horizontal axis, Y is vertical axis

Step-by-step explanation:

(x,y) in the notation

Answer:

|MF| = √109

|MK| = √ 229

Step-by-step explanation:

| MF| = √(-1×-3)² + (5×2)²

= √(3)² + (10)²

=√9 + 100

= √109

|MK| = √(-1×2)² + (5×3)²

= √(-2)² + (15)²

= √4 + 225

= √229

Answer:6.5

Step-by-step explanation:

Here j = 0.5 and k = 0.25

7j+5-8k

= 7(0.5)+5-8(0.25)

= 3.5+5-2

= 6.5

Babe Ruth's batting average is 0.037 more than that of Hank Aaron's

From the question, we have

difference = 0.342-0.305

=0.037

Babe Ruth's batting average is 0.037 more than that of Hank Aaron's

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

Below is a polynomial equation that is given:

0 = 3x⁵ − x⁴ − 5x² + 1

Which can also be written as

3x⁵ − x⁴ − 5x² + 1 = 0

A polynomial of degree 5 is used in the accompanying polynomial equation.

Using a graphing application to solve it graphically is the simplest approach.

The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.

Now that we have the graph, we can use it to find the equation's roots.

There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

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The distance traveled by a northland car is 8.7 km if two cars leave the same parking lot, with one heading north and the other heading east.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

It is given that:

Two cars leave the same parking lot, with one heading north and the other heading east.

From the data given in the question:

Hypotenuse = 9 km

Base = 2 km

The distance traveled northland car = √(9² - 2²)

The distance traveled northland car = √(81 - 4)

The distance traveled by northland car = √77 km

The distance traveled by northland car = 8.7 km

Thus, the distance traveled by a northland car is 8.7 km if two cars leave the same parking lot, with one heading north and the other heading east.

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Answer: 0.0000045

Step-by-step explanation:

Since it is -6, you move it to the right and add 6 zeros and take off the decimal between the 4 and the 5

Hope that helps you! :)

Answer: 14

Step-by-step explanation: do the parentheses first, 7+7 is 14, multiply by 7 to get 98 divide by 7 to get 14

Answer:

14

Step-by-step explanation:

bc 7x7 us 49 and u divided by 7 your answers is going to be 14

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

Given,

Number of samples in the population, n = 60

Sample mean of the population, μ = 25

Standard deviation of the population, σ = 7

We have to find the standard error of the mean and the margin of error at 95% confidence.

Here,

a) The standard error of the mean = Standard deviation / root of sample

= σ / √n

= 7/√60

= 0.90

b) The margin error;

Zₐ/₂ ×  σ / √n

= Zₐ/₂ × 7/√60

= 1.96 × 0.90

= 1.76

Therefore,

a) The standard error of the mean is 0.90

b) The marginal error is 1.76

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The formula that is used to calculate the midpoint for the given two point is written as ( (x₁ + x₂)/2 , (y₁ + y₂)/2).

Mid point:

Midpoint refers the point on a line that is at an equal distance from either end.

Given,

Here we have to explain the concept of midpoint in a simple manner.

According to the definition, midpoint refers the central point between the two points.

So, in a simple manner we have said that the mid point is calculated by finding the average of the two given point.

For example, (x₁, y₁) and (x₂, y₂) are the points, then the midpoint (xₙ, yₙ) is calculated by using the formula,

(xₙ, yₙ) = ( (x₁ + x₂)/2 , (y₁ + y₂)/2)

Similarly, if one point and the midpoint is given, then the another point is calculated by apply the remaining point as (x, y) and solve it accordingly, then we can get the value of it.

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I Think thatthe answer is 2

The solutions to the system of equation (x, y) are (-1, 2)

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

The equations given are;

2x - y = -4 ... eq(i)

6x + 5y = 4 ... eq(ii)

Solving the equations

x = -1 , y = 2

The solutions of the problem are x = -1 and y = 2

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The analysis of the tables based on the first difference values indicates

1 a. The function is a linear function

b The reason the function is linear is because the rate of change in the x and y-values are constant, such that the rate of change of the function is also constant

2. a. The function is not linear

b. This is so because the changes in the consecutive terms of the x-values is not constant while the change in the y-values is constant making the overall rate of change of the function (the slope of the function) to vary

3. a. The table is not a linear function

b. The reason why the table does not represent a linear function is because the change in the terms of the y-values is not constant

4. a. The table is a linear function

b. The reason why it is a linear function is because the changes in the x and y-values are constant

A linear function is a function that when plotted on a graph, forms a straight line.

