Select whether each fraction is a terminating decimal or a repeating decimalTerminating decimal Repeating decimal3489111212424100

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

Step-by-step explanation:

[-5/13] 3/5 +12+13 [-4/5 = - 63/65

Answer:

88 inches ^2

Step-by-step explanation:

Well find the side of a triangle first.

4*9=26

26/2=18

There are 4 identical triangles

18*4= 72

Now the bottom square

4*4=16

16+72= 88

88 inches ^2

answers

(Σx)*(Σx) = 11,664

(Σx)*(Σy) = 106 * 64.2 = 6805.2.

steps

add up all the numbers & multiply

bivariate data means data that often go together like

x is height & y is weight

(Σx)*(Σx)

Σx = 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16

= 108

(Σx)*(Σx) = Σx^2 = 108 * 108

= 11,664

Σx = 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16

= 108

Σy = 10.8 + 9.1 + 8.4 + 7.7 + 6.2 + 5.1 + 4.8 + 3 + 2.9

= 57.2

(Σx)*(Σy) = 108 * 57.2

= 6,177.6

open bard bing AI

Answer:

number of commercials: 6

Number of movies: 4

Step-by-step explanation:

Let x = the number of commercials

Let y = the number of movies

30x + 110 y = 620

x + y = 10     This can be written y = 10 - x (substitute 10 - x for y)

30x + 110y = 620

30x + 110(10 - x) = 620   Distribute the 110

30x + 1100 - 110x = 620    Combine like terms

-80x + 1100 = 620   Subtract 1100 from both sides

-80x = -480   Divide both sides by -80

x = 6

There are 6 commercials.

Substitute 6 for x

x + y = 10

6 + y = 10   Subtract 6 from both sides

y = 4

There are 4 movies.

Check:

x + y = 10

6 + 4 = 10

10 = 10  checks

30x + 110y = 620

30(6) + 110(4) = 620

180 + 440 = 620

620 = 620 checks

By the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

The Mean Value Theorem (MVT) states that if a function ƒ(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

ƒ(x) = 2lnx - 8 is continuous on the closed interval [1, 7], since it is the sum and composition of continuous functions.

ƒ(x) = 2lnx - 8 is differentiable on the open interval (1, 7), since its derivative ƒ'(x) = 2/x is defined and continuous on (1, 7).

Therefore, the Mean Value Theorem can be applied to ƒ(x) on [1, 7]. To find the value of c, we need to solve the equation:

ƒ'(c) = [ ƒ(b) - ƒ(a) ] / (b - a)

Substituting the given values, we get:

2/c = [ 2ln7 - 2ln1 ] / (7 - 1)

2/c = ln7

c = 2 / ln7

c ≈ 0.909

Therefore, by the Mean Value Theorem, there exists a number c in (1, 7) such that ƒ'(c) = 2/c and 2/c = ln7 / 6, and c ≈ 0.909.

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So the final equation in the standard form is: y = 2 sin(x - π/2) - 1.

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The purpose of an equation is to find the value of the variables that make both sides of the equation equal. This is done by performing mathematical operations on both sides of the equation in a way that maintains the equality. Equations are used in various fields of mathematics, physics, chemistry, and engineering to describe the relationships between different variables and to solve problems.

Here,

The given equation is in the form of a sinusoidal function:

y = a sin(bx - h) + k

where:

a: amplitude, represents the maximum displacement of the function from its mean position.

h: phase shift, represents the horizontal shift of the function.

k: vertical shift, represents the vertical shift of the function.

To find the values of a, h, and k in the given equation:

y = 2 sin(0 - π/2) + 1

We can rewrite the equation as:

y = 2 sin(-π/2) + 1

y = -2 + 1

y = -1

Therefore, a = 2 (the amplitude is 2), h = π/2 (the phase shift is π/2 to the right), and k = -1 (the vertical shift is down by 1 unit).

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Answer:

it's 6

Step-by-step explanation:

You can think of it 2 ways the first one is called the "bat and ball" method which is 12x15 then u divide it by 30. The other methos only works on very few if you look at the 30/15 one 15 is half of 30 so when you look at 12 half of that would be 6. Hope this helps :)

Answer:

I used Desmos Graphing Calculator  

Step-by-step explanation:

Answer:

994.74in²

Step-by-step explanation:

Are of circle: 21²×3.12=1384.74

Area of Triangle: 20×39/2=390

Then subtract

Answer:

...

Step-by-step explanation:

To find the number of calories Davis burns while running for 30 minutes, we can use the information that he burns 1080 calories running for 2.5 hours.

We know that 30 minutes is 1/120 of 2.5 hours. So, we can divide the total number of calories by 120 and we get the calorie burn for 30 minutes:

1080 calories / 120 = 9 calories

The number of calories Davis burns while swimming for 30 minutes can be determined by using the equation y = 266x, where x represents the number of hours he swims. We know that he swims for 30 minutes, or 1/120 hours, so we can plug that value into the equation:

y = 266(1/120) = 2.216 calories

So, Davis burns 7 calories more running for 30 minutes than swimming for 30 minutes, assuming the rates remain constant.

