Find the fifth term of the sequence.

Step-by-step explanation:

since there are z fishes

the number of angelfish = 1 × z

4

= 1 z

4

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

Learn more about PARENTHESIS here https://brainly.com/question/1473593

#SPJ4

Answer:

x = 2 or x = -1/4

Step-by-step explanation:

Let's solve your equation step-by-step.

4x2−7x−2=0

For this equation: a=4, b=-7, c=-2

4x^2+−7x+−2=0

Step 1: Use quadratic formula with a=4, b=-7, c=-2.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-2)} }{2(4)}[/tex]

[tex]x=\frac{7\pm\sqrt{81} }{8}[/tex]

x = 2 or x = -1/4

Answer:

x = 2 or x = -1/4

Answer:

a) Height of the ledge is 1.6 m.

b) roots of the equation are: [tex]\bf d = 2[/tex] ,  [tex]\bf d = -1[/tex]

c) Maximum height reached = 1.8 m.

Step-by-step explanation:

a) The height of the ledge is the same as the height at which Jake is when he hasn't moved any horizontal distance from the ledge yet, that is, when d = 0:

[tex]h = -0.8(0)^2 + 0.8(0) + 1.6[/tex]

⇒ [tex]\bf h = 1.6 \space\ m[/tex]

∴ Height of the ledge is 1.6 m.

b) The x-intercepts occur where y = 0, that is when h = 0:

[tex]-0.8d^2 + 0.8d + 1.6 = 0[/tex]

Divide both sides of the equation by -0.8:

[tex]d^2 - d -2 = 0[/tex]

Factorizing:

⇒ [tex]d^2 -2d + d - 2 = 0[/tex]

⇒ [tex]d(d-2) +1 (d-2) = 0[/tex]

⇒ [tex](d-2)(d+1) = 0[/tex]

⇒ [tex]d - 2 = 0[/tex]    or    [tex]d + 1 = 0[/tex]

∴ roots are :  [tex]\bf d = 2[/tex]   ,   [tex]\bf d = -1[/tex]

c) To find the maximum value of a quadratic equation in the form

y = ax² + bx + c , use the formula:

max = c - (b² / 4a).

Using the formula for [tex]h = -0.8x^2 + 0.8x + 1.6[/tex] :

max h =  [tex]1.6 - ( \frac{0.8^2}{4(-0.8)} )[/tex]

       = 1.8

∴ Maximum height reached = 1.8 m.

Answer:

  a) 1.6 m

  b) -1, 2 meters

  c) 1.8 m

Step-by-step explanation:

Apparently, technology tools are allowed when solving this problem. They readily show you the x- and y-intercepts and the vertex of the graph.

The height of the ledge is the value of h when d=0. It is the constant in the given equation, and the y-intercept of the graph.

The height of the ledge is 1.6 meters.

The x-intercepts are the values of d that make h equal to zero. The graph shows them to be ...

 d = -1

  d = 2 . . . . meters

The maximum height is the "h" coordinate of the vertex (d, h).

The maximum height is 1.8 meters.

__

Additional comment

"x" is the generic independent variable. The horizontal axis of a graph is often called the "x-axis" and places where the graph crosses that axis are called "x-intercepts" even when the independent variable is named something else. Here, the independent variable is "d", not "x".

Similarly, "y" is the generic dependent variable, and the vertical axis of a graph is often called the "y-axis" even when the dependent variable is something else. This is why we refer to h when d=0 as the "y-intercept". It is the point where the graph crosses the vertical axis.

Answer:

D

Step-by-step explanation:

Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For an inverse relationship, the function is:

[tex]y = \frac{k}{x}[/tex].

Then:

k = xy.

Which means that to find k, you take a point (x,y), and multiply the values of x and y.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

Domain: [0,∞)

Range: (-∞, 4]

Step-by-step explanation:

The required domain and range of the function shown in the graph are,
Domain = (0, ∞)
Range = (-∞, 4)

To calculate the domain and range of a function from its graph, you can follow these steps:

So, from the above definition, from the graph we have,
Domain = (0, ∞)
Range = (-∞, 4)

Learn more about domain and range here;

https://brainly.com/question/29452843

#SPJ5

Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]

⇒ [tex]E(X)=\infty[/tex]

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]

⇒ [tex]E(X)=\infty[/tex]

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

Learn more about discrete random variable here

https://brainly.com/question/27014983

#SPJ4

Based on the information in the table, an example of independent events is  the: P(policer officer and chooses car).

An independent event can be defined as an event that isn't dependent on other events. Thus, it isn't affected by any previous event.

Based on the information provided, we can infer and logically deduce that an example of independent events is  the probability of being a policer officer and chooses a car because they aren't overlapping probabilities.

