The following histogram shows part of the probability distribution of the size (in megatons of released energy) of large meteors that hit the Earth's atmosphere. (A large meteor is one that releases at least one megaton of energy, equivalent to the energy released by a small nuclear bomb.)
That a large meteor will release at least 6 megatons of energy.The following histogram shows part of the probability distribution of the size (in megatons of released energy) of large meteors that hit the Earth's atmosphere. A large meteor is one that releases at least one megaton of ene equivalent to the ene released nuclear bomb a Sma A Probability 026 023 020 018 17 015 013 012 3 4 6 8 90 10 13 14 15 16 17 Energy (megatons) Calculate or estimate the following probabilities. (Round your answers to three decimal places.) (a) That a large meteor hitting the Earth's atmosphere wi release between 1 and 4 megatons of energy. 0.304 (b) That a large meteor hitting the Earth's atmosphere will release between 9 and 10.5 m of energy. 0.029 (c) That a large meteor will release at least 6 megatons of energy. 0,387

Answer:

3

Step-by-step explanation:

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 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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     2. There is not sufficient evidence to support the claim that the average percentage of readers who own a particular make of car is above 53%

What is null and alternative hypothesis??|
The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

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The trigonometric function simplified as a single expression is cosec² t .

The given trigonometric function is  : [tex]\frac{sin^2t+cos^2t}{sin^2t}[/tex]

We know from trigonometric identity : that sin²t +cos²t = 1

hence the given expression simplifies to 1 / sin²t

Again trigonometric ratios states that :

1 / sin t =  cosec t

∴ 1 / sin²t = cosec² t

Hence the trigonometric function is of the form cosec² t .

The right-angled triangle's angle and the ratios of its two side lengths are connected by the trigonometric functions, which are actual functions. They are also referred to as goniometric functions, circular functions, and angle functions .

The three trigonometric functions that are used in modern mathematics the most commonly are sine, cosine, and tangent. The less frequent cotangent, cosecant, and secant are their reciprocals.

Disclaimer: The complete question is :

simplify sin² ( t ) + cos ² ( t ) / sin ² ( t ) to an expression involving a single trig function with no fractions.

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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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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

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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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 matrix cannot be inverted if any eigenvalue is 0, which also means that the determinant is zero. This suggests a linear dependence between the columns of A. As a result, A is not of full rank and is not invertible.

What does "linearly dependent" mean?

A set's ability to have at least one linear combination of its components equal to zero when the coefficients are taken from another provided set and at least one of those coefficients is not equal to zero.

                  This feature applies to matrices or vectors. adjective that depends on linearity.

What does it mean to be linearly dependent?

A group of non-zero vectors is said to be linearly dependent if at least one of them can be expressed as a linear combination of the others.

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The percent that is student's estimate off are, 40%.

What is percent?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

Given:

A student has a container with a volume of 1. 5 liters.

She estimates the volume to be 0. 9 liters.

The student is off by

1.5 - 0.9 = 0.6

Now, the percent that is student's estimate off are,

(0.6 / 1.5) x 100 = 40%

Hence, by 40% is the student's estimate off.

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Answers:

Domain = {12, 10, 8, 6}

Range = {1, 3, 5, 7}

============================================

Explanation:

The domain is the set of allowed x inputs. Simply list the x coordinates of each point.

The range will have us list the y coordinates of each point. This shows the list of possible outputs.

Use curly braces for the domain and range because each is a set of values.

Optionally you can sort the values. I decided not to sort them to keep the same order of coordinates mentioned from left to right.

{12,10,8,6} sorts to {6,8,10,12}

If there were any duplicate items, in either domain or range, then you would erase them. Simply list each unique item once.

-------------------

Extra info:

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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Answer:

Step-by-step explanation:

Ok:

1. Use PEMDAS to solve equations(Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

First parentheses:

4(x−5)=20

4x-20=20

Second add subtract from both sides by isolating variable x!

4x-20=20

4x=40

4*x=40

x=40/4

x=10

3. Answer: x=10

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 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 roots of the quadratic equation are x = (3±2i)/2

The meaning of quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0

Given a quadratic equation, 4x²+13 = 12x

4x²-12x + 13 = 0

Quadratic formula =

x = [-b ± (√b²-4ac)]/2a

a = 4, b = -12 and c = 13

x = [12 ± (√(-12)² - 4*4*13)]/2*4

x = (12 ± 8i)/8

x = (3 ± 2i)/2

Hence, The roots of the quadratic equation are x = (3±2i)/2

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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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Answer:

x=1,5

Step-by-step explanation:

X^2-6x+5<0

(x-5)(x-1)<0

x=1,5

We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated.

The complete question is:

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.

What is the difference between standard deviation and confidence interval?

The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.

According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.

Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

The difference between the values in the matched pairs' standard deviation is calculated

To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.

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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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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 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 regarding the statement is given as follows:

A. 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.

The variables are classified as qualitative or quantitative as follows:

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

The variables in this problem are given as follows:

As they are qualitative variables, they can have association, and thus option A is correct.

The options are given by the image presented at the end of the answer.

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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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[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

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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