2. You flip a coin that has a heads side and a tails side.
a. What are the odds that the coin will land on heads the first time you flip it?
b. You have flipped the coin 50 coins. You have landed on heads 31 times and tails 19 times. What are the odds that the coin will land on tails on the next flip?

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 number of flags that could possibly be created, given the palette of colors to work with, and the number of stripes, is 360, 360 flags.

The designer has the choice to pick from 15 colors to work with. They will then pick another color, and then another, until they pick five colors to make stripes.

When they pick a single color, the number of choices drops to 14 colors. When they pick 5 colors, they will be left with 11 colors.

The number of possible flags is therefore:

= 15 x 14 x 13 x 12 x 11

= 360, 360 possible flags

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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 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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Answer:

AB = 8cm ; BC = 6.5 cm

Step-by-step explanation:

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm

The spring is compressed to 95.5 cm to the right if 129 N of force are used.

In this question, we have been given the spring constant k = 283 N/m

if 129 N of force are used then we need to find distance  that the spring compressed to the right.

Let the spring stretch from the equilibrium position x.

An equation for the spring's potential energy is,

PE = 1/2 ​kx^2

129 = 1/2 * 283 * x^2

2 * 129 = 283 * x^2

258/283 = x^2

x^2 = 0.9117

x = 0.9548 m

x = 95.5 cm

Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.

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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:

3

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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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 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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There is exactly one more real solution or there is exactly one more complex solution

Given,

One solution to a quadratic equation is x = -5/3

We have to find the correct statements from the given ones;

A polynomial of degree two is a quadratic equation.

This implies that a polynomial has two solutions.

We already have an answer to the query, which is a true root.

Then, the additional response that we lack can appear in the form of two responses.

It may be a real root or a complicated root, depending on the situation.

The following is the response to this query:

There is exactly one more real solution or there is exactly one more complex solution

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &4 \end{cases} \\\\\\ A=600[1+(0.033)(4)] \implies A=600(1.132)\implies A = 679.2[/tex]

Answer: photo

Step-by-step explanation: picture

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

Step-by-step explanation:

the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).

the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).

y = 10 - 2x

when x = 0, that means y = 10 - 2×0 = 10.

when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5

x-intercept = (5, 0)

y-intercept = (0, 10)

4y + 9x = 18

x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5

y = 0, 9x = 18, x = 18/9 = 2

x-intercept = (2, 0)

y-intercept = (0, 4.5)

6x - 2y = 44

3x - y = 22

x = 0, -y = 22, y = -22

y = 0, 3x = 22, x = 22/3 = 7 1/3

x-intercept = ( 7 1/3, 0)

y-intercept = (0, -22)

2x = 4 + 12y

x = 2 + 6y

x = 0, 6y = -2, y = -2/6 = -1/3

y = 0, x = 2 + 6×0 = 2

x-intercept = (2, 0)

y-intercept = (0, -1/3)

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]

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 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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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 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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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 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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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 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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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 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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Answer:

4

Step-by-step explanation:

use slope formula y2-y1/x2-x1

6-2/2-1

4/1

4 is the slope

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