Read more on independent events here: https://brainly.com/question/26795996

#SPJ1

The range is -6.

To find the answer, calculate as follows:

Range = Maximum - Minimum

Range = 8 and Maximum = 2

Let, the minimum be x.

Now, substitute values in the formula.

8 = 2 - x

x = 2 - 8

x = -6

Therefore, the answer is -6.

Know more about a range here:

https://brainly.com/question/26098895

#SPJ4

It can be proved that Circles X and Y are similar.

We were told that circle Y have a  radius of s

And X have the  Radius r

Going with the theorem that Similar shapes are proportional, we can find the scale factor from circle X to circle Y  by making a division on the  radii of both circles.

Then the scale factor is [tex]\frac{s}{r}[/tex] which implies that circle Y will gotten by dilation of circle Y.

Therefore, both circles are similar

Read more about  circles at:

brainly.com/question/15000795

#SPJ1

These districts are best characterized as Proportional Representation districts.

What is Proportional Representation?

There are numerous types of proportional representation systems, but they all have two things in common. They start by using districts with multiple members.

Proportional Representation, abbreviated as PR, uses significantly bigger districts that elect multiple members at once, such as five or ten, rather than electing one member of the legislature in each local district. Second, the percentage of votes a party receives in these districts with several members determines which candidates gain the seats.

The Proportional Representation system of America overcomes the wide ranging drawbacks of single-district voting system like not representing the  large number of voters, discrimination against third parties, etc.

Learn more about Proportional Representation here:

https://brainly.com/question/27987112

#SPJ4

The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

The formula for finding the equation of a circle is expressed as:

(x-a)² + (y - b)² = r²

where

(a, b) is the centre

r is the radius

Given the following

(a, b) = (0, 0)

r = 12.5/2 = 6.25

Substitute

(x-0)² + (y - 0)² = 6.25²

x²+y²=39.0625

Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625

Learn more on equation of a circle here: https://brainly.com/question/1506955

#SPJ1

Answer: No solutions

Step-by-step explanation: there would be no solutions, because these equations have the same slope and different y-intercepts, so they would end up being parallel from each other, and would never intersect or be equivalent.

Answer:

No solution.

Explanation:

Given equations:

(1) y - 4x = -3

(2) y = 4x + 7

Substitute equation 2 into 1

y - 4x = -3

4x + 7 - 4x = -3

7 = -3

As L.H.S ≠ R.H.S, There are no solution.

The lines are parallel and do not intersect each other. Their slope is same.

All expressions whose sum represents the same vector as (r + s) + t. is Option b,c,e

Where

r= (2,3)

s= (5,-3)

t= (-8,6)

Generally, the equation for statement is  mathematically given as

(7,0)+(-8,6) ,(2,3)+(-3,3) and (-6,9)+(5,-3) are equal to (r+s)+t

Therefore

x=(2,3)+(5,-3)

x=(7,0)

Now we can calculate (r+s)+t as

(7,0)+(-8,6)

(7-8,0+6)

(-1,6)

For (b)

x=(7,0)+(-8,6)

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

For (c)

x=(2,3)+(-3,3,)

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

For (e)

[tex]x=(-6,9)+(5,-3)[/tex]

x=(-1,6)

in this scenario x expressions is equal to (r+s)+t

In conclusion, all expressions whose sum represents the same vector as (r + s) + t. is b,c,e

Read more about vector

https://brainly.com/question/13322477

#SPJ1

Answer:

1/3

Step-by-step explanation:

The numbers are 1, 2, 3, 4, 5, and 6.

Both 3 and 6 are multiples of 3.

So, 2/6 is the probability since there is an equal change that the arrow will land on each section.

This simplifies to 1/3.

Brainliest, please :)

Answer:

P (multiple of 3) =  [tex]\bf \frac{1}{3}[/tex]

Step-by-step explanation:

Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6}    (6 elements)

Multiples of 3 = {3, 6}   (2 elements)

P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner

                          =  [tex]\frac{2}{6}[/tex]

                          =  [tex]\bf \frac{1}{3}[/tex]

Beau can wrap 32 inches of ribbon outside the mirror.

Area of Beau Thai's mirror is 60 sq. inches.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Given information:

Length of mirror = 6 inches

Width of mirror = 10 inches

To Find:

The amount of ribbon Beau could wrap around the outside of the mirror.

Perimeter of the mirror = 2(6+10)

                                       = 2(16)

                                       = 32 inches

The area of Beau Thai's mirror.

Area of the mirror = 6*10

                              = 60 sq. inches

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

Using the Pythagorean theorem, the length of line segment FJ is: 42 ft.

To find the length of line segment FJ, we need to apply the Pythagorean theorem to find the length of the segment from F to the point, say point O, on FJ where a right triangle FOG will be gotten.

Thus, we have:

FO = √(GF² - GO²)

FO = √(30² - 24²)

FO = 18 ft.

FJ = FO + GH

Plug in the values

FJ = 18 + 24

FJ = 42 ft.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/654982

#SPJ1

Answer: B

Step-by-step explanation:

A) False. Rotations do not preserve parallelism.

B) True. Rotations are rigid motions and thus preserve angle measure.

C) False. A rotation that changes the location of every point except for the center of rotation.

total expenses= 1/4 + 1/8

the denominators should be equal to add the values.

1/4×2(divide both the numerator and denominator by two)

=2/8

=2/8+1/8

3/8//

3/8(fraction of the salary he spent)

3/8 of the salary

3/8×50,000

R.s 6250

balance = 50,000-6,250

= R.s 43,750//

Answer:

11.2 square meters

Step-by-step explanation:

This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:

[tex]\pi \times r^{2} [/tex]

Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:

[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]

Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)

Answer:

The solution for the expression is choice D 26√5 +2√10

Step-by-step explanation:

Hello!

First, apply distributive law: a(b+c)= ab+ac

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

Polynomials can be expressed as a product of binomials of the form (x - r) multiplied by a leading coefficient. The least polynomial contain the number of roots presented in statement, whose factor form is shown below:

f(x) = 1 · (x + 3)³ · x³ · (x - 3)

f(x) = (x + 3)³ · (x⁴ - 3 · x³)

f(x) = (x³ + 9 · x² + 27 · x + 27) · (x⁴ - 3 · x³)

f(x) = x⁷ + 9 · x⁶  + 27 · x⁵ + 27 · x⁴ - 3 · x⁶ - 27 · x⁵ - 81 · x⁴ - 81 · x³

f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³

The least polynomial in standard form is defined by the function f(x) = x⁷ + 6 · x⁶ - 54 · x⁴ - 81 · x³.

To learn more on polynomials: https://brainly.com/question/11536910

#SPJ1

The value of angle CFE in the diagram attached is 51 degrees.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

∠AFB = ∠CFD; ∠BFC = ∠DFE

Hence:

∠AFC = ∠CFE

∠AFD = ∠AFC + ∠CFD = ∠AFC + ∠AFB

90 = ∠AFC + 31

∠AFC = 51° = ∠CFE

The value of angle CFE in the diagram attached is 51 degrees.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

The midpoint of AB,  given any points A (x₁, y₁) and B(x₂, y₂) is given as point M = ({(x₁ + x₂)/2},{(y₁ + y₂)/2}).

In the question, we are given that the midpoint of PQ is (-3, 1) and point Q is (7, 5).

We are asked to find the coordinates of point P.

We assume the coordinates of point P as (x, y).

Thus, the midpoint of PQ = ({(x + 7)/2}, {(y + 5)/2}),

that is, (-3, 1) = ({(x + 7)/2}, {(y + 5)/2}).

Thus, we can show that:

(x + 7)/2 = -3,

or, x + 7 = -6,

or, x = -6 - 7 = -13.

(y + 5)/2 = 1,

or, y + 5 = 2,

or, y = 2 - 5 = -3.

Thus, the coordinates of P are (-13, -3), given the coordinates of Q as (7, 5) and the coordinates of the midpoint of PQ as (-3, 1).

Learn more about midpoints at

https://brainly.com/question/4521677

#SPJ4

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

Learn more about hexagon here:

https://brainly.com/question/28016053

#SPJ4

A conclusion which can be derived from these random samples is that: E. Cars are faster than SUVs.

A median can be defined as the middle number (center) of a sorted data set, which is typically when the data set is arranged in from the least to greatest or the greatest to least.

In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.

Based on the information provided for these random samples from the race, we can infer and logically conclude that Cars are faster than SUVs because a median speed of 132 is greater than a median speed of 115.

In conclusion, it is important to note that the Cars used in this survey (research) are faster than SUVs because the median for the SUVs in Sample 2 is equal to 115 while the median for the Cars in Sample 1 is equal to 132.

Read more on median here: brainly.com/question/9550536

#SPJ1

Answer:

x = 80 , y = 50

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact is 90°

given the angle between the tangent and the chord is 40° , then

angle inside triangle = 90° - 40° = 50°

the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then

y = 50°

the sum of the 3 angles in the triangle = 180° , then

x = 180° - 50° - 50° = 180° - 100° = 80°

Answer:

x = 80°

y = 50°

Step-by-step explanation:

the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.

that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.

the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.

one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.

since both leg angles must be equal (as described above), y = 50° too.

and as the sum of all angles in a triangle must be 180°, that gives us for x

180 = 50 + 50 + x

x = 180 - 50 - 50 = 80°