Find the value of each variable.
​

Answer:

[tex]\frac{1}{128}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a [tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio, hence

[tex]a_{10}[/tex] = 4 × [tex](\frac{1}{2}) ^{9}[/tex] = 4 × [tex]\frac{1}{512}[/tex] = [tex]\frac{1}{128}[/tex]

Final answer:

The tenth term of the geometric sequence with the first term 4 and the common ratio of 1/2 is calculated using the formula for the nth term. Substituting the given values into the formula and simplifying yields the tenth term as 1/128.

Explanation:

To find the tenth term of a geometric sequence, we use the formula for the nth term in a geometric sequence which is an = a1 x r(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

In this case, the first term a1 is given as 4 and the common ratio r is 1/2. To find the tenth term, we substitute n with 10 in the formula:

a10 = 4 x (1/2)(10-1)

This simplifies to:

a10 = 4 x (1/2)9 = 4 x 1/512 = 4/512 = 1/128

Therefore, the tenth term of the geometric sequence is 1/128.

Answer:

placement plan

Step-by-step explanation:

<3

As the senior marketing rep, Jake needs to develop a marketing plan. This plan would outline the business's advertising and marketing efforts for the year, including goals, strategies, tactics, a market analysis, and a budget.

Jake, as the senior marketing rep for a new chain of upscale hotels, is tasked with creating a marketing plan. A marketing plan is a comprehensive document or blueprint that outlines a company's advertising and marketing efforts for the coming year.

It would detail the business's marketing goals, the strategies and tactics to achieve those goals, an analysis of the current market situation, and a budget for the marketing activities. For an upscale hotel chain, it might include strategies such as premium pricing, high-quality service, and targeted advertising.

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Answer:

The recursive function is;

f(n)=f(n-1)×0.9 for n≥2

After 3 years, 11340 birds will remain.

Step-by-step explanation:

First the native population was 14,000 before decreasing started, hence this is your f(1)

f(1)=14000

⇒A decrease of 10% is similar to multiplying the native value of birds with 90%

New number of birds = native value × 90% ⇒f(1)×0.9

For second year ,  you multiply the value you get after the first decrease by 0.9 to get the new number of birds;

f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600

For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%

f(3)=f(2)×0.9=12600×0.9=11340

Apply the same for the 4th year and above, hence for nth year;

f(n)=f(n-1)×0.9 for n≥2

Answer:

B, irrational

Step-by-step explanation:

We know that π is irrational, since it can not be written as a division between  natural numbers (a sub class of Real numbers called N), it's value is 3,1415(a whole bunch of decimals after this)

If you remove the decimal part of π by subtracting the integer part of it, that is the number 3. the result will still being and irrational number

Since π= 3(the rational part) +0,1415... (the irrational part)

The resut of π-=3= 0,1415...

Answer:

B). Irrational

If you are doing this on khan academy this should work

Step-by-step explanation:

Answer:

7, -4

Step-by-step explanation:

The zeros are just another name for the x intercepts

7, -4

Answer:

41F

Step-by-step explanation:

41-32=9

9*5/9=5

Answer:

41 degrees F.

Step-by-step explanation:

C = 5/9(f -  32)

5 = 5/9 (f - 32) Multiply both sides by 9/5:

5 * 9/5 = f - 32

9 = f - 32

f = 9 + 32

= 41.

Answer:

4 and 11

Step-by-step explanation:

Lets call the smallest n

And the other one n+7

Then,

n.(n+7)=44

n²+7n=44

Subtract 44 from both sides.

n²+7n-44=44-44

n²+7n-44=0

Factorize the equation.

n²+11n-4n-44=0

n(n+11)-4(n+11)=0

(n+11)(n-4)=0

n+11=0 , n-4=0

n=-11 , n=4

n=4 is the only positive solution, so the numbers are:

4 and 11....

Answer:

The two integers are: 4 and 11.

Step-by-step explanation:

We are given that one positive integer is 7 less than another. Given that the product of two integers is 44, we are to find the integers.

Assuming [tex]x[/tex] to be one positive integer and [tex]y[/tex] to be the other, we can write it as:

[tex]x=y-7[/tex] --- (1)

[tex]x.y=44[/tex] --- (2)

Substituting x from (1) in (2):

[tex](y-7).y=44[/tex]

[tex]y^2-7y-44=0\\\\y^2-11y+4y-44=0\\\\y(y-11)+4(y-11)[/tex]

y = 11

Substituting y = 11 in (1) to find x:

[tex]x=11-7[/tex]

x = 4

Answer:

g(x) will eventually exceed f(x) because g(x) is an exponential function.

Step-by-step explanation:

From the first table we can observe the following patterns:

[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex]

[tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex]

[tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex]

[tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]

In general,

[tex]f(x) = {x}^{2} - 6 [/tex]

From the second table we can observe the following pattern:

[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex]

[tex]g(0) = {6}^{ 0} = 1[/tex]

[tex]g(1) = {6}^{1} = 6[/tex]

[tex]g(2) = {6}^{2} = 36[/tex]

In general,

[tex]g( x) = {6}^{ x} [/tex]

Conclusion:

Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).

The correct answer is C.

Answer: C.

Step-by-step explanation:

Go it right on my test

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]

Answer:

Step-by-step explanation:

When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.

Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]

     B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

Then the augmented matrix is(A|B)

Note that a vertical line is used to separate te columns of A from the columns of B

(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

This is a simple example of augmented matrix....

Answer:

An augmented matrix refers to a matrix formed by appending the columns of two matrices.

The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.

If we have the system

[tex]2x+3y=5\\x-4y=9[/tex]

The two maxtrix involved here are

[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]

However, to solve the system using matrices, we have to formed an augmented matrix

[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]

So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.

Answer:

Step-by-step explanation:

You take the upaid balance of $110 and multiply it by 2%

which will give you $2.20. Then you add the two together and you get your answer of $112.20.

$110.00 x 2% = $2.20

$110.00

   +2.20

$112.20

The new balance on the charge account after applying a 2% finance charge to the unpaid balance of $110 is $112.20.

The student is asking about calculating the new balance on a charge account after a monthly finance charge is applied. To find this, we use the original balance and calculate the finance charge based on the given percentage. Since the unpaid balance is $110 and the monthly finance charge is 2%, we compute the finance charge as $110 × 0.02 = $2.20. Adding this to the unpaid balance gives us the new balance: $110 + $2.20 = $112.20.

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Answer:

[tex]\large\boxed{7\sqrt2}[/tex]

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (-3, 2) and (4, -5). Substitute:

[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]

Answer:

see explanation

Step-by-step explanation:

Given

4(px + 1) = 64 ( divide both sides by 4 )

px + 1 = 16 ( subtract 1 from both sides )

px = 15 ( divide both sides by p )

x = [tex]\frac{15}{p}[/tex]

When p = - 5, then

x = [tex]\frac{15}{-5}[/tex] = - 3

Answer:

Option A. [tex]4x+3y\leq 12[/tex] and [tex]x\geq 0[/tex]

Step-by-step explanation:

we know that

The solution of the first inequality is the shaded area below the solid line [tex]4x+3y=12[/tex]

The solid line passes through the points (0,4) and (3,0) (the y and x intercepts)

therefore

The first inequality is

[tex]4x+3y\leq 12[/tex]

The solution of the second inequality is the shaded area to the right of the solid line x=0

therefore

The second inequality is

[tex]x\geq 0[/tex]

Step-by-step explanation:

When moving left, subtract from the x-coordinate and when moving right, add in the x-coordinate. When moving down, subtract from the y-coordinate and when moving up, add in the y-coordinate.

1) Given point = (0, 0). 3 units right and 4 units down means (0+3, 0-4) = (3, -4).

2) Given point = (5, 2). 4 units left and 2 units down means (5-4, 2-2) = (1, 0).

3) Given point = (-6, -1). 8 units right and 5 units up means (-6+8, -1+5) = (2, 4).

4) In Quadrant II, the x-coordinate is negative and the y-coordinate is positive. So taking R = (-6,6). 2 units right and 6 units down means (-6+2, 6-6) = (-4, 0).

5) In Quadrant IV, the x-coordinate is positive and the y-coordinate is negative. So taking R = (6,-6). 7 units left and 4 units up means (6-7, -6+4) = (-1, -2).

Answer:

(0,0),(0,15),(20,25),(40,0)

Step-by-step explanation:

we know that

The feasible region is a quadrilateral

Let

A,B,C and D the vertices of the feasible region

see the attached figure

Observing the graph we have that

The coordinates of point A are (0,0)

The coordinates of point B are (0,15)

The coordinates of point C are (20,25)

The coordinates of point D are (40,0)

therefore

The answer is

(0,0),(0,15),(20,25),(40,0)

Answer:

A

Step-by-step explanation:

(0,0),(0,15),(20,25),(40,0)

Answer:

P = 1 3  

Q = 1 6 8 3

Step-by-step explanation:

through factorization of 21879

Answer:

$ 254.85

Step-by-step explanation:

Total amount invested = $ 560

Interest rate = r = 4.8% = 0.048

Time in years = t = 8 years

The formula for compound interest is:

[tex]A =P(1+\frac{r}{n})^{nt}[/tex]

Here,

A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:

[tex]A=560(1+\frac{0.048}{1})^{8} = \$ 814.85[/tex]

Thus, the total amount accumulated after 8 years will be $ 814.85

The amount of interest earned will be:

Interest = Amount Accumulated - Principal Amount

Interest = $ 814.85 - $ 560 = $ 254.85

By the end of 8 years, $ 254.85 would be earned in interest.

Answer:

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Step-by-step explanation:

The formula for the perimeter of a rectangle is [tex]P=2L+2W[/tex].

If the width is [tex]W=12\:units[/tex] and the length is [tex]L=18\:units[/tex], then the perimeter becomes:

 [tex]P=2\times 12+2\times 18[/tex].

 [tex]\implies P=24+36[/tex].

 [tex]\implies P=60[/tex].

Therefore the answer is

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Answer:

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Step-by-step explanation:

The formula for the perimeter of a rectangle is .

If the width is  and the length is , then the perimeter becomes:

 .

 .

 .

Therefore the answer is

D)Yes. The rectangle can have P = 60 and L = 18 because P = 2(18) + 2(12) would equal 60

Answer:

6

Step-by-step explanation:

f(0) means let x=0

In the table when x=0 f(0) =6

Answer:

The exact probability that the student selected is a junior whose  favorite subject is Math is [tex]\frac{124}{459}[/tex].

Step-by-step explanation:

Let the following events represents by the alphabets A and B.

A: Student selects Math as the favorite subject

B: Student chosen is a junior

The probability that the  student selects Math as the favorite subject is 1/4.

[tex]P(A)=\frac{1}{4}[/tex]

The probability that the student chosen is a junior is

[tex]P(B)=\frac{116}{459}[/tex]

The probability that the student selected is a junior or that the student chooses Math as the  favorite subject is 47/108.

[tex]P(A\cup B)=\frac{47}{108}[/tex]

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

[tex]\frac{47}{108}=\frac{1}{4}+\frac{116}{459}-P(A\cap B)[/tex]

[tex]P(A\cap B)=\frac{1}{4}+\frac{116}{459}-\frac{47}{108}=\frac{31}{459}[/tex]

The exact probability that the student selected is a junior whose  favorite subject is Math is

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]P(\frac{B}{A})=\frac{\frac{31}{459}}{\frac{1}{4}}=\frac{124}{459}[/tex]

Therefore the exact probability that the student selected is a junior whose  favorite subject is Math is [tex]\frac{124}{459}[/tex].

