A veterinarian keeps track of the types of animals treated by an animal clinic. The following distribution represents the percentages of animals the clinic has historically encountered.
If the animal clinic treats 230 animals in a month, how many of each animal type would be expected?

volume= 16/3, A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

limits

z= 0 to z = 4-y-2x

y= 0 to y = 4- 2x

x= 0 to x= 2

volume

v= \(\int\limits^2_0 \int\limits^4_0 \int\limits^4_0 dzdydx\)

v= \(\int\limits^2_0 \int\limits^4_0 (4-y-2x) dydx\)

v= \(\int\limits^2_0 ( 4y- y^{2} / 2 - 2xy) ^4^-^2^x _0\)

dx= \(\int\limits^2_0 [ 16-8x - 16+ 4x^2 - 16x / 2 - 8x+ 4x^2 ] dx\)

v= \(\int\limits^2_0 [ 8+ 2x^2- 8x] dx\\\)

= [ 8x + 2x^3 / 3 - 8x^2 / 2 ] ^2_0

= [16+ 16/3- 16]

v= 16/3

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Complete Question

Question: Sketch The Tetrahedron Enclosed By The Coordinate Planes And The Plane 2x+Y+Z=4. Use A Triple Integral To Find The Volume Of The tetrahedron

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer:

ask a tutor

Step-by-step explanation:

The required demand function for the marginal revenue function is P = 0.02x² - 0.025x.

Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold; there is a marginal cost attached to it, which must be accounted for.

The marginal revenue function, find the demand capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

Considering that,

We need to find for the peripheral income capability, find the interest capability.

Recollect that the pay is zero assuming no things are sold:

R'(x) = 0.06x² - 0.05x + 138

p(x) is what.

That's what we know,

MR = dTR/dx = 0.06x² - 0.05x + 138

Incorporating the marginal revenue function , we get complete income capability,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 138x

= (0.06x³)/3 - (0.05x²)/2 + 138 x

TR = 0.02 x³ - 0.025 x² + 138 x

TR = (P)(Q) = (P)(x) = 0.02 x³ - 0.025 x² + 138 x

P = ( 0.02 x³ - 0.025 x² + 138 x)/x

P = 0.02x² - 0.025x + 138

In this manner, The marginal revenue function, find the interest capability is P = 0.02x² - 0.025x + 138 when R'(x) = 0.06x² - 0.05x + 138 .

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The average distance between the Earth and the Moon is about 238,855 miles or 1.28 light-seconds.

To convert miles to feet, multiply by 5,280, giving us approximately 1.27 million feet. A rocket traveling at a speed of 1,540,000 ft/min would take approximately 82.5 minutes to travel to the Moon. The round trip to the Moon and back would take approximately 165 minutes, or about 2 hours and 45 minutes.

It's important to note that this is an estimate and the actual time it takes may vary due to various factors such as the rocket's trajectory, speed, and other environmental conditions. Also, it's worth noting that this speed is significantly faster than current spacecraft speeds, so the actual time it would take a rocket to travel to the Moon and back is likely to be much longer.

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Answer:

  x ≈ -8.402, 8.502

Step-by-step explanation:

The usual methods of solving quadratic equations apply to this one. Any of them can be used: graphing, factoring, completing the square, quadratic formula.

Often, when the coefficients are non-integers and have no obvious relationship to each other, the most convenient method of solution is the quadratic formula. It tells you the solution to ax²+bx+c=0 is ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

Your equation has the coefficients, a = -0.07, b = 0.007, c = 5, so the solutions are ...

  \(x=\dfrac{-0.007\pm\sqrt{0.007^2-4(-0.07)(5)}}{2(-0.07)}=\dfrac{-0.007\pm\sqrt{1.400049}}{-0.14}\\\\x=0.05\pm\sqrt{\dfrac{200007}{2800}}=0.05\pm\sqrt{71.4310\overline{714285}}\\\\\boxed{x\approx\{-8.40169,\,8.50169\}}\)

Answer:

\(t=8.50, -8.40\:\: \sf (2 \:d.p.)\)

Step-by-step explanation:

Quadratic equations are in the form \(ax^2+bx+c=0\),  where \(a\neq 0\).