1) The changes in x-values are;

Δx₁ = -2 - (-3) = 1

Δx₂ = -1 - (-2) = 1

Δx₃ = 0 - (-1) = 1

Δx₄ = 1 - 0 = 1

The changes in y-values are;

Δy₁ = 2 - 1 = 1

Δy₂ = 3 - 2 = 1

Δy₃ = 4 - 3 = 1

Δy₄ = 5 - 4 = 1

a. Is it a linear function? Yes

b. Why it is a linear function is because the first difference of the y-values and the change between consecutive x-values are both constant

2. The changes in x-values are;

Δx₁ = -2 - (-5) = 3

Δx₂ = -1 - (-2) = 1

Δx₃ = 2 - (-1) = 3

Δx₄ = 5 - 2 = 3

The changes in y-values are;

Δy₁ = 4 - 2 = 2

Δy₂ = 6 - 4 = 2

Δy₃ = 8 - 6 = 2

Δy₄ = 10 - 8 = 2

a. Is it a linear function? No

b. The reason why it is not a linear function is because the rate of change in the y-values is constant while the rate of change in the x-values varies, which indicates that the rate of the function also varies resulting in a non linear function.

3. The changes in x-values are;

Δx₁ = -5 - (-10) = 5

Δx₂ = 0 - (-5) = 5

Δx₃ = 5 - 0 = 5

Δx₄ = 10 - 5 = 5

The changes in y-values are;

Δy₁ = 4 - 9 = -5

Δy₂ = 2 - 4 = -2

Δy₃ = 0 - 2 = -2

Δy₄ = -3 - 0 = 2

a. Is it a linear function? No

b. The reason why the table of values does not represent the values of a linear function is that the first difference, which is the change in the consecutive y-values is not constant, such that the rate of changes of the ordered pairs of the function function is not constant and the graph therefore does not follow a straight line pattern

4) The changes in x-values are;

Δx₁ = 3 - (-1) = 4

Δx₂ = 7 - 3 = 4

Δx₃ = 11 - 7 = 4

Δx₄ = 15 - 11 = 4

The changes in y-values are;

Δy₁ = -4 - (-9) = 5

Δy₂ = 1 - (-4) = 5

Δy₃ = 6 - 1 = 5

Δy₄ = 11 - 6 = 5

a. Is it a function? yes

b. The reason why it is a function is because the first difference in the y-values is constant and the difference between consecutive x-value terms is also constant

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The answer should be C.

The range of definition of the cosine function is all real numbers. [tex]R[/tex]

It is also periodic in [tex]2\pi[/tex].

It is an even function. [tex]f(x)=f(-x)[/tex]

It can also be written in this form.

Check the picture below.

so if we look at those dimensions in centimeters, let's get the area of the cross-section, keeping in mind the volume of the bar is simply the area of the cross-section times the length.

[tex]\stackrel{\textit{\Large area of the cross-section}}{(2)(15)cm^2~~ + ~~(2)(15)cm^2~~ + ~~(8)(2)cm^2\implies 76~cm^2} \\\\\\ \stackrel{\textit{\LARGE bar's volume}}{76cm^2\cdot 120cm\implies 9120~cm^3}[/tex]

now, we know the density of the metal for the bar is 8 g/cm³, so let's do a quick conversion for the whole bar

[tex]\begin{array}{ccll} grams&cm^3\\ \cline{1-2} 8 & 1\\ g& 9120 \end{array} \implies \cfrac{8}{g}~~=~~\cfrac{1}{9120}\implies 72960=g\implies 72.960Kg[/tex]

so if one bar has 72.960 Kg, how many bars are there in 250Kg?

[tex]\begin{array}{ccll} bars&Kg\\ \cline{1-2} 1 & 72.960\\ b& 250 \end{array} \implies \cfrac{1}{b}~~=~~\cfrac{72.960}{250} \\\\\\ 250=72.96b\implies \cfrac{250}{72.96}=b\implies 3.43\approx b\qquad \textit{so only \underline{three whole bars}}[/tex]

The sum of the infinite geometric sequence exists and is equal to 15.

We are given an expression for terms in a geometric progression. The term at position "n" is given by the following formula.

T(n) = 12(0.2)^(n - 1)

The general representation for the terms in a geometric sequence is given by : T(n) = a*r^(n - 1).

Here, the variables "a" and "r" represent the first term and the common ratio for the geometric progression. On comparing the given formula with the standard representation, we conclude that the first term of the given geometric progression is 12 and the common ratio is 0.2.

a = 12

r = 0.2

The sum of an infinite geometric sequence exists if the common ratio lies between -1 and 1.

-1 < r < 1

-1 < 0.2 < 1

The above inequality holds true, so the sum exists. Let the sum of the infinite geometric sequence be denoted by "S". The formula and calculations are below.

S = a/(1 - r)

S = 12(1 - 0.2)

S = 12/0.8

S = 15

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Answer:

a = 2

Step-by-step explanation:

the constant terms inside the factors will multiply to give the constant term of the expansion, that is

a × 9 × - 4 = - 72

- 36a = - 72 ( divide both sides by - 36 )

a = 2