Find the missing terms of the geometric sequence 81,____, _____ 3

Answer:

Step-by-step explanation:

Brackets in mathematics are a little like periods in grammar.

They tell you exactly what you need to do.

In the question you have listed

3z^3 means that only the z is raised to the third power.

(3z)^3 means both the 3 and the z are raised to the third power. 3^3 * z^3 =

27 z^3     This is a valuable question to know the answer to.

Answer:

(C) -11

Step-by-step explanation:

The given functions are;

[tex]f(x)=x+4[/tex]

Plug in x=3.

This implies that; [tex]f(3)=3+4=7[/tex]

and

[tex]g(x)=12x-6[/tex]

Plug in x=-1

This implies that; [tex]g(-1)=12(-1)-6=-18[/tex]

[tex]f(3)+g(-1)=7+-18=-11[/tex]

Assuming scores are normally distributed, a score of 82% on Ms. Smith's test corresponds to the [tex]p[/tex]-th percentile, i.e.

[tex]P(X_S\le82)=p[/tex]

where [tex]X_S[/tex] is a random variable denoting scores on Ms. Smith's test.

Transform [tex]X_S[/tex] to [tex]Z[/tex], which follows the standard normal distribution:

[tex]P(X_S\le82)=P\left(\dfrac{X_S-75}2\le\dfrac{82-75}2\right)=P(Z\le3.5)\approx0.9998[/tex]

which means Amy scored at the 99.98th percentile.

This makes it so that Karina needs to score [tex]X_A=x[/tex] on Mr. Adams' test so that

[tex]P(X_A\le x)=0.9998[/tex]

Their test scores have the same [tex]z[/tex] score computed above, so

[tex]\dfrac{x-73}3=3.5\implies x=83.5[/tex]

so Karina needs to get a test score of at least 83.5%.

Answer:

the answer is 84%

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=-8\ and\ y=9\to(-8,\ 9)}[/tex]

Step-by-step explanation:

[tex]a)\ \text{Elimination method:}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x+2y=10&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+4y=12\\-2x-4y=-20\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad \boxed{x=-8}\\\\\text{Put the value of x to the second equation:}\\-8+2y=10\qquad\text{add 8 to both sides}\\2y=18\qquad\text{divide both sides by 2}\\\boxed{y=9}[/tex]

[tex]b)\ \text{Substitution method:}\\\\\left\{\begin{array}{ccc}3x+4y=12\\x+2y=10&\text{subtract 2y from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}3x+4y=12&(1)\\x=10-2y&(2)\end{array}\right\qquad\text{subtract (2) to (1)}\\\\3(10-2y)+4y=12\qquad\text{use distributive property}\\(3)(10)+(3)(-2y)+4y=12\\30-6y+4y=12\qquad\text{subtract 30 from both sides}\\-2y=-18\qquad\text{divide both sides by (-2)}\\\boxed{y=9}\\\\\text{Put the value of y to (2):}\\x=10-2(9)\\x=10-18\\\boxed{x=-8}[/tex]

Answer: 6(x-2)

Step-by-step explanation:

(x·2-8)-(2x·2+4)

(2(x-4))+2x·2-4

2(x-4)+2x·2-4

2(x-4)+4x-4

2(x-4+2x-2)

2(3x-4-2)

2(3x-6)

2·3(x-2)

6(x-2)

Answer:

3x^2-12

Step-by-step explanation:

Just took it on USATestPrep, if that's where the question came from! ;)

The probability that the arrow will land on any of them once is 1/4.

The probability that the arrow will land on any of them twice is 1/4 * 1/4. This is because the probability of Event A and Event B is P(B) * P(A).

Based on this:

[tex]P(a\cap b\cap c\cap d) = \frac{1}{4}\times \frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\\\\=\frac{1}{4\times4\times4\times 4}\\=\frac{1}{256}[/tex]

1/256

Hope this helps, let me know if I missed anything!

Answer:

1/256 or 2/512

Step-by-step explanation:

A "100 chart" is a listing of all the numbers 1 to 100, in rows of 10. This results in columns of numbers that all end in the same digit. For your purpose of instructing your little brother, I recommend you web-search for "100 chart" and print one of the ones available.

Locating the given numbers on a "100 chart", you find they are in the last 4 columns of the rows ending in 20, 30, 40, 50. Overlaying the boxes onto the chart, you see they correspond to number positions ...

