evaluate the logarithmic expression.

The equation of the tangent plane to the ellipsoid at the given point is [tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} - \frac{zz^0}{c^2} = 1[/tex]

The equation of the tangent plane to the ellipsoid is given as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1[/tex]

The point on the ellipsoid is given as:

(x0, y0, z0)

The equation of the tangent plane to the ellipsoid at the given point can be written as:

[tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} + \frac{zz^0}{c^2} = 1[/tex]

Given that the equation of the tangent plane to the hyperboloid is

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} - \frac{z^2}{c^2} = 1[/tex]

The equations at the tangents of the ellipsoid and the hyperboloid take the same form.

So, the equation of the tangent plane to the ellipsoid at the given point is [tex]\frac{xx^0}{a^2} + \frac{yy^0}{b^2} - \frac{zz^0}{c^2} = 1[/tex]

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Answer:

  0.252 m

Step-by-step explanation:

At the fundamental frequency, a closed-end column has the same wavelength as an open-end column twice as long. Column B only needs to be half the length of Column A:

  0.504 m/2 = 0.252 m

Final answer:

There are 10 different radar detectors one can buy, considering the power source, detection capabilities (radar, laser, or both), and model type (no-frills or fancy).

Explanation:

To find out how many different radar detectors one can buy, we need to consider the options presented and calculate the total number of combinations. According to the problem statement, radar detectors are powered either by their own battery or by plugging into the cigarette lighter socket. They come in two models: no-frills and fancy. Moreover, battery-powered detectors can detect either radar, laser, or both, while plug-in types can only detect either radar or laser, but not both.

Adding these up, we get a total of 6 options for battery-powered and 4 options for plug-in detectors, making a grand total of 10 different radar detectors one can buy.

Answer: Probability that both are non smokers is 0.48.

Step-by-step explanation:

Since we have given that

Number of male smokers = 102

Number of male non smokers = 408

Total male = 102+408=510

Number of female smokers = 240

Number of female non smokers = 360

Total female = 240+360 = 600

According to question,

A male student and a female student from the college are randomly selected for a survey,

So, Probability that both are non smokers is given by

P(both are smokers ) = P(Male smoker) × P(female smoker)

[tex]P(both)=\dfrac{360}{600}\times \dfrac{408}{510}\\\\P(both)=\dfrac{146880}{306000}\\\\P(both)=0.48[/tex]

Hence, probability that both are non smokers is 0.48.

The probability that both the randomly selected male and female students from the college are non-smokers is 0.48.

To compute the probability that both the randomly selected male and female students are non-smokers, we start by finding the total number of male and female students. The total number of male students is 510 (102 smokers + 408 non-smokers), and the total number of female students is 600 (240 smokers + 360 non-smokers). Then, we calculate the individual probabilities of selecting a non-smoking male and a non-smoking female. The probability of selecting a non-smoking male is 408 / 510, and the probability of selecting a non-smoking female is 360 / 600.

To find the combined probability, we multiply these individual probabilities. So, the probability that both the male and the female students selected are non-smokers, is (408 / 510) * (360 / 600) = 0.8 * 0.6 = 0.48.

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Answer:

INF for first while D for second

Step-by-step explanation:

Ok I think I read that integral with lower limit 1 and upper limit infinity

where the integrand is ln(x)*x^2

integrate(ln(x)*x^2)

=x^3/3 *ln(x)- integrate(x^3/3 *1/x)

Let's simplify

=x^3/3 *ln(x)-integrate(x^2/3)

=x^3/3*ln(x)-1/3*x^3/3

=x^3/3* ln(x)-x^3/9+C

Now apply the limits of integration where z goes to infinity

[z^3/3*ln(z)-z^3/9]-[1^3/3*ln(1)-1^3/9]

[z^3/3*ln(z)-z^3/9]- (1/9)

focuse on the part involving z... for now

z^3/9[ 3ln(z)-1]

Both parts are getting positive large for positive large values of z

So the integral diverges to infinity (INF)

By the integral test... the sum also diverges (D)

To compute the value of the improper integral, we can integrate by parts. Using the formula for integration by parts, we find that the integral converges to a finite value of -ln(x)/x as x approaches infinity.

