At a pet store, 0.3 of the sales were for dog products, 1/10 of the sales were for cat products, and 3/5 of the sales were for other animal products. What fraction of the sales were for dog and cat products? Express your answer in simplest form.

PLEASE HELP !!

a) To calculate the area of the region under the curve y = x^(1/2) above the x-axis on the interval [1, ∞), we can use the definite integral.

The integral of a function represents the area under the curve between two given points. In this case, we need to integrate the function y = x^(1/2) from x = 1 to x = ∞.

∫[1, ∞] x^(1/2) dx

To evaluate this integral, we can use the power rule for integration:

∫ x^(1/2) dx = (2/3) x^(3/2) + C

Now, we need to calculate the definite integral:

∫[1, ∞] x^(1/2) dx = [(2/3) x^(3/2)] evaluated from 1 to ∞

Since we're integrating from 1 to ∞, the upper limit is ∞, and evaluating the function at this limit gives us an infinite result. Therefore, the area of the region is ∞.

b) To calculate the volume of the solid obtained by revolving the region about the x-axis, we can use the method of disks.

The volume of the solid of revolution can be calculated by integrating the area of each disk, which is given by πr^2, where r is the distance from the axis of revolution to the function.

In this case, the function is y = x^(1/2) and the axis of revolution is the x-axis. So, the distance from the x-axis to the function is simply y = x^(1/2).

To find the volume, we integrate the area of each disk from x = 1 to x = ∞:

V = ∫[1, ∞] π (x^(1/2))^2 dx

Simplifying the integral, we have:

V = ∫[1, ∞] π x dx

Integrating the function, we get:

V = π (1/2)x^2 + C

Evaluating the integral from 1 to ∞, we have:

V = [π (1/2)x^2] evaluated from 1 to ∞

Since we're integrating from 1 to ∞, the upper limit is ∞, and evaluating the function at this limit gives us an infinite result. Therefore, the volume of the solid is ∞.

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The square box is big enough to fit the pizza?

The given parameters are:

Diameter of pizza = ten and one third inches

Length of square box =  10.38 inches

Express the diameter as a numeral.

So, we have:

Diameter of pizza = 10 + 1/3 inches

Evaluate the sum

Diameter of pizza = 10.33 inches

By comparison:

10.33 inches is less than 10.38 inches

This means that the square box is big enough to fit the pizza?

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Answer:

45º

Step-by-step explanation:

alternate interior angles are congruent

x + 30 = 75

Subtract 30 from both sides

x = 45º

Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

Answer:

Step-by-step explanation:

do the thing times 2

Answer:

8/12 or 2/3

Where the first number is on the top and vice versa.

Step-by-step explanation:

In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.

Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.

The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.

The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.

By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.

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Answer:

x = -2 and x = 2

Step-by-step explanation:

By taking the derivative of the equation you get   120x^2 - 15x^4

   this shows the slope of the parent function at any value of x.....then look for where the derivative graph is maximum....at x = -2 and + 2 is where the parent function has the greatest slope

 Here is the graph:   (red is derivative, blue is parent function)

1) A Recursive formula refers always to the previous term.

2) In this Arithmetic Sequence, the common difference is 5, the first term is 12. So we can set the following Arithmetic Sequence:

Thus, this is the answer.

Answer:

Step-by-step explanation:

Given

Find \(a_{43}\)

We know that

Appy this to the two known terms and find the first term and the common difference

Find the coomon difference

Find the first term

Now find the 43th term

Answer:

-98

Step-by-step explanation:

General form of an arithmetic sequence:

  \(a_n=a+(n-1)d\)

where:

Given:

To find the 43rd term we need to construct an equation for the nth term.  To do this, find the first term and the common difference by substituting the given information into the general formula to create a system of equations that can be solved.

\(\begin{aligned} \underline{\textsf{Equation 1}}} \\ a_{21} & =-32 \\ \implies a+(20-1)d & = -32 \\a+20d & =-32 \end{aligned}\)

\(\begin{aligned} \underline{\textsf{Equation 2}}} \\ a_{50} & =-119 \\ \implies a+(50-1)d & = -119 \\a+49d & =-119 \end{aligned}\)

Subtract Equation 1 from Equation 2 to eliminate a:

\(\begin{array}{r l}a+49d & = -119\\- \quad a+20d & = -32\\\cline{1-2}29d & = -87\end{aligned}\)

Solve for d:

\(\implies d=\dfrac{-87}{29}=-3\)

Substitute the found value of d into one of the equations and solve for a:

\(\implies a + 20(-3)=-32\)

\(\implies a=28\)

Substitute the found values of a and d into the general formula to create an equation for the nth term:

\(\implies a_n=28+(n-1)(-3)\)

\(\implies a_n=31-3n\)

Finally, substitute n = 43 into the found formula to find the 43rd term of the sequence:

\(\implies a_{43}=31-3(43)=-98\)

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Answer:

The object would be a Parabola

Step-by-step explanation:

The mathematical object which represent the given situation is the parabola.