  17 _ _ 20

  27 _ 29 _

  _ 38 _ 40

  47 _ _ 50

Answer:

Interest Earned = $1958

Value of total investment - $6490

Step-by-step explanation:

We can solve for both the questions by using the formula:

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

Where,

A is the future amount (original PLUS interest)

P is the initial amount

r is the rate of interest

n is the number of times interest is compounded per year

t is the time in years

For out problem, P = 4532, r is 0.06 (6%), n is 12 (since monthly compounding in 1 year), t = 6. Plugging these into the equation, we get A (the future amount).

[tex]A=P(1+\frac{r}{n})^{nt}\\A=4532(1+\frac{0.06}{12})^{(12)(6)}\\A=4532(1.005)^{72}\\A=6490[/tex]

This is the amount including interest. Hence,

Interest earned = 6490 - 4532 = $1958

Your total investment would be A, which is $6490

Answer:

Step-by-step explanation:

The volume of a cuboid is given by the product of its dimensions. Here, that is ...

  (12 cm)·(6 cm)·(3.5 cm) = 252 cm³

We are told the mass of each cm³ is 8.6, so 252 of them will have a mass of ...

  8.6·252 cm³ = 2167.2 . . . . . no units specified

For this case we must indicate the value of the following expression, expressed in scientific notation:

[tex](1.2 * 10^{-3}) * (1.1 * 10^{8}) =[/tex]

We have that for multiplication properties of powers of the same base, the same base is placed and the exponents are added:

[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]

Then, rewriting the expression we have:

[tex](1.2 * 1.1) * 10 ^{- 3 + 8} =\\1.32 * 10 ^ 5[/tex]

Answer:

[tex]1.32 * 10 ^ 5[/tex]

Answer:

i also need the answer to this question

Step-by-step explanation:

Answer:

y= 8x +18

Step-by-step explanation:

Answer:

[tex]\frac{5}{12}[/tex]  feet

Step-by-step explanation:

Let height of mandy be m, sophia be s, and alexis be a

"sophia is 3/4 as tall as mandy":

[tex]s=\frac{3}{4}m[/tex]

"alexis is 5/6 as tall as mandy":

[tex]a=\frac{5}{6}m[/tex]

Since mandy is 5 feet, we plug in 5 into m in both of the equations to find height of alexis and sophia.

Sophia  =  [tex]\frac{3}{4}(5)=\frac{15}{4}[/tex]

Alexis  =  [tex]\frac{5}{6}(5)=\frac{25}{6}[/tex]

Difference in height of Alexis and Sophia is  [tex]\frac{25}{6}-\frac{15}{4}=\frac{5}{12}[/tex] feet

Answer:

4g = 64

Step-by-step explanation:

Let n = the number of nectarines

and g = the number of grapefruit

We have two conditions that must be satisfied to represent the situation:

(1)         n = 3g

(2) n + g = 64

If you need one equation, we can substitute (1) into (2) and get

4g = 64

Answer:

  C. not similar, dilations are involved

Step-by-step explanation:

For geometric figures, such as triangles, we generally study a couple of kinds of transformations.

One is the "rigid transformation" which lets us move, rotate, or reflect the figure any way we like, but we keep it the same size—as though it were cut from cardboard or anything else that holds its shape and size. Any figures transformed by a rigid transformation are congruent.

Another is very much like the "rigid transformation", but dilation is involved. That is, the figure is allowed to be stretched or shrunk uniformly (by the same factor in every direction). Figures transformed in this way are similar, but are not congruent.

In this diagram, your triangle has been reflected and changed in size by a different factor horizontally than vertically. Hence dilation is involved (answer choices A or C), but because the factors are different, the figures are not similar (answer choice C).

_____

Comment on the answer choices

Rotations may be involved in similarity transformations, too. For some reason, that possibility was left off of choices A and C. (On the other hand, rotation is equivalent to a suitable set of reflections.)

i jus want some point bro

Answer:

Step-by-step explanation:

The negative coefficient of x^2 tells you the parabola opens downward. (Any even-degree polynomial with a negative leading coefficient will open downward.)

Going through the steps for completing the square, we ...