To compute the value of the improper integral ∫∞18ln(x)/x2dx, we can integrate by parts. Let u = ln(x) and dv = 1/x2dx. Differentiating u with respect to x gives du = 1/x dx and integrating dv gives v = -1/x. Applying the formula for integration by parts, we get:

∫∞18ln(x)/x2dx = -ln(x)/x + ∫∞181/x2dx.

Simplifying the integral, we have:

∫∞181/x2dx = -1/x

As x approaches infinity, 1/x approaches 0. Therefore, the improper integral converges to a finite value of -ln(x)/x.

Answer:

less than 3

Step-by-step explanation:

3x+6y=18

then

3x+6y+−6y=18+−6y

next

3x=−6y+18

then

3x /3 =( −6y+18) /3

answer

x=−2y+6

First subtract 6y from both sides of the equation.

[tex]3x+6y-6y=18-6y\Longrightarrow 3x=18-6y[/tex]

Then divide both sides of the equation with 3.

[tex]3x=18-6y\Longrightarrow x=\dfrac{18-6y}{3}[/tex]

Which further simplifies to.

[tex]x=\dfrac{18}{3}-\dfrac{6y}{3}\Longrightarrow\boxed{6-2y}[/tex]

Hope this helps. I tried to made the steps very clear and easy.

r3t40

To calculate the 95% confidence interval for the mean life span of a sample of 105 people, use the formula Confidence interval = sample mean ± (z-score)*(standard deviation/√n). The z-score for a 95% confidence level is approximately 1.96.

The subject of this question is regarding statistics, specifically the calculation of confidence intervals for a sample mean. In this case, we will use the formula for a confidence interval for the mean:

Confidence interval = sample mean ± (z-score)*(standard deviation/√n)

Where the sample mean is the mean life span of humans (89.87 years), n is the sample size (105 people), the standard deviation is 16.63 years and the z-score corresponds with 95% confidence level (approximately 1.96). After performing the necessary computations:

Confidence interval = 89.87 ± (1.96 * 16.63/√105)

The final step would be calculating the upper and lower bounds by adding and subtracting the product from the mean respectively. Your results will indicate the range within which 95% of sample means of life spans at birth are expected to fall.

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For this case we have the following equation:

[tex]12x + 1 = 25[/tex]

We must find the solution!

Subtracting 1 from both sides of the equation we have:

[tex]12x = 25-1\\12x = 24[/tex]

Dividing between 12 on both sides of the equation we have:

[tex]x = \frac {24} {12}\\x = 2[/tex]

Thus, the solution is given by[tex]x = 2[/tex]

Answer:

[tex]x = 2[/tex]

Final answer:

The twenty-fifth term of the arithmetic sequence is 119. The first three terms of another arithmetic sequence are 17, 19, 21.

Explanation:

To find the twenty-fifth term of an arithmetic sequence, we can use the formula:
nth term = first term + (n-1) * common difference

Substituting the given values:
nth term = -1 + (25-1) * 5 = -1 + 24 * 5 = -1 + 120 = 119

Therefore, the twenty-fifth term of the arithmetic sequence is 119.

For the second part of the question, to find the common difference, we can use the formula:
common difference = (fiftieth term - twenty-first term) / (50 - 21)

Substituting the given values:
common difference = (75 - 17) / (50 - 21) = 58 / 29 = 2

Using the first term of 17 and the common difference of 2, we can write the first three terms of the arithmetic sequence:
17, 19, 21

Answer:

  (x, y, z) = (1, 1/3, 3 1/3)

Step-by-step explanation:

The normal to plane ABC can be found as the cross product ...

  AB×BC = (1, 0, 2)×(2, -2, -3) = (4, 1, 2)

Then the equation of the plane is ...

  4x +y +2z = 4·0 +5 +2·3 . . . . using point C to find the constant

  4x +y +2z = 11

__

The direction vector of the reference line is the vector of coefficients of t: (0, -1, 2). Then the line through point Q is ...

  (x, y, z) = (1, 2, 0) +t(0, -1, 2) = (1, 2-t, 2t)

__

The value of t that puts a point on this line in plane ABC can be found by substituting these values for x, y, and z in the plane's equation.

  4(1) +(2 -t) +2(2t) = 11

Solving for t gives ...

  t = 5/3

so the point of intersection of the plane and the line is

  (x, y, z) = (1, 2-t, 2t) = (1, 2-5/3, 2·5/3) = (1, 1/3, 3 1/3)

[tex]a^{p-1} \equiv 1 \pmod p[/tex] where [tex]p[/tex] is prime, [tex]a\in\mathbb{Z}[/tex] and [tex]a[/tex] is not divisible by [tex]p[/tex].

[tex]7^{13-1}\equiv 1 \pmod {13}\\7^{12}\equiv 1 \pmod {13}\\\\542=45\cdot12+2\\\\7^{45\cdot 12}\equiv 1 \pmod {13}\\7^{45\cdot 12+2}\equiv 7^2 \pmod {13}\\7^{542}\equiv 49 \pmod{13}[/tex]

Answer:

49 mod 13 = 10.

Step-by-step explanation:

Fermat's little theorem states that

x^p = x mod p where p is a prime number.

Note that 542 = 41*13 + 9 so

7^542 = 7^(41*13 + 9)  = 7^9 * (7^41))^13

By FLT (7^41)^13 = 7^41 mod 13

So 7^542 = ( 7^9 *  7(41)^13) mod 13

= (7^9 * 7^41) mod 13

= 7^50 mod 13

Now we apply FLT to this:

50 = 3*13 + 11

In a similar method to the above we get

7^50 = (7^11 * (7^3))13)  mod 13

=  (7^11 * 7^3) mod 13

= (7 * 7^13) mod 13

= ( 7* 7) mod 13

= 49 mod 13

= 10 (answer).

By definition of covariance,

[tex]\mathrm{Cov}(U,V)=E[(U-E[U])(V-E[V])]=E[UV-E[U]V-UE[V]+E[U]E[V]]=E[UV]-E[U]E[V][/tex]

Since [tex]U=2X+Y-1[/tex] and [tex]V=2X-Y+1[/tex], we have

[tex]E[U]=2E[X]+E[Y]-1[/tex]

[tex]E[V]=2E[X]-E[Y]+1[/tex]

[tex]\implies E[U]E[V]=(2E[X]+E[Y]-1)(2E[X]-(E[Y]-1))=4E[X]^2-(E[Y]-1)^2=4E[X]^2-E[Y]^2+2E[Y]-1[/tex]

and

[tex]UV=(2X+Y-1)(2X-(Y-1))=4X^2-(Y-1)^2=4X^2-Y^2+2Y-1[/tex]

[tex]\implies E[UV]=4E[X^2]-E[Y^2]+2E[Y]-1[/tex]

Putting everything together, we have

[tex]\mathrm{Cov}(U,V)=(4E[X^2]-E[Y^2]+2E[Y]-1)-(4E[X]^2-E[Y]^2+2E[Y]-1)[/tex]

[tex]\mathrm{Cov}(U,V)=4(E[X^2]-E[X]^2)-(E[Y^2]-E[Y]^2)[/tex]

[tex]\mathrm{Cov}(U,V)=4V[X]-V[Y]=4a-a=\boxed{3a}[/tex]

The answers are:

A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

To find which of the following pairs of numbers contains like fractions, we must remember that like fractions are the fractions that share the same denominator.

We are given two fractions that are like fractions. Those fractions are:

Option A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

We have that:

[tex]\frac{10}{12}=\frac{5}{6}[/tex]

So, we have that the pairs of numbers

[tex]\frac{5}{6}[/tex]

and

[tex]\frac{5}{6}[/tex]

Share the same denominator, which is equal to 6, so, the pairs of numbers contains like fractions.

Option D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

We have that:

[tex]1\frac{5}{7}=1+\frac{5}{7}=\frac{7+5}{7}=\frac{12}{7}[/tex]

So, we have that the pair of numbers

[tex]\frac{6}{7}[/tex]

and

[tex]\frac{12}{7}[/tex]

Share the same denominator, which is equal to 7, so, the pairs of numbers constains like fractions.

Also, we have that the other given options are not like fractions since both pairs of numbers do not share the same denominator.

The other options are:

[tex]\frac{3}{2},\frac{2}{3}[/tex]

and

[tex]3\frac{1}{2},4\frac{4}{4}[/tex]

We can see that both pairs of numbers do not share the same denominator so, they do not contain like fractions.

Hence, the answers are:

A.

[tex]\frac{5}{6}[/tex] and [tex]\frac{10}{12}[/tex]

D.

[tex]\frac{6}{7}[/tex] and [tex]1\frac{5}{7}[/tex]

Have a nice day!

Answer:

When you find the gradient (slope) of a graph, you divide a change of value on the vertical-axis (the 'rise') by a change of value on the horizontal axis (the 'run').  

Gradient = rise/run.  

The vertical axis has units of cm, so the rise in in cm.  

The horizontal axis has units of 1/grams = g⁻¹, so the rise is in g⁻¹.  

units for slip are  

rise/run ≡ cm/g⁻¹ ≡ cm.g

Step-by-step explanation:

The slope in the plotted graph in Excel is determined by the change in the vertical value ('x' - distance, in centimeters) with the change in the horizontal value ('1/m' - inverse of mass, in grams). Therefore, the unit of the slope will be grams centimeters (g.cm).

In this lab experiment using Excel to plot a graph, it's vital to understand the concept of slope. In a line graph, slope indicates the amount of vertical 'rise' for every unit of horizontal 'increase' and is calculated by the change in the dependent variable (in this case 'x' or distance, which is on the vertical axis) over the change in the independent variable (here, it is 1/mass or 1/m, on the horizontal axis).

Since 'x' is measured in centimeters (cm) and 'm', the mass, is measured in grams (g), when calculating the slope, we do a division of cm by the inverse of grams (1/g), which is equivalent to multiplication by its reciprocal (g/1). Therefore, the unit of the slope of the line would be g.cm, which is grams centimeters.

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Answer:

The discontinuity is x = 4

There no holes

The equation of the vertical asymptote is x = 4

The x intercept is 2

The equation of the horizontal asymptote is y = 1

Step-by-step explanation:

* Lets explain the problem

∵ [tex]f(x)=\frac{x-2}{x-4}[/tex]

- To find the point of discontinuity put the denominator = 0 and find

 the value of x

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

* The discontinuity is x = 4

- A hole occurs when a number is both a zero of the numerator

 and denominator

∵ The numerator is x - 2

∵ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

∵ The denominator is x - 4

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∵ There is no common number makes the numerator and denominator

   equal to 0

∴ There no holes

- Vertical asymptotes are vertical lines which correspond to the zeroes  

  of the denominator of the function

∵ The zero of the denominator is x = 4

∴ The equation of the vertical asymptote is x = 4

- x- intercept is the values of x which make f(x) = 0, means the

 intersection points between the graph and the x-axis

∵ f(x) = 0

∴ [tex]\frac{x-2}{x-4}=0[/tex] ⇒ by using cross multiplication

∴ x - 2 = 0 ⇒ add 2 to both sides

∴ x = 2

* The x intercept is 2

- If the highest power of the numerator = the highest power of the

 denominator, then the equation of the horizontal asymptote is

 y = The leading coeff. of numerator/leading coeff. of denominator

∵ The numerator is x - 2

∵ The denominator is x - 4

∵ The leading coefficient of the numerator is 1

∵ The leading coefficient of the denominator is 1

∴ y = 1/1 = 1

* The equation of the horizontal asymptote is y = 1

[tex]|\Omega|={_{48}C_6}=\dfrac{48!}{6!42!}=\dfrac{43\cdot44\cdot45\cdot46\cdot47\cdot48}{720}=12271512\\|A|={_6C_4}=\dfrac{6!}{4!2!}=\dfrac{5\cdot6}{2}=15\\\\P(A)=\dfrac{15}{12271512}=\dfrac{5}{4090504}\approx1.2\%[/tex]

The probability that the player wins the prize from a drawn of six in 1 to 48 numbers is 0.001052.

Probability is usually expressed as the number of favorable outcomes divided by the number of desired outcomes.

Mathematically;

Probability of winning = [tex]\mathbf{\dfrac{favorable \ outcomes}{number \ of \ desired \ outcomes}}[/tex]

The probability that the player wins can be computed by taking the following combinations.

From the given information;

Thus, the probability of winning can now be computed as:

[tex]\mathbf{P(winning \ prize) = \dfrac{^6C_4 \times ^{42}C_2}{^{48}C_6}}[/tex]

[tex]\mathbf{P(winning \ prize) = \dfrac{\Big (\dfrac{6!}{4!(6-4)!} \Big )\times \Big (\dfrac{42!}{2!(42-2)!} \Big )}{\Big (\dfrac{48!}{6!(48-6)!} \Big )}}[/tex]

[tex]\mathbf{P(winning \ prize) = \dfrac{12915}{12271512}}[/tex]

[tex]\mathbf{P(winning \ prize) =0.001052}[/tex]

Therefore, the probability that the player wins the prize from a drawn of six in 1 to 48 numbers is 0.001052.

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Answer:

[tex]-\frac{13\sqrt{x} }{x}[/tex]

Step-by-step explanation:

We have been given the following expression;

-13/√x

In order to rationalize the denominator, we multiply the numerator and the denominator by √x;

[tex]-\frac{13}{\sqrt{x}}=-\frac{13\sqrt{x} }{\sqrt{x}\sqrt{x}}\\ \\-\frac{13\sqrt{x} }{\sqrt{x^{2} } }\\\\-\frac{13\sqrt{x} }{x}[/tex]

Final answer:

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of √x is -√x. Multiply -13/√x by -√x/-√x to get -13√x / x.

Explanation:

To rationalize the denominator, we need to eliminate the square root from the denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of √x is -√x. So, multiplying the numerator and denominator by -√x gives us:

-13/√x * (-√x)/(-√x) = 13√x/(-x) = -13√x / x

Therefore, the rationalized form of -13/√x is -13√x / x.

Answer:

Step-by-step explanation:

The combined price of the separate obligations is $2000, so the package price is 1900/2000 = 0.95 of the total of separate items. We assume the allocation matches that proportion, so the allocations are ...

  TV: 0.95×$1500 = $1425

  remote: 0.95×$200 = $190

  installation: 0.95×$300 = $285

The revenue that would be allocated to the TV, the remote, and the installation service are;

New revenue for TV = $1425

New revenue for remote = $190

New revenue for installation= $285

Cost of 60-inch TV = $1,500

Cost of remote = $200

Installation service cost = $300

Total revenue to be generated when they pay individually = 1500 + 200 + 300 = $2000

This means, the discount here is; 1900/2000 × 100 = 95% or 0.95

New revenue for TV: 0.95 × $1500 = $1425

New revenue for remote: 0.95 × $200 = $190

New revenue for installation: 0.95 × $300 = $285

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Answer:

Question 6

There is not enough information to determine congruency

Question 9

yes; The triangles are congruent by hypotenuse-leg congruence

Step-by-step explanation:

* Lets revise the cases of congruence  

- SSS  ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ

- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and  

 including angle in the 2nd Δ  

- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ  

 ≅ 2 angles and the side whose joining them in the 2nd Δ

- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles  

 and one side in the 2ndΔ

- HL ⇒ hypotenuse - leg of the first right angle triangle ≅ hypotenuse

 - leg of the 2nd right angle Δ

- HA ⇒ hypotenuse - angle of the first right angle triangle ≅ hypotenuse

 - angle of the 2nd right angle Δ

- LL ⇒ leg - leg of the first right angle triangle ≅ leg - leg of the

 2nd right angle Δ

* Now lets solve the problem

# Question 6

- There are two right angle triangles

- They have two different legs

- There is no mention abut legs equal each other

- There is no mention about hypotenuses equal each other

- There is no mention about acute angels equal each other

∴ There is not enough information to determine congruency

# Question 9

- There are two right angle triangles

- Their hypotenuse is common

- There are two corresponding legs are equal

∵ The hypotenuse is a common in the two right triangles

∵ Two corresponding legs are equal

- By using hypotenuse-leg congruence

∴ yes; The triangles are congruent by hypotenuse-leg congruence

The volume of the solid is (81π - 128)/3 cubic units, found by integrating the volume of washer-shaped slices.

Sure, here is the step-by-step calculation of the volume V of the solid formed by rotating the region bounded by the curves y = −[tex]x^2[/tex] + 10x − 16, y = 0, about the x-axis:

Find the x-intercepts.

Set the two equations equal to each other to find the x-coordinates of the points of intersection:

[tex]-x^2 + 10x -16 = 0[/tex]

Factor the expression:

(x - 2)(x - 8) = 0

Therefore, the x-intercepts are x = 2 and x = 8.

Sketch the curves and the axis of rotation.

On a coordinate plane, graph the parabola y = −[tex]x^2[/tex] + 10x − 16 and the line y = 0. The x-axis is the axis of rotation.

Imagine the solid of revolution.

When the shaded region between the parabola and the x-axis is rotated about the x-axis, it forms a solid of revolution. This solid can be imagined as a collection of thin slices.

Consider one such slice.

Take a thin slice of the solid perpendicular to the x-axis. The slice is a cylinder with a hole in the middle, much like a washer. Let the thickness of the slice be dx and let the radius of the washer, as a function of x, be r(x).

Express the volume of the slice as a washer.

The volume of the washer is the difference between the volume of the larger cylinder and the volume of the smaller cylinder inside it. The volume of a cylinder is π[tex]r^2[/tex]h, where r is the radius and h is the height. In this case, the height of each cylinder is dx.

Therefore, the volume of the washer is:

π[([tex]r(x))^2 - (r'(x))^2[/tex])] dx

Express the radius as a function of x.

The radius of the washer is equal to the distance between the parabola and the x-axis. In other words, for any x-value, r(x) = −[tex]x^2[/tex] + 10x − 16.

Set up the definite integral.

To find the total volume of the solid, we need to sum the volumes of infinitely many such washers as the thickness dx approaches zero. This is done using a definite integral:

[tex]\int _a^b \pi[(r(x))^2 - (r'(x))^2] dx[/tex]

where a and b are the x-coordinates of the endpoints of the region. In this case, a = 2 and b = 8.

Differentiate r(x) to find r'(x).

r'(x) = -2x + 10

Evaluate the definite integral.

[tex]\int_2^8 \pi[(-x^2 + 10x - 16)^2 - (-2x + 10)^2] dx[/tex]

This integral can be evaluated using integration by parts or a computer algebra system. The result is:

(81π - 128)/3

Therefore, the volume V of the solid is (81π - 128)/3 cubic units.

Question:

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −[tex]x^2[/tex] + 10x − 16,    y =0;  about the x-axis.

Answer:

Given,

The initial population ( on 2010 ) = 40,000,

Let r be the rate of increasing population per year,

Thus, the function that shows the population after t years,

[tex]P(x)=40000(1+r)^t[/tex]

And, the population after 5 years ( on 2015 ) is,

[tex]P(5)=40000(1+r)^{5}[/tex]

According to the question,

P(5) = 50,000,

[tex]\implies 40000(1+r)^5=50000[/tex]

[tex](1+r)^5=\frac{50000}{40000}=1.25[/tex]

[tex]r + 1= 1.04563955259[/tex]

[tex]\implies r = 0.04653955259\approx 0.04654[/tex]

So, the population is increasing the with rate of 0.04654,

And, the population after t years would be,

[tex]P(t)=40000(1+0.04654)^t[/tex]

[tex]\implies 40000(1.04654)^t[/tex]

Since, the exponential function is,

[tex]f(x) = ab^x[/tex]

Hence, by comparing,

a = 40000,

b = 1.04654

Answer:

maryland. (c)

wyoming. (b)

reduced burning of fossil fuels. (b)

Step-by-step explanation:

if you're looking for the answer the question im looking for then those are the answers

ANSWER

[tex]x = \frac{1}{2} [/tex]

EXPLANATION

The given exponential equation is

[tex] {9}^{x + 1} = 27[/tex]

The greatest common factor of 9 and 27 is 3.

We rewrite the each side of the equation to base 3.

[tex]{3}^{2(x + 1)} = {3}^{3} [/tex]

Since the bases are equal, we can equate the exponents.

[tex]2(x + 1) = 3[/tex]

Expand the parenthesis to get:

[tex]2x + 2 = 3[/tex]

Group similar terms

[tex]2x = 3 - 2[/tex]

[tex]2x = 1[/tex]

[tex]x = \frac{1}{2} [/tex]

For this case we must solve the following equation:

[tex]9 ^ {x + 1} = 27[/tex]

We rewrite:

[tex]9 = 3 * 3 = 3 ^ 2\\27 = 3 * 3 * 3 = 3 ^ 3[/tex]

Then the expression is:

[tex]3^ {2 (x + 1)} = 3 ^ 3[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

[tex]2 (x + 1) = 3[/tex]

We apply distributive property to the terms within parentheses:

[tex]2x + 2 = 3[/tex]

Subtracting 2 on both sides of the equation:

[tex]2x = 3-2\\2x = 1[/tex]

Dividing between 2 on both sides of the equation:

[tex]x = \frac {1} {2}[/tex]

Answer:

[tex]x = \frac {1} {2}[/tex]

Answer:  (b) Systematic

Step-by-step explanation:

Given statement : To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at General Electric selects every 20th refrigerator that comes off the assembly line starting with the sixth until she obtains a sample of 130 refrigerators.

Periodic interval : Every 20th

Beginning point : 6th

Sample size : 130

Hence, this type of sampling is a systematic random sampling.

The type of sampling used by the General Electric quality control manager is systematic sampling. This method involves selecting subjects at fixed regular intervals, providing a balance between bias and needed sample size.

The quality control manager at General Electric is using systematic sampling to estimate the percentage of defects in a recent manufacturing batch. Systematic sampling involves selecting subjects at regular intervals from the population, in this case, every 20th refrigerator starting with the sixth one to achieve a sample of 130 refrigerators. This type of sampling is situated between other sampling methods such as random sampling and judgmental sampling in terms of bias and sample size needed to characterize the population adequately.

When considering the provided exercises, the answers to the type of sampling used would be:

Answer:

42

Step-by-step explanation:

Note that as x increases by 2 from 2 to 4, y increases by 12 from 12 to 24.  Thus, the slope of the line connecting the given points is m = rise / run = 12/2, or m = 6.  Thus, this direct proportion is written as y = 6x.

If x = 7, y = 6(7) = 42

Answer:

42

Step-by-step explanation:

Answer:

We need to find the domain, range, x-intercept and y-intercept of the following function:

[tex]f(x) = 1.6x^{-2} + 1[/tex] ⇒ [tex]f(x)=\frac{1.6}{x^{2} }+1[/tex]

To find the y-intercept, we have to make 'x=0'

[tex]f(x) = \frac{1.6}{x^{2} } + 1[/tex] ⇒ [tex]f(x) = \frac{1.6}{0}  + 1[/tex]. Given that divisions by zero are not possible, we conclude that there's no y-intercept. In other words, the function does not cross the y-axis,

To find the x-intercept, we have to make 'y=0'

[tex]f(x) = \frac{1.6}{x^{2} } + 1[/tex]  ⇒ [tex]\frac{1.6}{x^{2} } + 1 = 0[/tex]

⇒ [tex]x^{2} = -1.6[/tex]

Given that we cannot take the square rooth of a negative number, we can conclude that there's no x-intercept. In other words, the function does not cross the x-axis.

The domain is all the possible values that the independent variable 'x' can take. Given that we can not divide by zero, the domain is all real numbers except zero. In set notation: ℝ - {0}.

The Range is all the possible values that the dependent variable 'y' can take. Solving the expression for 'x' we have:

[tex]\frac{1.6}{x^{2} } + 1 = y[/tex]  ⇒ [tex]\frac{1.6}{x^{2} }= y-1[/tex]

⇒ [tex]\sqrt{(\frac{1.6}{y-1 })}= x[/tex]

Given that square roots can not be negative, and the denominator can't be equal to zero, the range is y>1. In set notation: Range: (1, +∞)

Answer:

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374

Step-by-step explanation:

It is given a geometric sequence,

–6, ? , ? , ? , ? , –1,458?

From the given sequence we get first term a₁ = -6 and 6th term a₆ = -1458

To find the common ratio 'r'

6th term can be written as

a₆ = ar⁽⁶ ⁻ ¹⁾

-1458 = 6 * r⁽⁶⁻¹⁾

r⁵ = -1458/-6 = 243

r = ⁵√243 = 3

To find the sequence

We have a = -6, r = 3

a₂ = -6 * 3 = -18

a₃ = a₂*3 = -18* 3 = -54

a₄  = a₃*3 = -54 * 3 = -162

a₅ = a₄*3 = -162* 3 = -486

a₆ = - 1458

a₇ = a₂*3 =-1458 * 3= -4374

The sequence is,

-6, -18, -54, -162, - 486, -1458, -4374

Answer: 4.29203

Explanation:

5^x=1008-8

5^x=1000

take the log of both sides

x=3 log 5 (10)

x=3+3log5(2)

or 4.29203

For this case we must solve the following equation:

[tex]8 + 5 ^ x = 1008[/tex]

Subtracting 8 on both sides of the equation:

[tex]5 ^ x = 1008-8\\5 ^ x = 1000[/tex]

We apply Neperian logarithm to both sides of the equation:

[tex]ln (5 ^ x) = ln (1000)[/tex]

We use the rules of the logarithms to draw x

of the exponent.

[tex]xln (5) = ln (1000)[/tex]

We divide both sides of the equation between[tex]ln (5)[/tex]:

[tex]x = \frac {ln (1000)} {ln (5)}\\x = 4.29202967[/tex]

Rounding:

[tex]x = 4.2920[/tex]

Answer:

[tex]x = 4.2920[/tex]

Answer:

A.) 3/7

B.) 5/7

C.) 2/7

D.) 2/7

Answer:

-3.3

Step-by-step explanation:

-2.3-(4.5-3 1/2)=-2.3-(4.5-3.5)=-2.3-(1)=-3.3