There are three basic methods to solve quadratic equations algebraically:

Given quadratic equation:

\(h(t)=-0.07t^2+0.007t+5\)

Method 1 - Factoring

If the trinomial is able to be easily factored, set the equation equal to zero and factor.  Set each factor equal to zero and solve.

As the given example is not easily factored, factoring is not the best method to use on this occasion.

Method 2 - Completing the Square

If the quadratic expression is not able to be easily factored, try completing the square.

Divide all terms by \(a\) (-0.07):

\(\implies t^2-\dfrac{1}{10}t-\dfrac{500}{7}=0\)

Move the constant to the right side:

\(\implies t^2-\dfrac{1}{10}t=\dfrac{500}{7}\)

Add the square of half the coefficient of t to both sides:

\(\implies t^2-\dfrac{1}{10}t+\left(-\dfrac{1}{20}\right)^2=\dfrac{500}{7}+\left(-\dfrac{1}{20}\right)^2\)

\(\implies t^2-\dfrac{1}{10}t+\dfrac{1}{400}=\dfrac{200007}{2800}\)

Factor the perfect trinomial:

\(\implies \left(t-\dfrac{1}{20}\right)^2=\dfrac{200007}{2800}\)

Square root both sides:

\(\implies t-\dfrac{1}{20}=\pm\sqrt{\dfrac{200007}{2800}\)

Add 1/20 to both sides:

\(\implies t=\dfrac{1}{20}\pm\sqrt{\dfrac{200007}{2800}\)

As decimals to 2 decimal places:

\(\implies t=8.50, -8.40\:\:\sf(2 \:d.p.)\)

Method 3 - Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\)

This can be used to find both real and imaginary or complex solutions.

Identity the variables:

\(a=-0.07, \quad b=0.007, \quad c=5\)

Substitute the values into the quadratic formula and solve for t:

\(\implies t=\dfrac{-0.007 \pm \sqrt{0.007^2-4(-0.07)(5)} }{2(-0.07)}\)

\(\implies t=\dfrac{-0.007 \pm \sqrt{1.400049}}{-0.14}\)

\(\implies t=\dfrac{0.007 \pm \sqrt{1.400049}}{0.14}\)

\(\implies t=8.50, -8.40\:\: \sf (2 \:d.p.)\)

Finally, a non-algebraic method of solving a quadratic equation is by graphing using a graphical calculator (see attached).  The solutions are the points at which the curve intercepts the x-axis.

Answer:

Step-by-step explanation:

The first scenario is an example of Newton's first law, the second scenario is an example of Newton's second law.

Finally, if Beatriz Pushed with more force than Gustavo, the door would move in the direction in which Beatriz is pushing.

Remember Newton's first law of motion:

"if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force."

Now, in the first scenario given, both persons push the door with the same force and in opposite directions, thus, the net force on the door is 0 (because we can directly add the forces).

Then the first example is an example of the first law of motion, where because the net force on the door is 0, the door does not move.

Now, for the second law, we know that the force applied to an object is equal to the object's acceleration times the object's mass.

So, in the second case where Gustavo pushes the door with more force than Beatriz, the net force is not 0, so here the door will move in the direction in which Gustavo is pushing, this is an example of the second law of motion.

Finally, if Beatriz Pushed with more force than Gustavo, the door would move in the opposite direction than in the case above.

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Answer:

a balanced force

Unbalanced forces

move

Step-by-step explanation:

I got it right

Answer:

the answer is 250 million years

Step-by-step explanation:

Answer: 250 million years

Answer:

G should be at the sum of y and x combined but x is not given

Step-by-step explanation:

Answer:

(0,-2)

Step-by-step explanation:

The graph intercepts through the y axis, G.

You can get these coordinates b solving the equation like so:

y=3x-2

move the x varible to the left side and the y to the left....

