2 This line has a _________._ slope.
Positive no slope undefined negative.

The object continues to roll without slipping, and the actual force of static friction stays constant.

A force that holds an object at rest is called static friction.

The definition of static friction is: The resistance people feel when they attempt to move a stationary object across a surface without actually causing any relative motion between their body and the surface they are moving the object across.

The range of static friction is 0 to the minimum force required to initiate motion.

The following is the formula to determine static friction: Normal Force x Static Friction Coefficient = Static Friction.

So, in the given situation the object keeps rolling without slipping, and the static friction's actual force remains constant.

Therefore, the object continues to roll without slipping, and the actual force of static friction stays constant.

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In the discrete distribution the probability that x equals 5 is 0.51

A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum

The summation of the discrete probabilities must be always equal 1,

The probaility of 2 is 0.16

The probaility of 6 is 0.30

The probaility of 8 is 0.21

We need to find The probaility of 5

To find the probaility of 5, we can subtract the probaility of all other numbers from 5.

Probability (X = 5) = 1 - (0.25+0.16+0.08) = 0.51

Therefore, in the discrete probability distribution the probability that x equals 5 is 0.51

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Answer:9/10

Step-by-step explanation:

make 3/4 equal to 3/20 by multiplying by 5

15/20 + 3/20 = 18/20

18/20 = 9/10

The exact value of tan(θ ) in simplest radical form is 1/9 .

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

(-9,-1), is a point with x= -9 = adjacent side, y= -1 = opposite side

tan(θ ) = opposite side/adjacent side = -1/-9  = 1/9

1/9 can't be simplified further

So, the exact value of tan(θ ) in simplest radical form is 1/9 .

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Answer:

129723

Explanation:

[tex]1800(1+0.13)^{35} \approx 129723[/tex]

The ratio of a:b is 3:16

What is Ratio?

Ratio ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division. That is, a:b = a/b

To find the ratio a:b

[tex]\frac{a+3b}{5}[/tex] = [tex]\frac{a-2b}{2}[/tex]

Cross multiply

2(a+3b) = 5(a-2b)

Open bracket

2a + 6b = 5a - 10b

Collect like terms

2a - 5a = -10b - 6b

-3a = -16b

Divides through by -1

-3a/-1 = -16b/-1

3a = 16b

The Ratio a:b is 3:16

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The quotient is 2x² + 10x − 5, and the remainder is 0.

What is synthetic division?

Synthetic division is a method in algebra for manually performing Euclidean division of polynomials that requires less writing and fewer calculations than long division. It is typically taught for division by linear monic polynomials, but the method can be applied to any polynomial.

The given polynomial is (2x³ + 4x² - 35x + 15) and we have to divide this polynomial by (x - 3).

By using synthetic division

   2x³ + 4x² - 35x + 15

Take the constant term of the divisor with the opposite sign and write it to the left

     3 |   [tex]x^3[/tex]    [tex]x^2[/tex]     [tex]x^1[/tex]      [tex]x^0[/tex]

        |   2     4     -35     15

   ----|----------------------------

Write down the first coefficient as it is

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

   3 |   2            4     -35     15

      |         3.2 = 6

 ----|----------------------------

         2           10    

Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

 3 |   2      4     -35     15

    |           6       30

-----|----------------------------

         2    10       -5

Again, we get

3 |   2      4     -35     15

    |           6      30   -15

-----|----------------------------

         2    10     -5      0

We have completed the table and have obtained the following resulting coefficients: 2,10,−5,0.

Thus, the quotient is 2x² + 10x − 5, and the remainder is 0.

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The value of (r + s) in the given equation, (x+r)(x+s) = x² + 3x - 10, is (r + s) = 3

From the question, we are to determine the value of the given expression.

The expression we are to determine its value is

(r + s)

To do this, we will compare the terms of the given equation.

From the given equation

(x+r)(x+s) = x² + 3x - 10

First, we will expand the left-hand side of the equation

Expanding the left-hand side of the equation

(x+r)(x+s)

x(x + s) + r(x + s)

x² + xs + xr + rs

Factor the middle expressions

x² + x(s + r) + rs

x² + x(r + s) + rs

x² + (r + s)x + rs

Now, compare the resulting expression to the expression on the right-hand side

x² + 3x - 10

By comparison,

r + s = 3

Hence, the value is 3

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If he has $2.34 to spent on oranges, then he can buy 6 oranges

Total number of oranges in a bag = 4 oranges

The cost of 4 oranges = $1.4

The total amount that he spent = $2.34

Here we have to use the unitary method

The cost of 1 orange = The cost of 4 oranges / 4

Substitute the values in the equation

= 1.4/4

= $0.35

Then the number of oranges that he bought =  The total amount that he spent / The cost of 1 orange

Substitute the values in the equation

= 2.34 / 0.35

Divide the terms

= 6.68

≈ 6

Hence, he can buy 6 oranges with $2.34

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The all the possibilities and combination for the x - intercepts , of the roots of the polynomial with degree 4 are :  

0 x-intercepts and 4 imaginary roots   ,

4 distinct x-intercepts  ,  

1 x-intercept with multiplicity 4  and

2 distinct x-intercepts each with multiplicity 2   .

In the question ,

it is given that ,

there is polynomial of degree 4 ,

and some statements about the roots of the polynomial is given ,

we have to find the suitable options that are for the roots .

We know that the fourth degree polynomial will have theoretically four roots .

So , the possible situations for the roots are

it can have ,

0 x intercepts and 4 imaginary roots ( where imaginary roots must occur in pairs )   OR

it can have 4 distinct x intercepts .    OR

1 x intercept that have multiplicity 4 ,     OR

2 distinct x intercepts that have multiplicity 2 .

Therefore  , the possibilities options are (b) , (d) , (e) and (h) .

The given question is incomplete , the complete question is

Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts .

(a) 2 distinct x-intercepts of which one has a multiplicity of 3 ,

(b) 0 x-intercepts and 4 imaginary roots

(c) 3 distinct x-intercepts of which one has a multiplicity of 2

(d) 4 distinct x-intercepts

(e) 1 x-intercept with multiplicity 4

(f) 1 x-intercept with 3 imaginary roots

(g) 3 distinct x-intercepts and 1 imaginary root

(h) 2 distinct x-intercepts each with multiplicity 2

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There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

What are qualitative and quantitative variables?

The variables are classified as qualitative or quantitative as follows:

Qualitative variables assume labels as values.

Quantitative variables assume numbers as values.

The relevance of the variables according to association and correlation are given as follows:

Qualitative variables can have association.

Quantitative variables can have correlation.

The variables in this problem are given as follows:

Television watching -> yes/no -> qualitative.

Crimes committed -> yes/no -> qualitative.

As they are qualitative variables, they can have association, and thus there is no correlation between the two variables

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Given two calculations are different.

What is a square of a number?

The square of any number can be calculated by multiplying the number by itself twice.

Let 'a' be any number then the square of this number 'a' will be

                        a² = a × a

Now  - 3² = - (3) × (3)

               = -9  ----------(I)

and (-3)² = (-3) × (-3)

              = 9 ----------(II)

By observing (I) and (II) we can say that in the second case just because of the scope of brackets the square of -3 would result in 9.

But in the first case square of 3 would give 9 and because of the minus sign, it gave -9.

Hence, These two calculations are different.

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The final answer to this Problem is 32000 pesos.

What is Company?

A company is an organization that provides goods or services to its customers in exchange for money. Companies are typically formed by entrepreneurs or business owners who have a vision for a product or service they want to offer. The company is responsible for producing the product or service, marketing it, and then distributing and selling it to the public. Companies must also manage their finances and comply with any legal or regulatory requirements. Companies are typically owned by shareholders who reap the profits of the business. Successful companies often have a strong corporate culture that is reflected in their mission and values.

Pesos that initially was available = 15000 pesos

During year Pesos purchased by company = 25000 pesos

Total pesos at end of the year = 15000 + 25000 pesos = 40000 pesos

Total pesos remaining at end of year = 8000 pesos

Hence pesos consumed in the complete year = 40000 - 8000= 32000 pesos

Hence 32000 pesos are left in the company

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

Answer: First number is 16, second number is 17.

Step-by-step explanation
16 + 17 = 33

16 x 7 = 112
17 x 5 = 85

112 + 85 = 197

The correct option is [tex]6x^2+3x[/tex] which is the area of triangle. It can be obtained by the formula of area of triangle and algebriac multiplication.

What is the are formula of area of a triangle?

Area of any shape is the measure of the 2 dimentional space occupied by that shape. Its SI unit is [tex]m^2[/tex].  Area of the triangle is given by the following formula:

[tex]A=\frac{1}{2}bh[/tex]

Here, A is the area, b is the base, and h is the height.

Substitute 4x+2 for b and 3x for h in the above equation.

[tex]A=\frac{1}{2}(4x+2)(3x)[/tex]

Now, multiply using algebriac multiplication as follows:

Initially, use distributive property as follows:

[tex]A=\frac{1}{2}[(4x)(3x)+(2)(3x)][/tex]

Now, multipliy and again open brackets as follows

[tex]A=\frac{1}{2}(12x^2+6x)\\=6x^2+3x[/tex]

This gives the area of the triangle is [tex]6x^2+3x[/tex]. Hence, the correct option is the last option.

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Answer:

d

Step-by-step explanation:

The mean and the standard deviation of the sampling distribution of x are given as follows:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The parameters for this problem are given as follows:

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/sqrt(10) = 19 seconds.

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Trigonometric functions have the same maximum value y = arcsinx and y = arccosx.

What is Trigonometric Function?

Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. It implies that these trig functions provide the relationship between a triangle's angles and sides.

Arcsin, Arccos, Arcsec, and similar symbols are used to represent inverse trigonometric functions.

Inverse functions refer to the trigonometric operations that are used to determine an angle from any of the angle's trigonometric ratios.

When solving inverse trigonometric equations, the following formula is used:

Arcsinx = Arcsinx -

arccosx = pi-arccosx.

Arctan = Arctan - Arctan

arsecx = pi - arsecx

The maximum values we obtain from the following equations are:

arcsinx = -1 to 1

arccosx = -1 to 1

arctanx = -pi/2 to pi/2

arcsecx = ∞

So the trigonometric functions which have the same maximum value is arcsinx and arccosx.

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Answer:

-626.8

Step-by-step explanation:

78 -716 + (0.8)(14)

78 - 716 + 11.2

(78 -716) + 11.2

-638 + 11.2

-626.8

The half-life of vanadium-48 is 16 days.

What is half life?

The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.

According to law of radio active decay, IN=N

N-- amount of sample present

N1--- initial amount of sample

Decay 0 constant

Half life = 16 days

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The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

  (2n -5)(3n -2)

Step-by-step explanation:

You want to factor 6n² -18n +10.

You want to start by finding factors of the product (6)(10), the first and last coefficients, that have a sum equal to -18, the linear term coefficient.

This sum is negative, but the product is positive, so both factors will be negative. Listing the smallest magnitude first, we have ...

  60 = (-1)(-60) = (-2)(-30) = (-3)(-20) = (-4)(-15) = (-5)(-12) = (-6)(-10)

The sums of these pairs are -61, -32, -23, -19, -17, -16. This identifies the pair of interest as (-4)(-15).

From here, there are a couple of ways you can proceed. One is to write the linear term as a sum using these values:

  6n² -4n -15n +10

Now, you can factor by grouping:

  = (6n² -4n) -(15n -10)

  = 2n(3n -2) -5(3n -2)

  = (2n -5)(3n -2) . . . . . . . . the factorization you want

Another way you can do this is to write binomial factors using the leading coefficient for each one. The product of these must be divided by the leading coefficient for it to remain equal to the original trinomial.

  = (6n -4)(6n -15)/6

The denominator of 6 is used to reduce each of the binomial factors.

  [tex]=\dfrac{(6n-4)(6n-15)}{2\cdot3}=\dfrac{6n-4}{2}\cdot\dfrac{6n-15}{3}[/tex]

  = (3n -2)(2n -5) . . . . . . . the factorization you want

-3 is less than 2

< is the symbol

Answer:

Step-by-step explanation:

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

[tex]A=5300(1+\frac{.08}{12} )^{12\times6[/tex]

[tex]A=5300(1.00666666667)^{72}[/tex]

[tex]A=5300\times1.613502[/tex]

[tex]A=8551.561489[/tex]

Now, it is up to you to round to the nearest cent.

Thanks,

Eddie

System A: (1, -1)

System B: No solution

Answer:

System A

The system has a unique solution: x=1, y=-1

System B

The system has no solution

Step-by-step explanation:

System A

Use simultaneous equations to see if we can solve the system by multiplying the second equation by -1 and adding them together:

5x + 3y = 2

-4x - 3y = -1

We get (5-4)x+(3-3)y=(2-1), which simplifies to x=1

If x=1:

5+3y=2

3y=-3

y=-1

Since we have specific answers for x and y, we can say the system has a unique solution.

System B

If y is equal to both 5x+8 and 5x+5, that means

5x+8=5x+5

Subtracting 5x from both sides we get 8=5, which is illogical.

Therefore the system has no solution

Ordered triplet (-2, -6, 3) is the solution of the system of equations

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

How to determine if an ordered triplet is solution to system of equations?

To determine if an ordered triplet is a solution to a system of three equations, we substitute the values of the variables into each equation. If the ordered triple makes all three equations true, it is a solution to the system.

According to the given question:

System of equations are

3x+4y-z = 5

5x-y + 3z = -7

9x + 5y + 7z = -21

Now, substituting (-1, 2, 0) in every equation to check if LHS = RHS for each.

1. 3x + 4y - z = 5

    LHS = 3(-1) + 4(2) - 0 = -3 + 8 = 5 = RHS

2. 5x-y + 3z = -7

   LHS = 5(-1) - 2 + 0 = - 5 -2 = -7 = RHS

3. 9x + 5y + 7z = -21

   LHS = 9(-1) + 5(2) + 0 = -9 + 10 = 1 ≠ RHS

Therefore (-1, 2, 0) is not the solution for the system of equations.

Similarly substituting (-2, -6, 3) in every equation.

Clearly (-2, -6, 3) satisfies the system of equations.

Hence (-2, -6, 3) is the solution to the system of equations.

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