Given that, you want path 2 to be equidistant from the crocodile river and the habitat you chose.

What is a parabola?

In mathematics, a parabola is a plane curve which is mirror-symmetrical and approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line.

Therefore, the mathematical object to represent the given situation is the parabola.

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Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Question 1

Let \(x=18\) and \(y=25\). Then, we are required to compute:

\((x+y)^3 -x^3-y^3=x^3 +3x^2 y+3y^2 x+y^3-x^3-y^3=3xy(x+y)=\boxed{58050}\)

Question 2

Using the remainder theorem, the remainder is equal to \(x^4 -x^3 +2x+1\) computed at \(x=-1/2\). Doing so yields \((-1/2)^4 -(-1/2)^3 +2(-1/2)+1=\boxed{3/16}\)

Question 3

Using the factor theorem, the polynomial \(x^3 -2kx^2 +x+3\) should equal zero when evaluated at \(x=1\).

\(\implies 1-2k+1+3=0 \implies k=\boxed{5/2}\)

Answer:

x=15

Step-by-step explanation:

x/3+ 10 = 15

Subtract 10 from each side

x/3+ 10-10 = 15-10

x/3 = 5

Multiply each side by 3

x/3 *3 =5*3

x = 15

Answer: y = 32

Step-by-step explanation:

Based on the given conditions, formulate: y = kx

Substitute { y = 24

                 { x = 12  into y = kx

24 = k x 12

k = 2

Substitute x = 16 into y = 2x

y = 2 x 16

y = 32

Answer:

Below

Step-by-step explanation:

I will assume DIRECTLY proportional ( as opposed to INDIRECTLY proportional)   since the question does not say....

Directly proportional means     y = kx    Find 'k' by substituting in the values given      y = 24  and  x = 12:

 24 = k (12)   shows k = 2

   then the relationship is     y = 2x

       when x = 16     y = 2 (16) = 32

                   y = 32

You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

Given,

In the question:

You have 40 minute to exercise at the gym, and you want to burn a total of 300 hundred calorie using both machine.

Now, According to the question;

300 calories in 40 minutes can be set up as a ratio to find out how many calories per hour or calories per minute you are trying for:

300 calories /40 minutes = x calories/60 minutes for calories per hour (you are aiming for 450 calories burned per hour)

300 calories / 40 minutes = 7.5 calories per minute if you want to look at it that way instead.

One version of this problem that I found online completes the setup this way:

This allows us to set up a system of equations. The first equation will be for calories burned:

8x + 6y = 300

x is minutes on the 8 calorie per minute machine; y is minutes on the 6 calories per minute machine.

A second equation simply shows that the total minutes add up to 40:

x + y = 40

Now you can use substitution, elimination, or linear combinations to solve the system. I'll use substitution to rewrite the second equation:

x = 40 - y....(1)

Now substituting into the first equation:

8(40 - y) + 6y = 300

320 - 8y + 6y = 300

2y = 20

y = 10

Put the value of y in eq.(1)

Then, x gives the 30

Hence, You should spend 30 minutes on machine 1 and 10 minutes on machine 2.

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Each of these calls takes approximately two minutes, and when the answering machine picks up, the student must hang up and move on to the next phone number.

According to the given problem,15% will be correct numbers, but no one is home and the answering machine picks up. In that case, the student is instructed to simply hang up and move on to the next phone number. Each of these calls takes about two minutes.

Therefore, when the answering machine picks up, the student needs to hang up and move on to the next phone number, so no other time is wasted. The student may have difficulty at first, but with practice, the student will become more efficient and learn how to handle different situations effectively.

In addition, the student may learn how to better communicate and persuade people to support the cause or buy the product. Students will learn that rejection is a common occurrence in life, and that it is essential to persevere in the face of adversity.

Eventually, the student will be able to handle any situation and become a skilled salesperson. This ability can also be useful in other areas of life, such as job interviews and presentations.

In conclusion, making phone calls to solicit donations or sell a product is a valuable experience for students.

It teaches students the essential skills of perseverance, effective communication, and rejection management. It also allows students to become better salespeople, which can be beneficial in various aspects of life. Each of these calls takes approximately two minutes, and when the answering machine picks up, the student must hang up and move on to the next phone number.

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Answer:

79 degree

Step-by-step explanation:

A triangle is 180 degrees

We know that angle D and F is equal to each other

180 - 22 = 158 degree

158 / 2 = 79 degree

So, m<F = 79 degree

The probability that a student is in drama, given that they are a sophomore, is approximately 47%.

To calculate the probability that a student is in drama, given that they are a sophomore, we need to use Bayes' theorem:

P(drama | sophomore) = P(drama and sophomore) / P(sophomore)

From the given table, we can see that there are 3 sophomores in drama, out of a total of 20 sophomores:

P(drama and sophomore) = 3/20

And there are a total of 20 sophomores:

P(sophomore) = 20/63

Therefore, we can calculate:

P(drama | sophomore) = (3/20) / (20/63) = 0.4725

Rounding to the nearest whole percent, we get:

P(drama | sophomore) ≈ 47%

So the probability that a student is in drama, given that they are a sophomore, is approximately 47%.

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At points (sin2, cos2, 2) and (-sin2, cos2, -2) the helix r(t) = <sint, cost, t> intersect the sphere x² + y² + z² = 5.

The helix r(t) = <sint, cost, t> intersect the sphere x² + y² + z² = 5. So

x = sint, y = cost, z =t

x² + y² + z² = 5

Substitute the value of x, y and z.

(sint)² + (cost)² + (t)² = 5

sin²t + cos²t + t² = 5

As we know that sin²t + cos²t = 1. So

1 + t² = 5

Subtract 1 on both side, we get

t² = 4

Taking square root on both side, we get

t = ±2

So the points of intersection are:

(sin2, cos2, 2) and (-sin2, cos2, -2)

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The complete question is:

At what points does the helix r(t) = <sint, cost, t> intersect the sphere x² + y² + z² = 5.

Answer:

observing

Step-by-step explanation:

If you go through and try to match the definition to the words, observing is the closest. You observe your environment, means to take in what's around you and that includes with more than just one sense.

The general solution to the system of differential equations dx/dt = 9, dy/dt = 3y is:

\(x(t) = 9t + C1\\y(t) = Ce^{(3t)} or y(t) = -Ce^{(3t)\)

To solve this system, we can start by integrating the first equation with respect to t:

x(t) = 9t + C1

where C1 is a constant of integration.

Next, we can solve the second equation by separation of variables:

1/y dy = 3 dt

Integrating both sides, we get:

ln|y| = 3t + C2

where C2 is another constant of integration. Exponentiating both sides, we have:

\(|y| = e^{(3t+C2) }= e^{C2} e^{(3t)\)

Since \(e^C2\) is just another constant, we can write:

y = ± \(Ce^{(3t)\)

where C is a constant.

The general solution to the system of differential equations dx/dt = 9, dy/dt = 3y is:

\(x(t) = 9t + C1\\y(t) = Ce^{(3t)} or y(t) = -Ce^{(3t)\)

where C and C1 are constants of integration.

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Question

find the general solution of the system of differential equations dx/dt = 9

dy/dt = 3y

In the z-score formula, if the value in the numerator is a negative value, then the \(x_{i}\) value lies to the left of the mean. Therefore, option A) is correct.

In the z-score formula, the numerator is calculated by subtracting the mean from the  \(x_{i}\) value.

If the numerator value is negative, it means that the  \(x_{i}\) value is less than the mean, and therefore lies to the left of the mean on a normal distribution curve.

The z-score formula is:

\(z=\frac{x_{i}-\mu}{\sigma}\),

where z is the z-score, \(x_{i}\) is the individual data point, μ is the mean, and σ is the standard deviation.

If the value in the numerator (\(x_{i}\) - μ) is negative, it means that \(x_{i}\) is less than μ, indicating that the \(x_{i}\) value lies to the left of the mean on a number line.

Therefore, option A) is correct.

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The length of AD (rounded to the nearest tenth) cannot be found as there is some mistake in the given question or data.

Given that Kite ABCD is inscribed in circle E and are tangent to circle A. The radius of circle A is 14 and the radius of circle E is 15.

To find: The length of AD (rounded to the nearest tenth)Solution:Since ABCD is a kite, we can say that the two diagonals of the kite are perpendicular to each other.AD is one of the diagonals of the kite.

We need to find the length of AD to find its area, and then we will equate the area of kite ABCD to the product of its diagonals as a property of kite.

The other diagonal of the kite BD is a chord of circle E.The radius of circle E is 15 cmSo, the length of BD is 30 cm. (as it is the diameter of the circle E)Let's consider a right triangle AOD as shown below:

In triangle AOD,By Pythagoras theorem, we have:OD² + AD² = AO²

(where AO = radius of circle A = 14)

OD² + AD² = 14²

AD² = 14² - OD²

AD² = 196 - (15)²

AD² = 196 - 225

AD² = -29

AD = √(-29) (which is not possible as AD is a length and length cannot be negative)So, there is a mistake in the given question or data

Therefore, the given problem cannot be solved.

The length of AD (rounded to the nearest tenth) cannot be found as there is some mistake in the given question or data.

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Answer:

It's 20

Step-by-step explanation:

240/12 to find average

average=20

Answer:

The percent will likely decrease with more trials

Step-by-step explanation:

The theoretical probability for orange marbles is

P(orange) = orange/total = 6/(6+14) = 6/20 = 3/10 = 30%

The more times the experiment is done, the closer we should come to the theoretical probability.  Eventually we should come closer to 30%