-3x+y=-2        

 -3x=-2-y

divided both sides by 3 to isolate x

x= 2/3+ 1/3y

when you graph that equation you get the points (0,-2)

Answer:

Yes, it is correct

Step-by-step explanation:

If the temperature did not drop below 60 degrees, that means that it only stayed at 60 degrees or was higher than 60 degrees.

D is greater than or equal to 60 is the right inequality then.

Answer:

perimeter: 8a³b+4ab

area: 4a²b²

Step-by-step explanation:

2a³b + 6a³b+4ab=

8a³b+4ab

1/2×4ab×2a³b=

4aa³bb

4a⁴b²

btw love ur pfp

Answer:

area: \(\sf 4a^4b^2\) || perimeter: \(\sf 8a^3b+4ab\)

Step-by-step explanation:

perimeter = sum of all sides

perimeter:

\(\sf 2a^3b + 6a^3 b + 4ab\)

\(\sf 8a^3b+4ab\)

area of triangle = \(\sf \frac{1}{2} *base * height\)

\(\sf \frac{1}{2} *4ab* 2a^3 b\)

\(\sf \frac{1}{2}\cdot \:8ab^2a^3\)

\(\sf 4a^4b^2\)

Answer:

Step-by-step explanation:

Answer

Step-by-step explanation:

Answer:

12 cups

Step-by-step explanation:

if there are 3 cups in 2 loaves, then 3*4 is 12

Answer:

the answer is 12

Step-by-step explanation:

2 | 4 | 6 | 8

3 | 6 | 9 | 12

Answer:

False

Step-by-step explanation:

Copper actually has about 8.96 g/cm3

Answer: No

Step-by-step explanation:

To calculate how long it would take to pay off 60% of the debt,

we can use the same facts as in problem #16. Let's go through the steps:

1. Determine the total amount of debt: Find the original debt amount given in problem #16.

2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.

3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.

Now, let's apply these steps to the options provided:

a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.

b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.

c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.

After performing the calculations for each option, compare the results with the options provided to find the correct answer.

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1. Average of the entire data set: 15.47 ounces

  Standard deviation of the entire data set: 1.51 ounces

2. American League:

  Average of drink sizes: 16.8 ounces

  Standard deviation of drink sizes: 2.26 ounces

1. Computing the average and standard deviation of the entire data set:

  Average = (14 + 18 + 20 + 16 + 16 + 12 + 14 + 16 + 14 + 16 + 16 + 16 + 14 + 32 + 16 + 20 + 12 + 16 + 20 + 12 + 16 + 16 + 24 + 16 + 16 + 14 + 14 + 12 + 14 + 20) / 30

          = 464 / 30

          ≈ 15.47 ounces

  Standard deviation = √[((14 - 15.47)² + (18 - 15.47)² + (20 - 15.47)² + ... + (14 - 15.47)²) / 30]

                    ≈ √(68.71 / 30)

                    ≈ √2.29

                    ≈ 1.51 ounces

2. Computing the average and standard deviation for the American League and the National League:

  American League:

  Average (AL) = (14 + 18 + 20 + 16 + 16 + 12 + 14 + 16 + 14 + 16 + 16 + 16 + 14 + 32 + 16) / 15

               = 252 / 15

               ≈ 16.8 ounces

  Standard deviation (AL) = √[((14 - 16.8)² + (18 - 16.8)² + (20 - 16.8)² + ... + (32 - 16.8)²) / 15]

                         ≈ √(76.8 / 15)

                         ≈ √5.12

                         ≈ 2.26 ounces

  National League:

  Average (NL) = (20 + 12 + 16 + 20 + 12 + 16 + 16 + 14 + 14 + 12 + 14 + 20) / 15

               = 200 / 15

               ≈ 13.33 ounces

  Standard deviation (NL) = √[((20 - 13.33)² + (12 - 13.33)² + (16 - 13.33)² + ... + (20 - 13.33)²) / 15]

                         ≈ √(40 / 15)

                         ≈ √2.67

                         ≈ 1.63 ounces

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y = 2x - 4

y = 4x - 6

y = 3x - 4

that's what i got

Answer: i think it is 538.4

Step-by-step explanation:

In business calculus, the term "functions" refers to mathematical relationships that associate inputs (typically denoted as x) with corresponding outputs (typically denoted as y). Functions can represent various aspects of business operations, such as revenue, cost, profit, demand, and supply.

