An element with a mass of 520 grams decays by 25.1% per minute. To the nearest tenth of a minute, how long will it be until there are 60 grams of the element remaining?

The sequence of transformation that produce similar image is (d) a dilation followed by a rotation

Transformation involves changing the position and/or size of a figure.

There are four types of transformation, and they are:

The representation of the types of transformation are:

A dilation transformation would produce a similar image, while other transformation types would produce a congruent image

Hence, the sequence of transformation is (d)

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The area of cheese is 38 square centimeters.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the height of the cheese is 2.5 inches and the base is 4.75 inches.

The value of 1 inch is 2.54 centimeters.

Now convert 2.5 inches and 4.75 inches into centimeter:

2.5 inches = (2.5 × 2.54) centimeters = 6.35 centimeters

4.75 inches = (4.75 × 2.54) centimeters = 12.065 centimeters

The area of triangle is (1/2) × base × height

The area of the cheese is [(1/2) × 6.35 × 12.065] square centimeter

=38.31 square centimeter

= 38 square centimeters (nearest square centimeter)

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The slope intercept form is given as  y = 1/6x - 3.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equation is y + 2 = 1/6(x - 6).

It can be written in terms of slope-intercept form y = mx + c as below,

y + 2 = 1/6(x - 6)

=> 6(y + 2) = x - 6

=> 6y + 12 = x - 6

=> 6y = x - 6 - 12

=> y = 1/6(x - 18)

=> y = 1/6x - 3

Hence,  slope-intercept form of the given equation is y = 1/6x - 3.

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The value of x is 17

Define Angle

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Define Mid-line in Triangle

In a triangle, a midline (or a midsegment) is any of the three lines joining the midpoints of any pair of the sides of the triangle.

We know, the x+6 is mid-line of 46.

So, according to that make it a half of 46 is 23

Now, equate the value and find x

23 = x + 6

23 - 6 = x

17 = x

swap the sides

x = 17

Hence, the value of x is 17

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The determinants using co - factor expansion across the first row is 1 .

Given :

compute the determinants in exercises 1-8 using a co - factor expansion across the first row.

[tex]\left[\begin{array}{ccc}3&0&4\\2&3&2\\0&5&-1\end{array}\right][/tex]

Determinant of a matrix :

The determinant of a matrix is the scalar value computed for a given square matrix. Linear algebra deals with the determinant, it is computed using the elements of a square matrix.

determinant = 3 ( 3 * -1 - ( 5 * 2 ) - 0 ( 2 * -1 - ( 0 * 3 ) + 4 ( 2 * 5 - 0 * 3 )

= 3 ( -3 - 10 ) - 0 ( -2 - 0 ) + 4 ( 10 - 0 )

= 3 * -13 - 0 + 4 * 10

= -39 + 40

= 1

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Full question:

is in the image uploaded

The value of the function f(x) which is differentiable at all x, at x = 2

Or f(2) = b. 4.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, The function 'f' is differentiable for all x.

Now, f(1) = 2 and f(4) = 8, So, f(x) can be 2x as it is satisfying the conditions.

∴ At x = 2 or f(2) = 2(2) = 4.

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95% confidence interval is wider than 90% confidence interval.

Given as that unknown mean and a known variance.

let's suppose parameter for mean as µ and

for standard deviation σ.

we have sample of size n  as x1,x2,x3,x4.......xn.

Confidence means what degree of assurance do we desire that the interval estimate contains the  populace mean µ.

The likelihood that the interval falls within the level of confidence c

The population parameter is contained in estimate.

If the level of confidence is 90%, this means that we are 90%

confident that the interval contains the population mean, µ

The corresponding z-scores for 90% confidence interval are ± 1.645.

If the level of confidence is 95%, this means that we are 95%

confident that the interval contains the population mean, µ

The corresponding z-scores for 95% confidence interval are ± 1.96.

So In comparison to a 95% Confidence Interval, a 90% Confidence Interval would be narrower. This happens because the reliability of an interval containing the actual mean declines as the confidence interval's precision rises (i.e., CI width decreases) (less of a range to possibly cover the mean). Consider the case of 100% confidence; the interval must contain all possible values in order to guarantee that the mean is captured with 100% certainty.

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We want to see for which one of the given functions, the inverse derivate evaluated in x = 20 is equal to 1/5.

The correct option is B:  f(x) = x^3 + 5x + 20

What is inverse derivative?

The inverse function rule in calculus is a formula that converts the derivative of the inverse of a bijective and differentiable function, f, into the derivative of f.

Remember that two functions f(x) and g(x) are inverses if:

f( g(x)) = g( f(x))) = x

And for the inverse derivate of a function, we have the rule:

[tex]\frac{d}{dx}[f^{-1} (f(x))]=\frac{1}{{f^'}(x)}[/tex]

So first we need to find for what value of x each function is equal to 20, and then we need to see if the derivate of the function evaluated in that same value of x is equal to 5.

For example, for the first option we have:

A: f(x) = x + 5

We find the x-value such that the function is equal to 20.

f(15) = 15 + 5 = 20

We derivate the function.

f'(x) = 1

We evaluate the function in the x-value we got above.

f'(15) = 1

This is not the correct option, as this is not 5.

Now we need to do that for all the given options.

The only correct option will be the second one:

B: f(x) = x^3 + 5x + 20

First we find the x-value such that this is equal to 20

f(0) = 0^3 + 5*0 + 20 = 20

Then the x-value is x = 0.

Now we find the derivate of f(x).

f'(x) = 3*x^2 + 5

Now we evaluate that in the x-value we got before:

f'(0) = 3*0^2 + 5 = 5

As wanted, this is equal to 5.

Then we have:

[tex]\frac{d}{dx}[f^{-1} (f(0))]=\frac{1}{{f^'}(0)}[/tex]

[tex]\frac{d}{dx} [f^{-1} (20)]=\frac{1}{5}[/tex]

As wanted.

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There are 3 more days will it take her to plant all the trees.

What is rate?

The numerator of a ratio in mathematics represents the rate of change in the other (dependent) variable if the denominator of the ratio is expressed as a single unit of one of the related quantities and it is assumed that this quantity can be changed systematically (i.e., is an independent variable).

Given:

Tamika must plant 432 trees.

In the past 6 days Tamika planted 288 trees.

She continues the planting tree at the same rate.

As she planted 288 trees in 6 days.

That means she plant 288 / 6 = 48 trees in a day.

The remaining trees are 432 - 288 = 144.

So, 144 trees will be planted in 144 / 48 = 3 days.

Hence, there are 3 more days will it take her to plant all the trees.

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Among both teenage boys and adult men, delinquency, hard drug use, and aggressive-bullying responses to frustration have been linked with higher-than-average levels of Testosterone.

The sex hormone testosterone has significant physiological functions. It is thought to control the creation of sperm, red blood cells, muscle mass, fat distribution, and sex drive (libido) in men.

Males and females may both have diminished bone mass and sex drive if a man has low testosterone, which can cause symptoms like erectile dysfunction.

Low sperm counts, testicular shrinkage, and impotence are issues connected to males having abnormally high testosterone levels. Cardiac attack risk is elevated when heart muscle is damaged. enlarged prostate and urination problems.

Therefore , Drug use and aggressive to frustration are licked with higher-than-average levels of Testosterone.

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Probability mass function of H and X is,

P(X=m∣H=1)P(H=1) =[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] b^N (1-b)^(n-s) q (Since, q=(1-p))

Let X be the number of successful surgeries.

From the question, we have

it is observed that H∈{0,1}

P(H=1) =E(H)

=p

Next, observe that X∈{0,1,…n}, Now, we want to find following:

f(h,m) =P(H=h,X=m)

=P(X=m∣H=h)P(H=h)

Probability mass function of H and X is,

P(X=m∣H=1)P(H=1)=[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] a^n (1-a)^(n-k) p

P(X=m∣H=0)P(H=0)= [tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex]b^N (1-b)^(n-k) (1-p)

=[tex]\left[\begin{array}{c\alpha }n\\m\end{array}\right][/tex] b^N (1-b)^(n-s) q (Since, q=(1-p))

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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Answer:

a.

Step-by-step explanation:

it is not clear what your teacher discussed and wants from you here.

formally, all triangles are similar, as the description says. and the sequence of the vertexes in the "name" does not make any difference in identifying the triangle. this would be only important when identifying a specific angle (the center letter). in other words : a triangle is identified by naming its three corners in any sequence. simply because for the similarity concern you can twist and turn the triangle until it has the same orientation as the other triangle to compare.

so, again, a very strange question from your teacher. many greetings from me.

as explained, formally all 4 statements are correct.

but in order to identify one, it has to be a.

because the sequence of the corners are the same.

in QTS the side QT (the shortest of the 3 sides) is named first. and TS (the longest of the 3 sides) is named last.

in PQT we have the same sequence. PQ is the shortest side first, and QT is the longest side last.

no other answer option has the same sequence on the left and the right side.

but again, this is actually irrelevant for the similarity relation.

e.g. triangle RQS = triangle SQR, they are just twisted and turned images of the same triangle.

Polynomial with integer coefficients that cannot be factored into polynomials of lower degree, also with integer coefficients, is called a prime polynomial.

A polynomial is an algebraic expression made up of at least one algebraic term. An algebraic term is the product of a variable or variables and constant, where the variable can have no rational or negative exponents. A polynomial that has a single term is called a monomial, binomials have two terms and a trinomial has three terms.

A polynomial with integer coefficients that cannot be factored is called an irreducible or prime polynomial .

In order to identify whether a polynomial is prime or not, try factoring it. If it can be factored, then it is not prime but if it cannot be factored then it is prime.

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the measure of the value a is 24°

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angles of triangle = 180

Here given 3 angles are 2a, 3a and a+36°

So the sum of all the angles should be 180°

⇒2a+ 3a +a+36° = 180

⇒6a = 180-36

⇒a = 144/6= 24

Hence the measure of the value a is 24°

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a) A is better for the better experiment. A creates similar with respect to forest exposure. This are because of the orthogonal effect in quadratic main model.

b) Randomization of variety of trees to plot within each block reduces any bias due to comforting variable.

Blocking Scheme:

In this subsection, the goal is to construct a blocking design such that the blocking effects are orthogonal to the terms in the linear main effects model so that a linear plus quadratic main effects model can be estimated. Assume that all m-factors are quantitative and an m0-factor DSD is constructed. where m0 = m + k and n = 2(m + k) + 1 runs.  Removing the intermediate run from  results in a 2(m + k) run design.

Randomization:

When you randomize an experiment, you select subjects at random. For example, you can use simple random sampling. In this case, participant names are randomly drawn from a pool with each having an equal probability of being selected. You can also randomly assign treatments to participants by assigning random numbers from a random number table.

If you use randomization in your experiments, protect yourself from bias. For example, selection bias (where some groups are underrepresented) is eliminated and accidental bias (where random imbalance occurs) is minimized. If your sample is random, you can also run various statistical tests on the data (to test hypotheses).

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A linear equation is an algebraic equation with two or more variables in which the highest degree of the variables is one. Linear equations can be written in the form ax + b = c, where a, b, and c are all constants.16. x = 32

To solve the equation 8x - 5 = 257, we need to isolate the variable x. We can do this by adding 5 to both sides.

8x - 5 + 5 = 257 + 5

8x = 262

Then, we can divide both sides by 8 to isolate x.

8x/8 = 262/8

x = 32

To solve the equation 8x - 5 = 257, we can add 5 to both sides to isolate the variable x. This gives us 8x = 262. Dividing both sides by 8 then gives us x = 32. This is the solution to the equation.

The complete question is :

algebra 2: cc 2015 > chapter 7: solving rational equations > section exercises 7.5 > exercise 16 previous 16 answer sheet .What is the solution to the equation 8x - 5 = 257?

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The value of x in the absolute value equation |3x + 12| = 0 is -4

From the question, we have the following parameters that can be used in our computation:

|3x + 12| = 0

The above equation is an absolute value equation

So, we start by removing the absolute brackets

So, we have the following representation

3x + 12 = 0

Evaluate the like terms

This gives

3x = -12

Divide both sideso of the equation by 3

x = -4

Hence. the solution is -4

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The answer will be [tex]a^{-20-12a}[/tex] that can be find out using exponential function.

What are exponential function ?

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Like, f(x) = [tex]x^{a}[/tex]

x is base and a is power.

Basic rules to solve this function :

1. If we take the product of two exponentials with the same base, we simply add the exponents:

x^ a * x^ b = x^ a + b.

2. If we take the quotient of two exponentials with the same base, we simply subtract the exponents:

x^ a / x^ b =  x^ a-b

3. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents:

x^ (a)^ b = x^ (ab).

In given equation, [tex]{a^{2^{-2^5}}/{a^{4a^3}}[/tex]

So the answer is a^(-20-12a).

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Answer:

her sales would be 56.9

Step-by-step explanation:

Answer:

56.9

Step-by-step explanation:

The given expression can be simplified to obtain the quotient and remainder as 3x + 4 and -4 respectively.

The polynomial p(x) divided by the other polynomial g(x) gives remainder r(x) and quotient as q(x) such that degree of r(x) is not greater than g(x).

The given expression is (3x²+ 22x + 27)/(x+6).

The division can be done as follows,

First take the quotient as 3x so that that the remainder is,

3x²+ 22x - 3x(x + 6)

= 4x

Now, the new dividend is 4x + 6.

Take the quotient as 4 to get the remainder as,

4x + 6 - 4(x + 6)

= -18

It cannot be further divided because the degree of -18 is less than x + 6.

Which implies that the quotient is 3x + 4 and the remainder is -18.

Hence, the quotient and remainder for the given division of polynomials is 3x + 4 and -4 respectively.

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Answer:

83

Step-by-step explanation:

30+54=83

Answer:

The number is 6.

Step-by-step explanation:

30+54 = (?)(5+9)

30+54=80

5+9=14

30+54=80=(?)(5+9)

14x6=84

Answer:

So a circle with diameter 17 m has a circumference of 53.4 m

Step-by-step explanation:

Divide the circumference by π, or 3.14 for an estimation. The result is the circle's diameter.

Divide the diameter by 2.

There you go, you found the circle's radius

The systems of equations to solve for this quadratic function to model the values in the table is y =  -2x^2 + 4x - 2

The general form of a quadratic function is --> y = ax2 + bx + c

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

substitute c value

(-1 , -8) substitute

-8 = a ( -1 )2 + b ( -1 ) - 2

-8 = a - b - 2

-6 = a - b

( 3 , -8)

-8 = a ( 3 )2 + b ( 3 ) - 2

-8 = 9a + 3b - 2

-6 = 9a + 3b

a - b = -6

9a + 3b = -6

on solving :

9 ( b - 6 ) + 3b = -6

9b - 54 + 3b = -6

12b - 54 = -6

12b = 48

b = 4

a - 4 = -6

a = -2

The quadratic equation for this table is y = -2x^2 + 4x - 2

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Full question:

set up the systems of eqautions to solve for this quadratic function to model the values in the table.

x | y

-1 | -8

0 | -2

3 | -8

1. The equation of the line is:

y=-2x/3 + 5

2. The equation of the line in slope intercept form is:

y=3x+5

1. Given:

we have two points:

(-3,7) = (x₁,y₁)

(9,-1) = (x₂,y₂)

equation of the line is:

y - y₁ = m(x-x₁)

₁first calculate slope m = y₂-y₁/x₂-x₁

m = -1-7/9-(-3)

m = -8/12

m = -2/3

now, y - 7 = -2/3 (x-(-3)

y-7=-2/3(x+3)

y-7=-2x/3-2

y=-2x/3-2+7

y=-2x/3 + 5

hence equation of the line is y=-2x/3 + 5

2. Given two points:

(2, 11) and (4, 17)

(2, 11) = (x₁,y₁)

and (4, 17) = (x₂,y₂)

slope intercept form:

y=mx+c

we need to calculate the m value:

m = 17-11/4-2

m = 6/2

m=3

now substitute in the given form:

y - 11 = 3(x-2)

y-11=3x-6

y=3x-6+11

y=3x+5

Hence we get the required answer.

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The minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of is 55.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Assuming that the standard deviation of the number of hours worked by college graduates is 6.30 hours per week

We need to find the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.4 hours per week of.

The formula to determine sample size is n = [zs/E]²

z is standardization value indicating confidence level.

s is sample standard deviation.

E is acceptable acceptance error.

n = [invNorm(0.95)×6.3/1.4]²

n = [1.645×6.3/1.4]²

n=54.79=55

Hence, 55 is the minimum sample size needed in order for us to be 90% confident that our estimate is within 1.2 hours per week of.

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Answer: $6,000,000 = 40%

               $2,800,000 = 18.66666667%

Step-by-step explanation:

Divide the sales by the total sale.

Ex:

6,000,000/15,000,000 = .4

2,800,000/15,000,000 = .1866666667

A parametrization of path C is x= 4t and y = 8t

Line segments on nearly trivial to parametrize. It is often it easiest to do in interval t∈ [0,1]

Then we just need to think about what we need to add to each first coordinate to get the second

Since, 0+ 4 = 4  and 0+ 8 = 8

So, parametrization is

=> x = 4t

y = 6t

(b) To evalute the line integral, we have to derivate parametrize

dx/dt = 4

dy/dt = 8

So, the differential line element is

[tex]ds = \sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2}[/tex]

=> √(4)²+(8)²

=> 4√5

Integrating ,

[tex]\int\limits_{c} {x^2 + y^2} \, ds\\ = \int\limits^1_0 {(4t)^2 + (8t)^2 } 4\sqrt{5} \,dt\\=4\sqrt{5} [\frac{80}{3} t^3]^{1}_{0}\\[/tex]

Putting the limits

=> 285.51

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False. The orthogonal projection of y onto a subspace W is never reliant on any particular basis and always depends simply on W.

The term "orthogonality" can be used when the vector space contains an inner product and is complete (i.e., wh

en it's a Hilbert space). When the range and the null space are orthogonal subspaces, the projection is said to be orthogonal.

In order to portray three-dimensional objects in two dimensions, orthographic projection (also known as orthogonal projection and analemma) is used. Every plane of the picture appears in an affine transformation on the viewing surface thanks to orthographic projection, a type of parallel projection in which all of the projection lines are orthogonal to the projection plane. An oblique projection, also known as a parallel projection in which the projection lines are not orthogonal to the projection plane, is the reverse of an orthographic projection.

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The descending order of the multiplied polynomial is 4x² - 3x + 8xy - 6y

The word polynomial in math refers the algebraic expression in which the exponents of all variables should be a whole number.

Here we have given the polynomial l (x + 2y)(4x - 3).

And we need to do the multiplication operation on it and then write your answer in descending order of x.

AS per the following formula, the multiplication of the polynomial is calculated as,

=> (a + b) ( c + d) = (ac + ad + bc + bd)

Here let us consider a = x and b = 2y, c = 4x and then d = -3

Then the resulting value after the multiplication, it can be written as,

=> (x(4x) + x(-3) + 2y(4x) + 2y(-3))

When we simplify this one then we get

=> 4x² - 3x + 8xy - 6y

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