Which properties are present in a table that represents a logarithmic function in the form y = logo when b>

1. The y-values are always increasing or always decreasing.

II. The point (0, 1) exists in the table.

III. The y-values will decrease rapidly as the x-values approach zero.

IV. There will only be one x-value in the table with a y-value of zero.

O

O

O

O

I only

I and II only

1, 111, and IV

II and III only

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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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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 value  of x and y is  3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

Let the equations be

x + 3y = 8    ..............(1)

x + y = 2    ..............(2)

substracting equation 1 from 2

(x + 3y) - (x + y ) = 8 - 2

x + 3y - x + y = 6

3y - y = 6

2y =6

y = 6/2

y = 3

multiply the equation 2  with value of 3

x + y=2*3

x+y =6

x+3 = 6

x = 6 - 3

x = 3

Therefore the value of x and y is both are 3

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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 ordered pair is (3, 1) which is the intersecting point of these two equations.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.

Now the solution to this system is the common intersecting point of these equations.

With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.

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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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As we dilate rectangle ABCD by a scale factor of 1/2 and use E as the center, the coordinates of the point D' = (2, -1).

A rectangle is a quadrilateral in Euclidean plane geometry with four right angles.

The coordinates of the rectangle's points A'B'C'D' are as follows:

A' = the point's coordinates (-2, -1)

B' = the coordinates of the point (-2, 1)

C' = the coordinates of the point (2, 1)

D' = the coordinates of the point (2, -1)

Using the point P as the chart's origin, we get;

The coordinates of point B are (-4, 2), and the coordinates of point C are (4, 2).

Given that the sides are parallel to each other, the coordinates of point A = (-4, -2) The coordinates of point D = (4, -2)

We have; given that the sides are parallel to the axis.

The segment length AB = 2 - (-2) = 4

The segment length BC = 4 - (-4) = 8

The segment length CD = 2 - (-2) = 4

The segment length AD = 4 - (-4) = 8

As a result, a 1/2 dilation yields;

The segment length A'B' = AB/2 = 4/2 = 2

The segment length B'C' = BC/2 = 8/2 = 4

The segment length C'D' = CD/2 = 4/2 = 2

The segment length A'D' = AD/2 = 8/2 = 4

Point A' coordinates = Point A/2 coordinates = (-4, -2)/2 = (-2, -1)

= (-4, 2)/2 = (-2, 1) (-2, 1)

The coordinates of the point B' = (-2, 1) The coordinates of the point C' = (4, 2)/2 = (2, 1)

C' = the coordinates of the point (2, 1)

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The following are crucial factors in hypothesis testing:

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.

Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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-3 is less than 2

< is the symbol

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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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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Answer: x+5

Step-by-step explanation:

Because we don't have a number so we call it x. And to increase by 5 just need to +5. So x+5

Answer: (0, -3)

Step-by-step explanation:

You start from the x axis which is zero and then u go to the y axis and look for -3

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 proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.

What is coefficient of determination?

The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.

R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.

R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.

You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:

Dots represent the observations.

The line of best fit, or predictions of the model, is displayed as a black line.

Purple lines represent the deviations (the residuals) between the data and their expected values.

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The length of the photo having a width to length ratio of 2:3  is 6.9 cm.

Length is the distance between two points.

To calculate the length of the photo, use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the length of the photo is 6.9 cm.

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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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The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.

Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:

(x - h)² / a² + (y - k)² / b² = 1, b > a

Where:

If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:

(x - 3)² / 12² + (y - 5)² / 14² = 1

(x - 3)² / 144 + (y - 5)² / 196 = 1

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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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The rate of change of the function is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the function are 3 and 5

The inputs of the function are 1 and 2.

We have,

We will find two points on the graph.

The points on the graph are:

(0, 5), (1, 3), and (2, 1)

We can choose any two points.

(0, 5) and (1, 3)

The rate of change of the function.

= (3 - 5) / (1 - 0)

= -2/1

= -2

Thus,

The rate of change of the function is -2.

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If one of the brightest stars in the sky is Sirius ​, which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. The distance is 5.29 x 10^13 miles.

Distance can be defined as the length of an object or how far an object is from another object.

Given data:

9 light years

5.88 x 10^12 miles

Now let find the how far, in​ miles, is Sirius ​

Distance = 5.88 x 10^ 12 miles× 9  light year

Distance = 52,920,000,000,000

Distance = 5.29 x 10^13 miles

Therefore we can conclude that the distance is  5.29 x 10^13 miles.

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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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Answer:

3

Step-by-step explanation:

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:

Answer:

4

Step-by-step explanation:

use slope formula y2-y1/x2-x1

6-2/2-1

4/1

4 is the slope

Hopes this helps please mark brainliest

if we take 360 to be the 100%, what's 18 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 360 & 100\\ 18& x \end{array} \implies \cfrac{360}{18}~~=~~\cfrac{100}{x}\implies 20=\cfrac{100}{x} \\\\\\ 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]