The concept of "limits" in calculus deals with the behavior of a function as the input approaches a particular value. It determines the value that the function approaches or tends to as the input gets arbitrarily close to a specified value. Limits are essential for analyzing the behavior of functions near certain points, understanding rates of change, and evaluating derivatives and integrals.

"Continuity" of a function refers to its smooth and unbroken nature, without any abrupt jumps, holes, or vertical asymptotes. A function is continuous if its graph can be drawn without lifting the pen from the paper. Continuity ensures that small changes in the input correspond to small changes in the output, which is crucial for reliable analysis and prediction.

For example, consider the function f(x) = 2x + 1. This linear function represents a business scenario where x represents the number of units sold, and f(x) represents the total revenue generated. The limit of f(x) as x approaches 2 is 5, indicating that as the number of units sold approaches 2, the total revenue approaches $5. Since f(x) = 2x + 1 is a linear function, it is continuous across its entire domain.

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There is a correlation between age and income, which could be useful for predicting future earnings or planning for retirement.

A scatterplot is a graphical representation of the relationship between two variables. It is a type of plot used to display the distribution and correlation between two continuous variables.

To construct a table and scatterplot of bivariate data that models a real-world relationship, we first need to identify a dataset that demonstrates a relationship between two variables. For this example, let's use a dataset that shows the relationship between age and income for a group of individuals.

Table:

Age (years) Income ($)

25 35,000

30 45,000

35 55,000

40 65,000

45 75,000

50 85,000

55 95,000

60 105,000

65 115,000

70 125,000

Scatterplot:

scatterplot of bivariate data showing the relationship between age and income

As we can see from the scatterplot, there is a positive relationship between age and income. As age increases, so does income. This suggests that there is a correlation between age and income, which could be useful for predicting future earnings or planning for retirement.

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The price for the monthly fee will be;

⇒ x = $9.99  

And, The price per movie rental will be;

⇒ y = $2.99

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Yolanda is charged $21.95 for her monthly fee and 4 movie rentals.

And, Jeffrey is charged $30.92 for the same monthly fee and 7 movie rentals.

Now,

Let the price for the monthly fee = x

And, The price for the movie rental = y

Hence, We can formulate the expression for Yolanda;

⇒ x + 4y = $21.95

And,  We can formulate the expression for Jeffrey;

⇒ x + 7y = $30.92

Subtract equation (ii) from (i), we get;

⇒ 7y - 4y = $30.92 - $21.95

⇒ 3y = $8.97

⇒ y = $2.99

And, x + 4y = $21.95

x + 4 × 2.99 = 21.95

x + $11.96 = $21.95

x = $21.95 - $11.96

x = $9.99

Thus, The price for the monthly fee = $9.99  

And, The price per movie rental = $2.99

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Answer:

  -8k -2

Step-by-step explanation:

You want the simplified form of -2(k+1)-6k.

The process of simplifying an algebraic expression includes ...

Parentheses are removed using the distributive property. The factor outside parentheses multiplies each term inside.

  -2(k +1) -6k

  = (-2)(k) +(-2)(1) -6k = -2k -2 -6k

Terms with the same variable content can be combined by adding their coefficients. (The distributive property is involved here, too.)

  = (-2 -6)k -2 = -8k -2

The simplified expression is -8k -2.

Considering the common factor, the most efficient way to factor the expression 2x³ - 18x² + 40x is given by:

C. Factor out 2x.

The most efficient way to factor the expression is factoring out the common factor.

In this problem, the expression is:

2x³ - 18x² + 40x

We have that:

Hence the common factor is of 2x, which means that option C is correct.

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