The exact probability that the student selected is a junior whose favourite subject is maths is 124/459

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The probability that the student selects Maths the favourite subject:

P(A) = 1/4

The probability that the student chosen is a junior:

P(B) = 116/459

The probability that the student selected is a junior or that the student chooses maths the favourite subject:

P(A∪B) = 47/108

We know:

P(A∩B) = P(A) + P(B) _P(A∪B)

P(A∩B) = 1/4 + 116/459 - 47/108

P(A∩B) = 31/459

The exact probability that the student selected is a junior whose favourite subject is maths:

P(B|A) = P(A∩B) /P(A)

= (31/459)/(1/4)

= 124/459

Thus, the exact probability that the student selected is a junior whose favourite subject is maths is 124/459

Learn more about the probability here:

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Answer:

The Slope Formula ( x1, y1 ) And ( x2, y2 )

Given

Substitute m with -3

a = -3*2 + 2

a = -6 + 2

a = -4

Answer

The value of a when m = -3 is -4

Answer:

=11

Step-by-step explanation:

The equation given is a=m²+2

To find a when m= -3 , we substitute for m in the equation.

a=(-3)²+2

=9+2

=11

Therefore a=11 when m is -3

Answer:

A. 12 mm

Step-by-step explanation:

May I have brainliest please? :)

Answer: A: 12 mm

Step-by-step explanation:

^^

Answer:

The answer is ∠C= 20 degree

Step-by-step explanation:

The answer is ∠C= 20 degree

We have given:

AB= 5

AC = 14

and we have to find ∠c to the nearest degree.

So,

We know that:

tan(C)= AB/AC

tan(C)= 5/14

tan(C)= 0.3571

C=20 degree

Thus the answer is ∠C = 20 degree ....

Ok.

So an hour contains 60 minutes.

The fraction is therefore,

[tex]\dfrac{33}{60}=\boxed{\dfrac{11}{20}}[/tex]

Hope this helps.

r3t40

Answer:

33 minutes is 11/20 of an hour.

Explanation:

So we know that 30 minutes is equal to half an hour. 30÷60 = 0.5

0.5 as a fraction is equal to 1/2.

Now let's use that same method for 33.

33÷60= 0.55.

0.55×100== 55.

55 as a fraction would be 55/100.

Let's convert that to its simplest form.

55÷5 = 11

100÷5 = 20

33 minutes is 11/20 of an hour.

Answer:

Blank 1: 3 is the remainder

Blank 2: not a factor

Step-by-step explanation:

If p(x)=(x-7)(x^2-2x+4)+3, then dividing both sides by (x-7) gives:

[tex]\frac{p(x)}{x-7}=(x^2-2x+4)+\frac{3}{x-7}[/tex].

The quotient is [tex](x^2-2x+4)[/tex].

The remainder is [tex]3[/tex].

The divisor is [tex](x-7)[/tex].

The dividend is [tex]p(x)=x^3-9x^2+18x-25[/tex].

It is just like with regular numbers.

[tex]\frac{11}{3}[/tex] as a whole number is [tex]3\frac{2}{3}[/tex].

[tex]3\frac{2}{3}=3+\frac{2}{3}[/tex] where 3 is the quotient and 2 is the remainder when 11 is divided by 3.

 Here is the division just for reminding purposes:

                        3 <--quotient

                      ----

divisor->  3  |   11  <--dividend

                       -9

                        ---

                         2   <---remainder

Anyways just for fun, I would like to verify the given equation of

p(x)=(x-7)(x^2-2x+4)+3.

I would like to do by dividing myself.

I could use long division, but I have a choice to use synthetic division since we are dividing by a linear factor.

Since we are dividing by x-7, 7 goes on the outside:

         x^3-9x^2+18x  -25

7   |    1     -9        18    -25

    |            7       -14     28

     -------------------------------

          1      -2       4         3

We have confirmed what they wrote is totally correct.

The quotient is [tex]x^2-2x+4[/tex] while the remainder is 3.

If p/(x-7) gave a remainder of 0 then we would have said (x-7) was a factor of p.

It didn't so it isn't.

Just like with regular numbers. Is 3 a factor of 6? Yes, because the remainder of dividing 6 by 3 is 0.

Answer:

(a^3/7) - 4 + 3

Step-by-step explanation:

We need to translate the words into equations:

The quotient of a number cubed and seven: (a^3/7)

four less than the quotient of a number cubed and seven: (a^3/7) - 4

four less than the quotient of a number cubed and seven, increased by three:

(a^3/7) - 4 + 3

Answer:

a = 3/2

Step-by-step explanation:

Multiply both sides by -3

Simplify

Divide both sides by -4

Take a look at the photo: