What is the GCF of the expression a2b2c2 + a2bc2 - a2b2c

let's recall that a rational whose numerator and denominator are of the same degree, has a horizontal asymptote at the fraction provided by the leading term's coefficients.

so we can simply pick any two polynomials, make them the same degree and give their leading term 2 and 9 respectively.

hmmmm say for the numerator x⁴ - 3x³.... and the denominator hmm say x⁴ + 7x, so then let's give them 2 and 9 respective... so

[tex]\bf \cfrac{\stackrel{\stackrel{\textit{leading term}}{\downarrow }}{2x^4}-3x^3}{\underset{\underset{\textit{leading term}}{\uparrow }}{9x^4}+7x}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{2}{9}}[/tex]

Step-by-step explanation:

First, use trig to find the height of the slide.

The slide forms a right triangle.  We know the hypotenuse is 8.80 ft, and the angle opposite of the height is 25.0°.  So using sine:

sin 25.0°  = h / 8.80

h = 3.72 ft

Converting to meters:

h = 3.72 ft × (1 m / 3.28 ft)

h = 1.13 m

Potential gravitational energy is:

PE = mgh

where m is the mass, g is the acceleration due to gravity, and h is the relative height.

At the bottom of the slide, h = 0:

PE = (63.0 kg) (9.8 m/s²) (0 m)

PE = 0 J

At the top of the slide, h = 1.13 m:

PE = (63.0 kg) (9.8 m/s²) (1.13 m)

PE =  700 J

The change is the final potential energy minus the initial potential energy.

ΔPE = 0 J - 700 J

ΔPE = -700 J

The probability that the team will win exactly 7 matches over the course of one season is:

                         0.1977

We know that the probability of k successes out of n successes is given by the binomial distribution as:

[tex]P(X=k)=n_C_kp^k(1-p)^{n-k}[/tex]

where p is the probability of success .

Here we are asked to find the probability that the team will win exactly 7 matches over the course of one season.

Since, there are 8 matches over the course of season.

This means n=8

and k=7

and p=0.70

(Since, 0.70 probability of winning a match )

Hence, we get:

[tex]P(X=7)=8_C_7\times (0.70)^7\times (1-0.70)^{8-7}\\\\i.e.\\\\P(X=7)=8\times (0.70)^7\times 0.30\\\\i.e.\\\\P(X=7)=0.1977[/tex]

         Hence, the answer is:

                  0.1977

Final answer:

The probability that a collegiate video-game competition team with a 0.70 chance of winning will win exactly 7 out of 8 matches is approximately 25.41%.

Explanation:

The question asks to calculate the probability that a collegiate video-game competition team, which has a 0.70 probability of winning a match, wins exactly 7 out of 8 matches in a season. This scenario can be modeled using the binomial distribution formula, which is given by P(X = k) = (n C k) * p^k * (1 - p)^(n - k), where 'n' is the total number of trials (matches), 'k' is the number of successful outcomes (wins), and 'p' is the probability of a single success.

To find the probability of winning exactly 7 matches, we set n = 8, k = 7, and p = 0.70. Thus, the calculation becomes P(X = 7) = (8 C 7) * (0.70)⁷ * (0.30)¹. Calculating further, we have P(X = 7) = 8 * (0.70)⁷ * (0.30) = 0.254121. Therefore, the probability that the team will win exactly 7 matches over the course of one season is approximately 25.41%.

Answer:

The logarithmic function modeled by the given table:

f(x) = log₃x

Step-by-step explanation:

Given Table:

x     f(x)

9     2

27    3

81    4

We can see that x increases as powers of 3. And f(x) is the power.

We assume that f(x) = log₃x

Checking using the table:

for x = 9

f(x) = log₃9 = 2

for x = 27

f(x) = log₃27 = 3

for x = 81

f(x) = log₃81 = 4

Hence proved.  

Step-by-step explanation:

Let's say the position of the fire is point C.

Bearings are measured from the north-south line.  So ∠BAC = 55°, and ∠ABC = 60°.

Since angles of a triangle add up to 180°, ∠ACB = 65°.

Using law of sine:

190 / sin 65° = a / sin 60° = b / sin 55°

Solving:

a = 181.6

b = 171.7

Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.

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

-10x - 3 = -10 - 3x

Bring -10x to the other side by adding it to both sides

(-10x + 10x) - 3 = -10 + (-3x + 10x)

0 - 3 = -10 + 7x

-3 = -10 + 7x

Bring -10 to the oposite side by adding 10 to both sides

-3 + 10 = (-10 + 10) + 7x

7 = 0 + 7x

7 = 7x

Isolate x by dividing 7 to both sides

7/7 = 7x/7

x = 1

Hope this helped!

~Just a girl in love with Shawn Mendes

-10x-3= -10-3x

-10x+10x-3= -10x+10x-3x

-3=-3x

divide by -4 for -3 and -3x

-3/-3= -3x/-3

1=x

x= 1

check answer by using substitution method

-10x-3= -10-3x

-10(1)-3=-10-3(1)

-13=- 13

Answer is x= 1

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:

Amount of  vinegar. 100% : 20 milliliters

Amount of  Italian dressing: 140 milliliters

Step-by-step explanation:

Let's call A the amount of  vinegar. 100%

Let's call B the amount of  Italian dressing . 12% vinegar

The resulting mixture should have 23%  vinegar, and 160 milliliters.

Then we know that the total amount of mixture will be:

[tex]A + B = 160[/tex]

Then the total amount of pure antifreeze in the mixture will be:

[tex]A + 0.12B = 0.23 * 160[/tex]

[tex]A + 0.12B = 36.8[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:

[tex]-A -B = -160[/tex]

[tex]-A -B = -160[/tex]

               +

[tex]A + 0.12B = 36.8[/tex]

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

[tex]-0.88B = -123.2[/tex]

[tex]B = \frac{-123.2}{-0.88}[/tex]

[tex]B = 140\ milliliters[/tex]

We substitute the value of B into one of the two equations and solve for A.

[tex]A + 140 = 160[/tex]

[tex]A = 20\ milliliters[/tex]

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:

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, +∞)

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]

Answer:4,500

Step-by-step explanation:

720 multiple by 25 gives you 18,000 then you find 25% of 18,000 by multiplying 18,000 times 25/100 which gives you 4,500. Or you can find 25%of 25 then multiple the answer by 720

Answer: 4,500.00

Step-by-step explanation:

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:

Step-by-step explanation:

If you simply need to identify the inequality, it is

n + 5 ≥ 12

since "sum" means to add and "at least" is the inequality sign that is greater than or equal to.

If you are solving it, then the solution set will be

n ≥ 7

Answer:

5 + n ≥ 12.

Step-by-step explanation:

Given  :  sum of five and a number n is at least 12.

To find : Write expression .

Solution : We have given sum of five and a number n is at least 12.

According to given statement :

Sum of 5 and n

5 + n

At least 12 mean the number is 12 or greater than 12

So ,

5 + n ≥ 12.

Therefore, 5 + n ≥ 12.

Theoretical probability is calculated based on the number of expected outcomes, while experimental probability is based on observed outcomes. They are used in different situations for predictions and estimates, respectively.

Theoretical probability is calculated by dividing the number of times an event is expected to occur by the number of possible outcomes.

For example, if you flip a fair coin, there is one way to obtain heads and two possible outcomes, so the theoretical probability of heads is 1/2 or 0.5.

Experimental probability, on the other hand, is based on observations from an experiment.

If you flip a coin 10 times and get 6 heads, the experimental probability of heads is 6/10 or 0.6.

Both theoretical and experimental probability have their uses in different situations, but theoretical probability is often used to make predictions based on known probabilities, while experimental probability provides a more accurate estimate based on actual observations.

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:

-3.3

Step-by-step explanation:

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

Answer:

It's B

Step-by-step explanation:

180 - 105 = 75 +55 = 130; the recangle has a sum of 180, hence 180-130 =50

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:

Step-by-step explanation:

Let d represent the number of dimes. Then the number of quarters is 2d-3 and the total value of the coins is ...

  0.10d + 0.25(2d-3) = 7.05

  0.60d -0.75 = 7.05 . . . . . . . simplify

  d = (7.05 +0.75)/0.60 = 13 . . . . add 0.75, divide by 0.60

  2d-3 = 2·13 -3 = 23

Brandon has 23 quarters and 13 dimes.

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

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]

Answer:

a) x = 7

b) x = 2

Step-by-step explanation:

* Lets revise some facts in the circle

- If two secant segments are drawn to a circle from a point outside the

 circle, the product of the length of one secant segment and its

 external part is equal to the product of the length of the other secant

 segment and its external part.

# Example:

- If AC is a secant intersects the circle at points A and and B

- If DC is another secant intersects the circle at points D and E

- The two secants intersect each other out the circle at point C

∴ AC × CB = DC × CE , where AC is the secant and CB is its external

  part and DC is the secant and CE is its external part

* Lets solve the problem

a) There are two secants intersect each other at point outside the circle

∵ The first secant is x + 5

∵ Its external part is 5

∵ the second secant is 4 + 6 = 10

∵ Its external part is 6

∴ (x + 5) × 5 = 10 × 6 ⇒ simplify

∴ 5x + 25 = 60 ⇒ subtract 25 from both sides

∴ 5x = 35 ⇒ divide both sides by 5

∴ x = 7

* x = 7

b) There are two secants intersect each other at point outside the circle

∵ The first secant is 5 + 3 = 8

∵ Its external part is 3

∵ the second secant is x + 4

∵ Its external part is 4

∴ 8 × 3 = (x + 4) × 4 ⇒ simplify

∴ 24 = 4x + 16 ⇒ subtract 16 from both sides

∴ 8 = 4x ⇒ divide both sides by 4

∴ 2 = x

* x = 2

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: Our required linear equation would be [tex]x+48y=148[/tex]

Step-by-step explanation:

Since we have given that

Cost of deep fried bananas on a stick = $1.00

Number of sales reached = 100 per day

Cost of deep fried bananas on a stick becomes = $2.00

Number of sales reached = 52 per day.

Let x is the number of dollars each.

Let y be the number of vendors sale.

So, we need to form the linear equation:

As we know the formula for two point slope form:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-1=\dfrac{2-1}{52-100}(x-100)\\\\y-1=\dfrac{1}{-48}(x-100)\\\\-48(y-1)=(x-100)\\\\-48y+48=x-100\\\\-48y=x-100-48\\\\-48y=x-148\\\\x+48y=148[/tex]

Hence, our required linear equation would be [tex]x+48y=148[/tex]

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

[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: 0.0433

Step-by-step explanation:

Given: Sample size : n= 133

The number of females in sample = 65

Then the proportion of females : [tex]P=\dfrac{65}{133}[/tex]

The formula to calculate the standard error of the proportion is given by :-

[tex]S.E.=\sqrt{\dfrac{P(1-P)}{n}}[/tex]

[tex]\Rightarrow S.E.=\sqrt{\dfrac{\dfrac{65}{133}(1-\dfrac{65}{133})}{133}}\\\\\Rightarrow\ \Rightarrow S.E.=0.0433444676341\approx0.0433[/tex]

Hence, the standard error of the proportion of females is 0.0433.

The standard error of the proportion of females in the given sample is calculated using the formula SE = sqrt[p * (1-p) / n]. In this case, the proportion (p) is 0.4887 and the sample size (n) is 133, giving a standard error of 0.0432.

The question is asking for the standard error of the proportion of females in the said sample. The standard error (SE) of a proportion is a measure of uncertainty around a proportion estimate. It is calculated using the formula SE = sqrt[p * (1-p) / n], where p is the proportion and n is the sample size.

So, we have a sample size, n = 133, and the proportion of females, p = 65/133 = 0.4887.

Substitute these values into the formula, we get: SE = sqrt[0.4887 * (1 - 0.4887) / 133] = 0.0432 (rounded to four decimal places).

Therefore, the standard error of the proportion of females in this sample is 0.0432.

https://brainly.com/question/13179711

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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