1. Factor out the leading coefficient from the x-terms

  -1(x^2 +14x) +1

2. Add the square of half the x-coefficient inside parentheses, subtract the same amount outside parentheses.

  -1(x^2 +14x +49) -(-1·49) +1

3. Simplify, expressing the content of parentheses as a square.

  -(x +7)^2 +50

4. Compare to the vertex form to find the vertex. For vertex (h, k), the form is

  a(x -h)^2 +k

so your vertex is ...

  (h, k) = (-7, 50) . . . . . . . . . a = -1 < 0, so the curve opens downward. The vertex is a maximum.

The maximum value of the expression is 50.

❤️Hello!❤️ The answer is 11.31 feet                                                                    arc length = radius * central angle (in radians)

arc length = 12.6 * 2*PI/7

arc length = 25.2 * PI/7  

arc length = 11.31 feet ☯️Hope this helps!☯️  ↪️ Autumn ↩️

Answer:

11.31 ft is the arc length.

Step-by-step explanation:

We have given the radius r = 12.6 ft and arc intercept by central angle

Ф = 2π/7.

We have to find the arc length.

We know the formula to find the arc length that is:

L = rФ

Putting the values we get,

 L= 12.6 × 2π/7

L = 25.2 π/7

L = 11.31 ft  is the answer.

11.31 ft is the arc length.

Try this suggested option (see the attached picture).

Answer:

Hope this helps you on your Assignment :D

Center (-1,1), radius 5 so

[tex](x - -1)^2 + (y - 1)^2 = 5^2[/tex]

[tex](x+1)^2 + (y-1)^2 = 25[/tex]

Third choice

Answer:

○ (x + 1)² + (y - 1)² = 25

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the center into the formula with their CORRECT signs. Then in the end, square the radius.

The radius is five, so squaring this will give you twenty-five.

I am joyous to assist you anytime.

Answer:

C. A(7) = 800·(1 +0.03)^(7-1)

Step-by-step explanation:

Note that the times are described as "the beginning of year 1" and "the beginning of year 7." If you consider the formula to be the one marked (choice D), you find the general case is ...

A(n) = 800·1.03^n

When you put in 1 for n, you see it gives you ...

A(1) = 800·1.03^1 = 824 . . . . . . . incorrect value for "the beginning of year 1"

The exponent of 1.03 needs to be the difference in year numbers: 7-1, as in choice C.

The appropriate formula is ...

A(7) = 800·(1 +0.03)^(7-1)

Answer:

[tex]-4.8[/tex] degrees Fahrenheit

Step-by-step explanation:

Let [tex]t[/tex] be temperature.

[tex]t[/tex] at 3:00PM: [tex]5.2[/tex] degrees.

Every hour, the temperature falls by [tex]2.5[/tex] degrees per hour for the next four hours. Let's multiply 2.5 by 4 to find out the total temperature drop in four hours.

[tex](2.5)(4)=10[/tex]

In four hours, the temperature dropped 10 degrees. Since it is getting colder, let's subtract this from the original 5.5 degrees to get the temperature at 7:00PM.

[tex]5.2-10=-4.8[/tex]

The temperature at 7:00PM was -4.8 degrees Fahrenheit.

Answer:

  6y -8

Step-by-step explanation:

Use the distributive property. It tells you the product can be simplified to the product of the outside factor and each of the individual terms in parentheses:

  2(3y - 4) = 2·3y + 2·(-4) = 6y -8

Answer:

x = 1/14

Step-by-step explanation:

You can work it as is by subtacting ln(14), then taking antilogs:

ln(x) = -ln(14)

x = 14^-1

x = 1/14

___

Or you can rewrite to a single log and then take antilogs:

ln(14x) = 0

14x = 1

x = 1/14 . . . . . divide by the coeffient of x

Answer:

  see below

Step-by-step explanation:

This is solved by simplifying each expression and identifying the column heading it matches.

1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5))

= (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply

= (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel

= 3x/(x -2) . . . . matches column 1

__

2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5))

= (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor

= (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor

= ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator

= (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product

= (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms

= (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator

= x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2

__

3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x)

= 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1

__

4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x)

= 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2

__

5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)

__

6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)

In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.

Answer:

  see the attachment

Step-by-step explanation:

f(x) = x defines a line with a slope of 1 (upward to the right). Only the bottom two graphs have such a line.

The inequality symbol ≥ means the function has this definition for the case when x = 1. That is, f(x) ≥ x for x≥1 means f(1) = 1. The solid dot means that point on the graph is a point that satisfies the function definition.

The graph at lower right is a graph that includes the point f(1) = 3, which is not the same function as the one in the problem statement.

Answer:

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle create two smaller triangles, all of which are similar to the original. This means corresponding sides are proportional.

3. Using the above relationship, ...

short-side/hypotenuse = 8/y = y/(8+23)

y^2 = 8·31

y = 2√62

__

long-side/hypotenuse = z/(8+23) = 23/z

z^2 = 23·31

z = √713

__

short-side/long-side = 8/x = x/23

x^2 = 8·23

x = 2√46

_____

4. The picture is fuzzy, but we think the lengths are 25 and 5. If they're something else, use the appropriate numbers. Using the same relations we used for problem 3,

y = √(5·25) = 5√5 . . . . . . . = √(short segment × hypotenuse)

z = √(20·25) = 10√5 . . . . . = √(long segment × hypotenuse)

x = √(5·20) = 10 . . . . . . . . . = √(short segment × long segment)

Answer:

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

Step-by-step explanation:

To find the equation of this line, start by using the two points with the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - 1)/(1 - -1)

m = 3/(1 + 1)

m = 3/2

Now that we have the slope, we can use that and either point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 4 = 3/2(x - 1)

y - 4 = 3/2x - 3/2

y = 3/2x + 5/2

Answer:

4 hours

Step-by-step explanation:

Let h represent the number of hours the high-power pump requires to fill the pool. Then the number of pools it can fill per hour is 1/h. The low-power pump can fill 1/(h+2) pools in an hour. Together, they can fill 1 pool in 1.2 hours:

1/h + 1/(h+2) = 1/2.4

h+2 +h = h(h+2)/2.4 . . . . . . . multiply by h(h+2)

4.8h +4.8 = h^2 +2h . . . . . . multiply by 2.4

h^2 -2.8h = 4.8 . . . . . . . . . . put in form suitable for completing the square

h^2 -2.8h +1.96 = 6.76 . . . add (2.8/2)^2 = 1.96 to complete the square

h - 1.4 = √6.76 . . . . . . . . . . take the square root of both sides

h = 1.4 +2.6 = 4 . . . . . . . . . hours

The answer is: 22 inches.

We are given a cylinder shape, with the information about it's diameter, meaning that we also can know the radius.

The height of a cylinder goes from the bottom to the top of the shape, so, from the given shape, the height is 22 inches.

With the information, we can also calculate the volume of the cylinder using the following formula:

[tex]V=\pi *r^{2}*h\\\\V=\pi *(\frac{Diameter}{2})^{2} *h\\\\\V=\pi *(\frac{16}{2})^{2}*22=\pi *8^{2} *22=4423.4inches[/tex]

Have a nice day!

Answer:

22 inches

Step-by-step explanation:

We are given a figure of a cylinder with two known lengths. We are to determine whether which of them is the height of the cylinder.

We know that the base of the cylinder is round so the length mentioned on the round base is its diameter.

While the other length running from the top to bottom (or from left to right as shown in the picture) is the height of the cylinder which is 22 inches.

Answer:

[tex]m\angle MEJ=25^{\circ}.[/tex]

Step-by-step explanation:

The arcs LY, KM, KL and MJ together form the full revolution angle, thus

[tex]4x+50^{\circ}+6x+x+10^{\circ}+4x=360^{\circ},\\ \\15x=300^{\circ},\\ \\x=20^{\circ}.[/tex]

Note that

[tex]m\angle MOJ=4x=80^{\circ},[/tex]

then

[tex]m\angle MLJ=\dfrac{1}{2}\cdot 80^{\circ}=40^{\circ}.[/tex]

So,

[tex]m\angle ELM=180^{\circ}-40^{\circ}=140^{\circ}.[/tex]

Also

[tex]m\angle LOK=30^{\circ},[/tex]

so

[tex]m\angle KML=\dfrac{1}{2}\cdot 30^{\circ}=15^{\circ}.[/tex]

In triangle EML,

[tex]m\angle MEL+m\angle EML+m\angle ELM=180^{\circ},\\ \\m\angle MEL=180^{\circ}-15^{\circ}-140^{\circ}=25^{\circ}.[/tex]

Thus, [tex]m\angle MEJ=25^{\circ}.[/tex]