An Annual is not an example of an agreement.

I think you want 8/3 or 2.666666 or mabye 37%

Answer:

In the two distinct acute triangles ABC and DEF, ∠B ≅ ∠E. ... Use the figure below to find the measure of Angle Z. Lines EF and GH are parallel.

Answer: The correct answer is B - 102°

Step-by-step explanation: I got it right on my quiz.

Hope this helps :)

Answer:

Step-by-step explanation:

Let the amount brought in the first day be x

In the second day brought:

Total in two days:

Solve the following equation for x:

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

y=200(0.5)2t  this functiοn represents decay, y=12(2.5)t6 this functiοn represents grοwth and y=(0.65)t4 this functiοn represents decay.

In mathematics, a functiοn is a relatiοnship between twο sets οf elements, called the dοmain and the range, such that each element in the dοmain is assοciated with a unique element in the range.

In general, we can determine whether a functiοn represents grοwth οr decay by examining the base οf the expοnential term.

If the base is greater than 1, the functiοn represents grοwth.

If the base is between 0 and 1, the functiοn represents decay.

Here are the classificatiοns fοr each οf the given functiοns:

y=200(0.5)2t

The base οf the expοnential term is 0.5, which is between 0 and 1. Therefοre, this functiοn represents decay.

y=12(2.5)t6

The base οf the expοnential term is 2.5, which is greater than 1. Therefοre, this functiοn represents grοwth.

y=(0.65)t4

The base οf the expοnential term is 0.65, which is between 0 and 1. Therefοre, this functiοn represents decay.

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Complete Question:

Select "Growth" or "Decay" to classify each function.

Function Which ones are growth or decay

f(x)=(1.05)t4

y=100(0.4)t

f(x)=14(10)t12

Answer:

36

Step-by-step explanation:

f(x)=x^2+2x+1

Let x = -7

f(-7)=(-7)^2+2*-7+1

     = 49 -14+1

     = 36

Answer:

thanks !!

Step-by-step explanation: have a wonderful day :)

Answer:

Thank you!!

Step-by-step explanation:

Have a great day:)

Answer:

(a) \(y=(2x+6)(x-1)\)

(b)  \(y=2x^2+4x-6\)

Step-by-step explanation:

Part (a)

The zeros are where the curve intersects the x-axis (where \(y = 0\))

From the points given, the points of intersections are (-3, 0) and (1, 0)

\(x=-3\implies x+3=0\)

\(x=1 \implies x-1=0\)

Therefore, we can write the equation as:

\(y=a(x+3)(x-1)\)

(where \(a\) is some constant to be determined)

The y-intercept is when \(x = 0\).

From the points given, the point of intersection with the y-axis is (0, -6)

Therefore, substitute \(x = 0\) into the equation, set it to -6 and solve for \(a\):

\(\implies a(0+3)(0-1)=-6\)

\(\implies a(3)(-1)=-6\)

\(\implies -3a=-6\)

\(\implies a=\dfrac{-6}{-3}=2\)

Therefore, the final equation of the parabola is:

\(y=2(x+3)(x-1)\)

in fully factored form: \(y=(2x+6)(x-1)\)  or  \(y=(x+3)(2x-2)\)

Part (b)

Standard form of a quadratic equation:  \(y=ax^2+bx+c\)

To express the equation in standard form, simply expand:

\(\implies y=(2x+6)(x-1)\)

\(\implies y=2x^2-2x+6x-6\)

\(\implies y=2x^2+4x-6\)

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

a) The first mistake that Fatima made was in the first step.

b) She incorrectly changed the place value of 0.02 in the subtraction operation.

c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.

The place value shows the position of a digit in a number.

The right place values are essential for correct mathematical operations.

The quantity of rose petals that Fatima bought initially = 0.454 kilograms

The quantity of rose petals used for making rose water = 0.02 kilograms

The remaining quantity of rose petals = 0.434 (0.454 - 0.02)

The additional quantity of rose petals Fatima bought = 0.056

The quantity of rose petals used for making the second rose water = 0.095

The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)

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The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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The number of laps it has made to a stop is 300 laps

Given the following

The rate at which the fan blows = 30rps

The time it takes to blow  = 10s

Required

number of laps it has made to a stop

Using the formula

Rate = Number of laps/time

30 = Number of laps/10

Number of laps = 30 * 10

Number of laps = 300

Hence the number of laps it has made to a stop is 300 laps

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Answer:correct answers are 3.96

2.32

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

-7u^2 + 4u + 6 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -7, b = 4, and c = 6. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(-7)(6))) / 2(-7)

u = (-4 ± sqrt(136)) / (-14)

u = (2 ± sqrt(34)) / 7

Therefore, either:

cos(θ) = (2 + sqrt(34)) / 7

or:

cos(θ) = (2 - sqrt(34)) / 7

Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse cosine function:

θ = arccos((2 + sqrt(34)) / 7)

θ = arccos((2 - sqrt(34)) / 7)

Using a calculator, we find: