Scientist released 5 foxes into a new habitat in year 0. Each year, there were four times as many foxes as the year before. How many foxes were there after x years? Write a function to represent this scenario

For each Y value to have more than one x value would be a linear function.

It would make a straight line.

The correct answer is B: many-to-one function. This is the type of function where one y value is associated with multiple x values, differing from linear, nonlinear, and one-to-one functions.

A function in which each y value has more than one corresponding x value is known as a many-to-one function. This type of function allows for multiple x values to be paired with a single y value. This should not be confused with nonlinear functions or one-to-one functions. Moreover, while linear function is often associated with straight lines, in algebra, a linear function may actually include more than one term, each having a single multiplicative parameter. For example, y = ax + bx² is linear in this algebraic sense because terms x and x² each have one parameter (a and b). However, a function like y = [tex]x^b[/tex], where b is an exponent rather than a multiplicative parameter, is an example of a nonlinear function as it cannot be accurately described using linear regression.

Answer:

[tex]127,000\ members[/tex]

Step-by-step explanation:

In this problem we have an exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

The base is equal to

b=1+r

r is the average rate

In this problem we have

a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

[tex]f(x)=23,000(1.05)^{x}[/tex]

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

[tex]f(x)=23,000(1.05)^{35}=126,868\ members[/tex]

Round to the nearest thousand

[tex]126,868=127,000\ members[/tex]

The club is expected to have about 126868 members in 2020.

[tex]\[N(t) = N_0 \times (1 + r)^t\][/tex]

In this problem:

[tex]- \( N_0 = 23,000 \)- \( r = 0.05 \) (5% growth rate)- \( t = 2020 - 1985 = 35 \)[/tex]

Substituting these values into the formula, we get:

[tex]\[N(35) = 23,000 \times (1 + 0.05)^{35}\][/tex]

[tex]\[N(35) = 23,000 \times (1.05)^{35}\][/tex]

[tex]\[(1.05)^{35} \approx 5.516\][/tex]

Now, multiply by the initial number of members:

[tex]\[N(35) = 23,000 \times 5.516 \approx 126,868\][/tex]

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

1/2

Step-by-step explanation:

sin(K)=5/10=1/2

The sine function in mathematics relates angles of a right triangle to the ratios of its side lengths. The value of sin(K) depends on the value of angle K, measured in radians.

In mathematics, the sine function is a trigonometric function that relates the angles of a right triangle to the ratios of the side lengths. The value of sin(K) depends on the value of angle K, which is measured in radians.

For example, if K = π/2, then sin(K) = 1. If K = 0, then sin(K) = 0.

To find the value of sin(K), you can use a calculator or reference table that provides the values of sine for different angles.

Answer:

D

Step-by-step explanation:

[tex]\left[\begin{array}{cc}Flow Rate&Eroded Soil\\0.31&0.82\\0.85&1.95\\1.26&2.18\\2.47&3.01\\3.75&6.07\end{array}\right][/tex]

As we can see, as flow rate increases, eroded soil also increases.  So the association is positive.

The association between flow rate and amount of eroded soil is positive.

The association between flow rate and amount of eroded soil is:

D. positive

The data shows that as the water flow rate increases, the amount of eroded soil also increases. This positive relationship indicates that higher water flow leads to more soil erosion.

Answer: False

Step-by-step explanation:

The measure of the created angle is equal to the difference of the measure of the arcs.

The angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc, not the sum of the measures of the intercepted arcs.

The statement is False. The angle formed by the intersection of a secant and a tangent is half the measure of the intercepted arc, not equal to the sum of the measures of the intercepted arcs.

For example, let's consider a circle with a secant and a tangent line intersecting at a point. The intercepted arc is represented by the section of the circumference between the two points of intersection. The angle formed by the intersection of the secant and the tangent is equal to half the measure of this intercepted arc.

So, in conclusion, the angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc.

Answer:

[tex]f(g(x))=x^{6}-19x^{3}+90[/tex]

Step-by-step explanation:

We have been given the following equations;

f(x)=x^2−3x+2

g(x)=x^3−8

We are required to determine the composite function (f⋅g)(x). This simply means that we shall substitute the function g(x) in place of x in the function f(x);

[tex]f(g(x)) = g(x)^{2}-3g(x)+2\\\\f(g(x))=(x^{3}-8)^{2}-3(x^{3}-8)+2\\\\f(g(x))=x^{6}-16x^{3}+64-3x^{3}+24+2\\\\f(g(x))=x^{6}-19x^{3}+90[/tex]

Step-by-step explanation:

First we need to find which function is the outside radius and which is the inside radius (by which I mean which is farther and which is closer to the axis of rotation).  We can do this by graphing, but we can also do this by evaluating each function at the end limits.

At x = 0:

y = 5 sin 0 = 0

y = 5 cos 0 = 5

At x = π/4:

y = 5 sin π/4 = 5√2 / 2

y = 5 cos π/4 = 5√2 / 2

So y = 5 cos x is the outside radius because it is farther away from y = -1, and y = 5 sin x is the inside radius because it is closer to y = -1.

Here's a graph:

desmos.com/calculator/5oaiobcpww

The volume of the rotation is:

V = π ∫ₐᵇ [(R−y)² − (r−y)²] dx

where a is the lower limit, b is the upper limit, R is the outside radius, r is the inside radius, and y is the axis of rotation.

Plugging in:

V = π ∫₀ᵖ [(5 cos x − -1)² − (5 sin x − -1)²] dx

V = π ∫₀ᵖ [(5 cos x + 1)² − (5 sin x + 1)²] dx

V = π ∫₀ᵖ [(25 cos² x + 10 cos x + 1) − (25 sin² x + 10 sin x + 1)] dx

V = π ∫₀ᵖ [25 cos² x + 10 cos x + 1 − 25 sin² x − 10 sin x − 1] dx

V = π ∫₀ᵖ [25 (cos² x − sin² x) + 10 cos x − 10 sin x] dx

V = π ∫₀ᵖ [25 cos (2x) + 10 cos x − 10 sin x] dx

V = π [25/2 sin (2x) + 10 sin x + 10 cos x] from 0 to π/4

V = π [25/2 sin (π/2) + 10 sin (π/4) + 10 cos (π/4)] − π [25/2 sin 0 + 10 sin 0 + 10 cos 0]

V = π [25/2 + 5√2 + 5√2] − 10π

V = π (5/2 + 10√2)

V ≈ 52.283

In this exercise it is necessary to calculate the volume of the rotating solid, in this way we have:

[tex]V= 52.3[/tex]

First we need to find which function is the outside radius and which is the inside radius (by which I mean which is farther and which is closer to the axis of rotation).  We can do this by graphing, but we can also do this by evaluating each function at the end limits.

[tex]x=0\\y=5sin(x)\\y=5sin(0)=0\\y=5cos(0)= 5\\\\x=\pi/4\\y=5sin(\pi/4)= 5(\sqrt{2/2})\\y=5cos( \pi/4)= 5/\sqrt{2}[/tex]

So [tex]y = 5 cos x[/tex] is the outside radius because it is farther away from y = -1, and [tex]y = 5 sin x[/tex] is the inside radius because it is closer to y = -1. Here's a graph (first image). The volume of the rotation is:

[tex]V=\pi\int\limits^a_b {[(R-y)^2-(r-y)^2]} \, dx[/tex]

Where a is the lower limit, b is the upper limit, R is the outside radius, r is the inside radius, and y is the axis of rotation. Plugging in:

[tex]V=\pi\int\limits^a_b {[(R-y)^2-(r-y)^2]} \, dx\\= \pi\int\limits^p_0 {[(5 cos(x) + 1)^2-(5 sin(x) + 1)^2]} \, dx\\=\pi\int\limits^p_0 {[(25 cos^2 (x) + 10 cos (x) + 1)-(25 sin^2 (x) + 10 sin (x) + 1)]} \, dx\\=\pi\int\limits^p_0 {[(5 cos^2 (x) + 10 cos (x) + 1 -25 sin^2 (x)- 10 sin (x)- 1]} \, dx\\=\pi\int\limits^p_0 {[(25 (cos^2( x)- sin^2( x)) + 10 cos( x)- 10 sin( x)]} \, dx\\=\pi\int\limits^p_0 {[(25 cos (2x) + 10 cos (x)- 10 sin (x)]} \, dx\\[/tex]

[tex]=\pi[(25/2 sin (2x) + 10 sin x + 10 cos (x)]\\\\=\pi[(25/2 sin (\pi/2) + 10 sin (\pi/4) + 10 cos (\pi/4)] - \pi [25/2 sin( 0) + 10 sin( 0) + 10 cos(0)]\\\\=\pi[25/2+5\sqrt{2}+5/\sqrt{2}]-10\pi\\\\\V= 52.3[/tex]

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Answer:

Step-by-step explanation:

The leftmost piece of the function is constant at -3.

The middle piece is a line with a slope of 2 that intersects the y-axis at -3, so has equation y = 2x-3. (The slope-intercept form of the equation of a line is y = slope·x + y-intercept. The slope is found by counting the number of vertical grid squares that correspond to each horizontal grid square.)

The rightmost piece is constant at +5.

___

We don't know what your choices are, so we can't tell you which to select.

The piecewise function is a horizontal line restricted between x = 0 and x = 20. To evaluate the function, substitute the given values into the function.

The given piecewise function is:

f(x) =

To evaluate the function for given values of the domain, you can substitute the given values of x into the function and calculate the corresponding y-values. For example, to find f(5), substitute x = 5 into the function and evaluate.

It is important to note that the question does not provide the equation or specific values of the function, so the evaluation of the function cannot be performed without additional information.

Answer:

C

Step-by-step explanation:

Answer:  The correct option is

(A) 7.

Step-by-step explanation:  Given that for a school fundraiser, Jeff sold large boxes of candy for three dollars each and small boxes of candy for two dollars each.

Also, Jeff sold 37 boxes in all for total of $96.

We are to find the number of large boxes more than that of small boxes.

Let x and y represents the number of large boxes and small boxes respectively.

Then, according to the given information, we have

[tex]x+y=37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+2y=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Multiplying equation (i) by 2 and subtracting from equation (ii), we get

[tex](3x+2y)-(2x+2y)=96-37\times2\\\\\Rightarrow x=96-74\\\\\Rightarrow x=22.[/tex]

From equation (i), we get

[tex]22+y=37\\\\\Rightarrow y=37-22\\\\\Rightarrow y=15.[/tex]

We have,

[tex]x-y=22-15=7.[/tex]

Thus, there are 7 more large boxes than small boxes.

Option (A) is CORRECT.

For this case we have that according to the order of PEMDAS algebraic operations, it is established that:

P: Any calculation is made inside the parentheses, making the most internal ones first.

E: Any exponential expressions are simplified.

MD: All the multiplications and divisions are made, from left to right, as they appear.

AS: All sums and subtractions are made, from left to right, as they appear.

So:

[tex]2 ^ 3[/tex] + 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + (11-8) =

[tex]2 ^ 3[/tex]+ 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + 3 =

8 + 5 * 10 ÷ 2-27 + 3 =

8 + 50 ÷ 2-27 + 3 =

8 + 25-27 + 3 =

33-27 + 3

6 + 3 =

9

Answer:

9

ANSWER

undefined

EXPLANATION

We want to find the slope of a line that is perpendicular to the line y = 1

The line y=1 is parallel to the x-axis.

In other words, the line y=1 is a horizontal line.

The line perpendicular to y=1 is a vertical line.

The slope of a vertical line is undefined

Answer:

its an undefined slope

Step-by-step explanation:

the line y=−1 has slope 0 so any line perpendicular to it will have an undefined slope

Answer:

hi

Step-by-step explanation:

Answer:

240 feets

Step-by-step explanation:

In this question , apply Pythagorean relationship

Lets assume ;the climbing, sliding and walking back to the base forms a right-angle triangle

The tower height = the height of the triangle, h=60f

The sliding lane= the hypotenuse of the triangle=?

\

The distance covered to the base= base of the triangle=80f

Applying the relation ;

a²+b²=c²

80²+60²=c²

6400+3600=c²

10000=c²

√10000=c

100=c

Distance traveled in all=100+60+80=240 feet

Zachary traveled a total of 140 feet including climbing the tower and walking back from the splash pool to the tower.

The question is asking how far Zachary has traveled in total. He first climbs a 60-foot tower and then he lands in the splash pool. After that, he walks 80 feet back to the base of the tower.

To find the total distance he traveled, we need to add the distance he climbed up the tower to the distance he walked back to the tower. This can be done using simple addition.

Therefore, the total distance= distance climbed + distance walked = 60 feet + 80 feet = 140 feet.

So, Zachary traveled a total of 140 feet in all.

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Answer:

π/49·(44 -π)

Step-by-step explanation:

Using the "shell" method, a differential of volume is the product of the area of a cylindrical shell and its circumference around the axis of rotation. Here, that area is ...

dA = y·dx = cos(7x)dx

The radius will be the difference between x and the axis of rotation, x=3, so is ...

r = 3 -x

Then the differential of volume is ...

dV = 2πr·dA = 2π(3-x)cos(7x)dx

The volume will be the integral of this over the limits x ∈ [0, π/14].

∫dV = 6π·∫cos(7x)dx -2π·∫x·cos(7x)dx . . . from 0 to π/14

= (6/7)π·sin(7x) -(2/49)π·(cos(7x) +7x·sin(7x)) . . . from 0 to π/14

= (6/7)π(1 -0) -(2/49)π((0 -1) +(π/2-0))

= π(42/49 +2/49 -π/49)

= (π/49)(44 -π) . . . . cubic units . . . . . approx 2.61960 cubic units

Final answer:

The volume of the solid created by rotating the bounded region about the axis x=3 is found using cylindrical shells and evaluating the integral from x=0 to x=π/14 of the expression 2π(3-x)cos(7x)dx.

Explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves y=0, y=cos(7x), x=π/14, and x=0 about the axis x=3, we need to use the method of cylindrical shells.

For a small strip at position x with height y and thickness dx, rotating around x=3 creates a cylindrical shell with circumference 2π(3-x), height cos(7x), and thickness dx.

The volume of each shell is V = 2π(3-x)cos(7x)dx, and summing these from x=0 to x=π/14 gives us the total volume.

So, the volume V is the integral:

∫0π/14 2π(3-x)cos(7x)dx.

This volume is found by evaluating the definite integral.

3³ X 3⁶ > 3⁸ is the correct expression.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, Let first equation is true,

then, LHS = 2⁴ X 2³

                  = 2⁴⁺³

                 = 2⁷

                ≠ RHS

Option A is false.

Again assume option B is true.

Now check, LHS = 3³ X 3⁶

                           = 3³⁺⁶

                          = 3⁹

                          >3⁸

                 LHS > RHS

Thus, 3³ X 3⁶ > 3⁸ is the correct expression.

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In matrix form, we're looking for coefficients [tex]b_3,b_2,b_1,b_0[/tex] such that

[tex]\underbrace{\begin{bmatrix}3^3&3^2&3^1&3^0\\1^3&1^2&1^1&1^0\\(-1)^3&(-1)^2&(-1)^1&(-1)^0\\6^3&6^2&6^1&6^0\\7^3&7^2&7^1&7^0\end{bmatrix}}_{\mathbf A}\underbrace{\begin{bmatrix}b_3\\b_2\\b_1\\b_0\end{bmatrix}}_{\mathbf x}=\underbrace{\begin{bmatrix}4\\2\\1\\5\\9\end{bmatrix}}_{\mathbf b}[/tex]

The best-fit solution is given by [tex]\mathbf x=(\mathbf A^\top\mathbf A)^{-1}\mathbf A^\top\mathbf b[/tex]. You should end up with

[tex]\mathbf x=\begin{bmatrix}b_3\\b_2\\b_1\\b_0\end{bmatrix}\approx\begin{bmatrix}0.0495\\-0.3463\\0.9157\\2.1149\end{bmatrix}[/tex]

Attached is a plot of the given points and the best-fit solution.

To find the polynomial of degree three that best fits the given points, we can use the method of least squares.

To find the polynomial of degree three that best fits the given points, we can use the method of least squares. First, we can rewrite the equation in matrix form as:

[3 4 1] [b3]   [4]

[1 2 1] [b2] =  [2]

[-1 1 1] [b1]   [1]

[6 5 1] [b0]   [5]

[7 9 1]

Using matrix algebra, we can solve for the values of b3, b2, b1, and b0 that give us the best fit polynomial.

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The correct statement is: Angle G is congruent to angle P.

Congruency in geometry refers to the similarity between two shapes or figures. When two shapes are congruent, their corresponding angles and sides are equal in measure, preserving the same shape and size but allowing for possible reflection or rotation.

The correct statement that compares the angles is: Angle G is congruent to angle P. Congruent angles are angles that have the same measure. So, if angle G is congruent to angle P, it means that they have the same measure. For example, if angle G measures 30 degrees, then angle P would also measure 30 degrees.

Answer:

x= 1.8

Step-by-step explanation:

We have been given the equation;

-(6)^(x-1)+5=(2/3)^(2-x)

We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;

y = -(6)^(x-1)+5

y = (2/3)^(2-x)

We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;

The value of x is 1.785. To the nearest tenth we have x = 1.8

Answer:

x = 3

Step-by-step explanation:

3/2.25 = 4/x                 Cross multiply

3x = 2.25 * 4                Combine the right

3x = 9                           Divide by 3

3x/3 = 9/3

x = 3

Answer:

Step-by-step explanation:

The ratio of interest rates is 8% : 4% = 2 : 1. Since the amount of interest earned in each account is the same, the ratio of amounts invested will be the inverse of that, 1/2 : 1/1 = 1 : 2.

Then 1/(1+2) = 1/3 of the money is invested in the 8% account. That amount is ...

  $9102/3 = $3034 . . . . invested at 8%

The remaining amount is invested at 4%:

  $9102 - 3034 = $6068 . . . . invested at 4%

_____

The interest earned in 1 year in each account is

  0.08·$3034 = 0.04·$6068 = $242.72

_____

If you really need an equation, you can let x represent the amount invested at the higher rate. (Using this variable assignment avoids negative numbers later.) Then 9102-x is the amount invested at the lower rate.

  0.08x = 0.04(9102-x)

  0.12x = 0.04·9102 . . . . . eliminate parentheses, add 0.04x

  x = (0.04/0.12)·9102 = 9102/3 . . . . . divide by the coefficient of x. Same answer as above.

Since the 5 is in the tens place, that means it represents 5 tens, or 50.

Answer:

the tens' place

Step-by-step explanation:

refer to the attachment

Answer:

5

Step-by-step explanation:

We can use the distance formula with 3 different vertices to figure out the shortest of the three sides.

The distance formula is [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where (x_1,y_1) is the first points and (x_2,y_2) is the second set of points, respectively.

Now let's figure out the length of 3 sides.

1. The length between (-6,-5) & (-5,6):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(6--5)^2+(-5--6)^2}\\ =\sqrt{(6+5)^2+(-5+6)^2} \\=\sqrt{11^2+1^2} \\=\sqrt{122}[/tex]

2. The length between (-6,-5) & (-2,2):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(2--5)^2+(-2--6)^2} \\=\sqrt{(2+5)^2+(-2+6)^2}\\ =\sqrt{7^2+4^2}\\ =\sqrt{65}[/tex]

3. The length between (-5,6) & (-2,2):

[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(2-6)^2+(-2--5})^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{25} \\=5[/tex]

Thus, length of the shortest side is 5.

Answer:

5 units

Step-by-step explanation:

Draw the triangle with the vertices given. Identify the smallest side and draw in a right triangle using the smallest side of the original triangle as the hypotenuse of the right triangle, as shown on the grids below.

The horizontal side of the small right triangle measures 3 units and the vertical side of the small right triangle measures 4 units.

Use the Pythagorean theorem to find the length of the hypotenuse.

Therefore, the length of the shortest side of the triangle measures 5 units.

3^2 + 4^2  =  c^2

9 + 16  =  c^2

25  =  c^2

5  =  c

ANSWER

[tex]{x}^{3} - {y}^{3} = (x - y)[ {x}^{2} + xy + {y}^{2}][/tex]

EXPLANATION

We want to factor:

[tex] {x}^{3} - {y}^{3} [/tex]

completely.

Recall from binomial theorem that:

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

We make x³-y³ the subject to get:

[tex] {x}^{3} - {y}^{3} = ( {x - y)}^{3} + 3 {x}^{2} y - \:3x {y}^{2}[/tex]

We now factor the right hand side to get;

[tex]{x}^{3} - {y}^{3} = ( {x - y)}^{3} + 3 {x} y(x - y)[/tex]

We factor further to get,

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

[tex]{x}^{3} - {y}^{3} = (x - y)[ {x}^{2} - 2xy + {y}^{2} + 3 {x} y][/tex]

This finally simplifies to:

[tex]{x}^{3} - {y}^{3} = (x - y)[ {x}^{2} + xy + {y}^{2}][/tex]

To factor the expression x³ - y³ completely, use the formula for factoring a difference of cubes: a³ - b³ = (a - b)(a² + ab + b²). Plug in x for a and y for b to get (x - y)(x² + xy + y²).

To factor the expression x³ - y³ completely, we can use the formula for factoring a difference of cubes. The formula is:

a³ - b³ = (a - b)(a² + ab + b²)

Using this formula, we can plug in x for a and y for b.

x³ - y³ = (x - y)(x² + xy + y²)

Therefore, the expression x³ - y³ can be factored completely as (x - y)(x² + xy + y²).

Answer:

[tex]P=25\%[/tex]

Step-by-step explanation:

We have a sample of 100 clients.

To find the probability that a randomly selected customer chooses a cold drink, we must first count how many people in the sample chose cold drinks.

The table shows that cold drinks were

8 small, 12 medium and 5 large.

Then the number of cold drinks was:

[tex]8 + 12 + 5 = 25[/tex]

Now the probability of someone selecting a cold drink is:

[tex]P = \frac{25}{100}[/tex]

[tex]P = 0.25 = 25\%[/tex]

Answer:p=25%

For the acellus people

Step-by-step explanation:

The answer is C. rectangular prism.

Hope this helps.

r3t40

Answer:

Number of adult tickets = 3 tickets

Number of children tickets = 5 tickets

Step-by-step explanation:

A- The system of equations:

Assume that the number of adult tickets is x and that the number of children tickets is y

We are given that:

i. The total number of people in the group is 8, which means that the total number of tickets bought is 8. This means that:

x + y = 8 ..................> equation I

ii. The price of an adult ticket is $12 and that of a child ticket is $10. We know that the group spent a total of $86. This means that:

12x + 10y = 86 ...............> equation II

From the above, the systems of equation is:

x + y = 8

12x + 10y = 86

B- Solving the system using elimination method:

Start by multiplying equation I by -10

This gives us:

-10x - 10y = -80 .................> equation III

Now, taking a look at equations II and III, we can note that coefficients of the y have equal values and different signs.

Therefore, we will add equations II and III to eliminate the y

    12x + 10y = 86

+( -10x - 10y = -80)

Adding the two equations, we get:

2x = 6

x = 3

Finally, substitute with x in equation I to get the value of y:

x + y = 8

3 + y = 8

y = 8 - 3 = 5

Based on the above:

Number of adult tickets = x = 3 tickets

Number of children tickets = y = 5 tickets

C- Explanation of the meaning of the solution:

The above solution means that for a group of 8 people to be able to spend $86 in a theater having the price of $12 for an adult ticket and $10 for a child' one, this group must be composed of 3 adults and 5 children

Hope this helps :)

Answer:

1. a. 25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671

2. b. Mark’s average < Jay’s average

Step-by-step explanation:

1. What is Mark’s slugging average?

The slugging average gives more weight to the multi-base hits (compared to single-base hits) in opposition with the batting average.

So, a single hit is worth 1 point, a double is worth 2 points, a triple 3 points and a homerun is worth 4 points.  It's a weighted average calculation.

Mark had 25 singles, 10 doubles, 3 triples and 10 homeruns during 140 presences 140 at bat.

25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671

2. How does Mark's average compares to Jay's?

Let's first calculate Jay's slugging average then we'll be able to decide.

Jay had 10 singles, 6 doubles, 5 triples and 14 homeruns in 90 presences.

10 (1) + 6 (2) + 5 (3) + 14 (4) = 10+12+15+56 = 93 / 90 = 1.033

We can definitely say that Mark's slugging average (0.671) calculated above is lower than Jay's average (1.033).  So,

b. Mark’s average < Jay’s average

iits probalty like based analyse

Answer:

A.Probability-based inference

Step-by-step explanation:

Inferential statistics uses a random sample of data from a population to draw inferences about the population. One can make generalizations about a population.

The answer as per scenario is A.Probability-based inference.

The manager made an inference based on probability.

Answer:

24cm and 225cm

Step-by-step explanation:

Answer:

1) [tex]24cm^2[/tex]

2) [tex]30cm[/tex]

Step-by-step explanation:

1) Remember that: The area of a quadrilateral circumscribed about a circle equals  semi-perimeter (half the product of the perimeter of the quadrilateral) and the radius of the circle.  

By the other hand in a quadrilateral circumscribed the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Then you know that the sum of all sides should be 12cm+12cm=24cm

Area= Semi-perimeter*r

where

Semi-perimeter= perimeter/2= sum of all sides/2

r= radius of the circle

Then:

[tex]Area=(24cm/2)*(2cm)= 24cm^2[/tex]

2) Perimeter= sum of all sides

And as the sum of the measures of any pair of two opposite sides is equal to the sum of the measures of the other pair of the opposite sides.

Perimeter=15cm+15cm=30cm