5
complete the vector to fully describe
the single transformation which
takes shape a to shape b.
4
3
a a
a
2
1
translate shape a by the vector
1
2
3 4
5
-5 -4 -3 -2 -1 0
-1
a
b.
ch a. no

Answer:

-1 1/5

Step-by-step explanation:

Change the whole number 4 to an improper fraction

-4 4/5 ÷ 4/1 = -4 4/5 ÷ 4/1

Reciprocal the 4/1 will become 1/4 then go to multiplication

-4 4/5 ÷ 4/1 = -4 4/5 × 1/4

Change to improper fraction the -4 4/5

-4 4/5 ÷ 4/1 = -24/5 × 1/4

Then simply multiply the two numerators and the two denominators

-4 4/5 ÷ 4/1 = -24/20

Finally, Simplify it to get the answer

-4 4/5 ÷ 4/1 = -1 1/5

Answer:

Inverse g(x) = -x/3-6

Step-by-step explanation:

To understand this just think g(x) as y so

we got y= -3(x+6) after that we change the minus three to left

so we got -y/3 because -3 is multiply. After that plus 6 came and become minus 6.

After all,you have to replace x in y place.

y = -3(x +6)

-y/3 = x +6

-y/3 -6 = x

-x/3 -6 = g(x)

The Laplace Transform Method can be used to solve all of these equations except for equation (e).

a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.

b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.

c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.

e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.

f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.

h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.

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The type of sample being used in this scenario is a cluster sample, where the municipality surveys all households in 149 randomly-selected neighborhoods door-to-door to gather residents' opinions on the proposed property tax increase.

In a cluster sample, the population is divided into groups or clusters, and a subset of clusters is selected for data collection. In this case, the neighborhoods are considered the clusters, and 149 randomly-selected neighborhoods are surveyed.

The advantage of using a cluster sample is that it simplifies the sampling process by grouping individuals together based on their proximity. By visiting homes door-to-door within each selected neighborhood, the municipality can efficiently gather information from a diverse range of households without the need to individually select households from the entire population.

However, it's important to note that the use of a cluster sample introduces a potential for clustering effects, where individuals within the same cluster may have similar opinions or characteristics. This clustering effect needs to be taken into account during data analysis to ensure accurate representation of the entire population.

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In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.

The probability that k out of n trials will be successful is given by the binomial probability mass function:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.

To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

using the above formula we can find the probability of getting k winning tickets

P(x<20) = P(0) + P(1) + P(2) +...+ P(19)

= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81

This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.

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1. Linearization of f(x, y) = √(34 - x^2 - 5y^2) at the point (-2, 1):

The linearization L(x, y) = -2x + 3y + 5.

2. Using linear approximation to estimate f(-2.1, 1.1):

f(-2.1, 1.1) ≈ √(34 - (-2.1)^2 - 5(1.1)^2) ≈ 4.9.

3. Equation of the tangent plane to z = e^(3x)/(17ln(3y)) at (3, 2, 3.04229):

The tangent plane's equation is z = (3x - 6) + (2y - 4) + 3.04229.

1. Linearization:

The linearization of a multivariable function at a point is the linear approximation that best approximates the function's behavior near that point. To find the linearization of f(x, y) = √(34 - x^2 - 5y^2) at (-2, 1), we first compute the partial derivatives with respect to x and y:

∂f/∂x = -x / √(34 - x^2 - 5y^2)

∂f/∂y = -5y / √(34 - x^2 - 5y^2)

Then, we evaluate these derivatives at the point (-2, 1) to get:

∂f/∂x(-2, 1) = 2 / √27

∂f/∂y(-2, 1) = -5 / √27

Using the point-slope form of a linear equation, the linearization L(x, y) is:

L(x, y) = f(-2, 1) + (∂f/∂x(-2, 1))(x - (-2)) + (∂f/∂y(-2, 1))(y - 1)

L(x, y) = -2x + 3y + 5.

2. Linear Approximation:

To estimate the value of f(-2.1, 1.1) using linear approximation, we plug these values into the linearization L(x, y):

f(-2.1, 1.1) ≈ L(-2.1, 1.1) ≈ -2(-2.1) + 3(1.1) + 5 ≈ 4.9.

3. Tangent Plane:

To find the equation of the tangent plane to the surface z = e^(3x)/(17ln(3y)) at the point (3, 2, 3.04229), we first find the partial derivatives of z with respect to x and y:

∂z/∂x = (3e^(3x))/(17ln(3y))

∂z/∂y = -(3e^(3x))/(17yln(3y))

Then, we evaluate these derivatives at (3, 2):

∂z/∂x(3, 2) = (3e^9)/(17ln6)

∂z/∂y(3, 2) = -(3e^9)/(34ln6)

The equation of the tangent plane is given by:

z = z0 + ∂z/∂x(x - x0) + ∂z/∂y(y - y0)

where (x0, y0, z0) represents the given point. Plugging in the values, we get:

z = 3.04229 + (3e^9/(17ln6))(x - 3) - (3e^9/(34ln6))(y - 2)

Simplifying, we obtain the equation of the tangent plane as:

z = (3x - 6) + (2y - 4) + 3.04229.

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The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

To calculate the mean value, we add up all the values and divide by the

number of values:

(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000

So the mean value is 1000 rpm.

To calculate the standard deviation, we need to first calculate the

variance:

Variance =\([(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6\)

Variance = 12000 / 6 = 2000

So the variance is \(2000 (rpm)^2\).

The standard deviation is the square root of the variance:

Standard deviation = √(2000) = 44.7 rpm

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

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Answer:

None

Step-by-step explanation:

For me, the easier way to see that the answer is 30 students (12 years and older) is to convert the 60% to a decimal, 0.60, and multiply by the total number of students:

(0.06)*(50) = 30 students are 12 and older.

None of the listed answers make sense to me.  Yes, a couple have the correct answer, but their derivation is incorrect.

100 ÷ 20 = 50   [who, what??]

100 ÷ 2 = 50       [who, what, why??]

60 ÷ 2 = the number of students who are 12 years old.  [Correct, but where did the 2 come from?]

60 ÷ 20 = 3 students  [gimmee a break]

30 of the 50 students are 12 years old. [Yes, but what is the calculation that led to this conclusion?]

Tom earns $32,660.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean. The mean salary is $27,800 and the standard deviation is $5400, so Tom's salary is $27,800 + 0.9 * $5400 = $32,660.

Here is a more detailed explanation of how to calculate Tom's salary:

The mean salary is $27,800.

The standard deviation is $5400.

A z-score of 0.9 means that Tom's salary is 0.9 standard deviations above the mean.

To calculate Tom's salary, we can use the following formula:

Salary = Mean + (Z-score * Standard deviation)

Substituting the known values into the formula, we get:

Salary = $27,800 + (0.9 * $5400)

Salary = $32,660

Therefore, Tom earns $32,660.

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Answer:

$98.14

Step-by-step explanation:

150.99 x 0.35. Subtract answer from total to get final price.

Step-by-step explanation:

that's it b is for brings

b compliment is for doesn't bring

Answer:

292116.8

Step-by-step explanation:

The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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Answer:

Robie made an image but I'll give you points to plot in case you are confused.

Step-by-step explanation:

(0,-2)

(1,0)

(2,2)

etc.

(x goes up by 1, y goes up by 2 start from -2 y)

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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The multiplication of \((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)in scientific notation is \(9.6 \times {10}^{21} \)

Multiply the decimal numbers to multiply the integers in scientific notation. Add the 10 power exponents after that. In scientific notation, place the new power of 10 with the decimal.

given that \((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)

Now, find the answer in scientific notation

\((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\)

combine the all the like terms

\((2.4 \times 4)( {10}^{14} \times {10}^{7} )\)

According to the exponent same base rule, an exponent will be added if the bases of two exponents are the same.

\((9.6) \times ( {10}^{14 + 7)} ) \\ 9.6 \times {10}^{21} \)

Hence,the multiplication of\((2.4 \times {10}^{14} ) \times (4 \times {10}^{7} )\) in scientific notation is \(9.6 \times {10}^{21} \)

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In problem 2, we are comparing the Lagrange form of interpolation polynomial and the Newton form of the interpolating polynomial of degree 3. To solve this problem, we first need to understand the concepts of interpolation, polynomial, and Lagrange.

A set of basis polynomials are used to create the interpolating polynomial in the Lagrange method of polynomial interpolation.

Returning to issue 2, we are given the degree 3 interpolating polynomial, which is a degree 3 polynomial that traverses a specified set of data points.

We are asked to contrast this polynomial with the interpolation polynomial in the Lagrange form.

Another approach to creating a polynomial that traverses a given set of data points is to use the Lagrange form of interpolation polynomials.

We must assess the degree 3 interpolating polynomial and the Lagrange form of the interpolation polynomial at the specified point p(0) in order to compare the two findings.

In conclusion, we can say that to compare the Lagrange form of interpolation polynomial and the Newton form of the interpolating polynomial of degree 3, we need to evaluate both polynomials at the given point and choose the one that gives the same value as the data point.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

Answer:

hope this answer helps you dear.....take care and may u have a great day ahead!

Answer:

18

Step-by-step explanation24/0.75 is 18

Answer:

18

Explanation:

Not sure what you mean by AGONSA but the method to get 18 is;

\(\frac{24}{1} *\frac{3}{4} = \frac{72}{4} = 18\)

Answer:

it is 5

Step-by-step explanation:

102% x 5 =5.1

if you times each answer with you percentage you get the answer

Using the principle of percentage approximation, the value of the number, n is 5

Let the number = n

We then write the expression thus :

(102/100) × n = 5.1

1.02n = 5.1

n = 5.1 / 1.02

n = 5

Therefore, the number, n in which 102% gives a value of 5.1 is 5

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Answer:

B. -9, 7

Step-by-step explanation:

For the rational expression to be undefined the denominator has to equal 0.

x² + 2x - 63 = 0

Factor left side.

(x - 7)(x + 9) = 0

Set factors equal to 0.

x - 7 = 0

x = 7

x + 9 = 0

x = -9

x = -9 or x = 7

Answer:

B

Step-by-step explanation:

A rational expression is undefined when the denominator of the expression equals 0 (this is because anything over 0 is undefined). In other words, to find the values for which the given expression is undefined, we simply have to find the zeros of the denominator. We can ignore the numerator. Thus, let:

\(0=x^2+2x-63\)

This is now a quadratic. Solve for the quadratic. I will factor but you can do whatever you like (complete the square, quadratic formula, etc.).

We notice that two factors that multiply to -63 and also add to +2 is 9 and -7. Thus:

\(0=(x+9)(x-7)\)

\(x+9=0 ; x=-9\)

\(x-7=0; x=7\)

The zeros are -9 and 7.

The denominator will equal 0 at these values, and the expression will be undefined.

Answer:

78

Step-by-step explanation:

Given:

h + 9g

Required:

Evaluate when g = 8 and h = 6

Solution:

Plug in the values of the variables into the expression

Thus,

6 + 9(8)

= 6 + 72

= 78

If I were required to survey Fresno City College students regarding their employment status, I would use a stratified random sampling technique.

Stratified random sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the survey. In this case, the relevant characteristic is employment status. The population consists of all Fresno City College students, and the two strata are employed and unemployed students.

Once the population has been divided into strata, a random sample is taken from each stratum. The sample size for each stratum is proportional to the size of the stratum in the population. For example, if 60% of Fresno City College students are employed, then 60% of the sample should consist of employed students.

Using a stratified random sampling technique ensures that the sample is representative of the population and that each subgroup is represented in the sample. It also reduces sampling error and increases the precision of the estimates.

The expression that can be used to find the value of x is ∘23sin85∘​/sin55∘, the correct option is A

We are given that;

In triangle DEF, EF=23, DE=x, angleD=85degree, angleF=55degree

Now,

To find the value of x, we can use the law of sines with the given information:

sin85∘x​=sin55∘23​

Solving for x, we get:

x=sin55∘23sin85∘​

Using a calculator, we can approximate x as:

x≈26.6

Therefore, by the given angles the answer will be ∘23sin85∘​/sin55∘

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An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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The extreme values of f subject to the given constraints are -(5/4)^(1/4) and (5/4)^(1/4).

How we can find the extreme value of f subject to both constraints?

We can use the method of Lagrange multipliers to find the extreme values of f subject to the given constraints. Let L(x,y,z,λ,μ) be the Lagrangian function defined as:

Setting the partial derivatives of L with respect to x,y,z,λ and μ to zero, we obtain the following system of equations:

From equation (3), we have x = λy. Substituting this into equation (4), we obtain y^2λ - 1 = 0. Therefore, λ = 1/y^2. Substituting this value of λ into equations (1) and (2), we obtain:

Substituting equation (6) into equation (5), we obtain z^4 = 25/16. Therefore, z = ±(5/4)^(1/4).

The critical points are obtained by substituting the values of y and z obtained from equations (6) and (7) into the expression for x = λy. Therefore, the critical points are:

To determine the extreme values of f, we evaluate the function f at each of the critical points. Therefore, we have:

Hence, the minimum value of f is -(5/4)^(1/4), and the maximum value of f is (5/4)^(1/4).

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