Based on the graph, is there an association between pet preference and lunch preference?

There is an association because the distribution of lunch preference differs among the pet groups.
There is an association because distribution of lunch preference is approximately the same among the pet groups.
There is no association because the distribution of lunch preference differs among the pet groups.
There is no association because the distribution of lunch preference is approximately the same among the pet groups.

The number of containers needed is given as follows:

3 containers.

The number of containers needed is obtained applying the proportions in the context of this problem.

She has 2 cups, hence the number of fluid ounces that she has is given as follows:

16 fluid ounces.

Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:

16/6 = 3 containers.

(rounding up).

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Step-by-step explanation:

16 feet is equal to 192 inches.

Hope it helps :)❤

Answer:

192 inches is equal to 16 feet.

(Hope this helps! Btw, I answered first. Brainliest please! :D)

Answer: The first box in the model is 60. The box above it is 300. The box above 20 is 70. The answer is 74.

Step-by-step explanation: Self-explanatory.

The equation is as follows:

(x/3)^2 - (y/5)^2 + (z/8)^2 = 1

This is a one-sheet hyperboloid since the signs of the squared terms differ.

We enter z = 1 in the equation to get: when intersecting with the plane where z = 1.

(x/3)^2 - (y/5)^2 + (1/8)^2 = 1

When we simplify this equation, we obtain:

(x/3)^2 - (y/5)^2 = 63/400

This is the hyperbola's equation, which is formed when the hyperboloid of one sheet intersects with a plane. As a result, a hyperbola is what is produced when the trace is intersected with the plane z = 1. The second option is hyperbola.

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The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

876763 979.6

Step-by-step explanation:

Answer:

  27π/2

Step-by-step explanation:

The differential of volume is the product of a differential of area and the circumference of the revolution of that area about the given axis. The limits of integration in the x-direction are where y=28 crosses the curve, at x=4 and x=7.

   \(dV=2\pi(x-4)(y-28)\,dx\\\\dV=2\pi(x-4)(-x^2+11x-28)\,dx=2\pi(-x^3+15x^2-72x+112)\,dx\\\\\displaystyle V=\int_4^7{dV}=2\pi\int_4^7{(-x^3+15x^2-72x+112)}\,dx\\\\=2\pi\left(\dfrac{4^4-7^4}{4}+15\dfrac{7^3-4^3}{3}-72\dfrac{7^2-4^2}{2}+112(7-4)\right)=2\pi\dfrac{27}{4}\\\\\boxed{V=\dfrac{27\pi}{2}}\)

_____

Check

The parabola's vertex is (5.5, 30.25), so its area above the line y=28 is ...

  A = (2/3)(7 -4)(30.25 -28) = 4.5 . . . square units

The centroid of that area lies on the line x=5.5, a distance of 1.5 from the axis of rotation. So, the volume of revolution is ...

  V = 2π(1.5)(4.5) = 27π/2 . . . matches the above

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

The multiplicative rate of change for the function  is approximately.

To find the multiplicative rate of change for the exponential function f(x) = , we need to calculate the derivative of the function. However, it's important to note that the function you provided is not an exponential function. An exponential function has a base raised to a variable exponent.

The given functioncan be rewritten as. Now, we can proceed to find the multiplicative rate of change by taking the derivative of f(x) with respect to x.

Using the chain rule, the derivative of is:

Here, ln(2/5) is a constant representing the natural logarithm of 2/5. The multiplicative rate of change is given by the derivative, which is

The value of ln(2/5) is approximately -0.916.

It's important to note that the multiplicative rate of change is not constant for this function. It depends on the value of x and decreases exponentially as x increases.

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The sample of hospitals would we need to be 99 percent confident that the sample mean is within 0.5 days of the population mean is A. 48

We want to find the sample size (n) that would give us a confidence interval of 0.5 days, so we can rearrange the formula to solve for n:

n = (z*σ/CI)^2

Plugging in the given values:

z = 2.576 (for 99% confidence level)

σ = 1.2 days

CI = 0.5 days

n = (2.576 × 1.2/0.5)²

n ≈ 48

Therefore, the correct option is A.

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Answer:

Step-by-step explanation:

7 days= 1 week

42 days= 42/7 = 6 weeks

For 1 week 1 bag of food

For 6 weeks 6 bags of food

Answer:

Total paint left over = \(\frac{13}{12}L\)

Step-by-step explanation:

Given - To paint a house, 5/4 L of white paint and 1/2 L of blue paint

             were mixed. In the end only 2/3 L of the mixture were used.

To find - How many liters of paint were left over ?

Proof -

Given that,

5/4 L of white paint and 1/2 L of blue paint were mixed.

So, total mixture = \((\frac{5}{4} + \frac{1}{2})L\)

                          = \(\frac{5 + 2}{4}L\)

                          = \(\frac{7}{4}L\)

⇒Total mixture =  \(\frac{7}{4}L\)

Now,

Given that ,

In the end only 2/3 L of the mixture were used.

So, total mixture left = \((\frac{7}{4} - \frac{2}{3})L\)

                                = \(\frac{21 - 8}{12}L\)

                                = \(\frac{13}{12}L\)

∴ we get

Total paint left over = \(\frac{13}{12}L\)

Answer:

335.4

Step-by-step explanation:

You can use the Pythagorean Theorem (a^2 + b^2 = c^2)

300^2 + 150^2 = 112500

The square root of 112500 is 335.4

Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Based on calculation, the highest hourly wage is $2,840 per month which gives us $17.75 per hour.

For purpose of making a comparison, we can calculate the hourly wage for each option.

Hourly wage for $34,000 per year:

= $34,000 / (40 hours per week * 52 weeks per year)

= 16.3461538

= $16.35 per hour.

Hourly wage for $2,840 per month:

= $2,840 / (4 weeks per month * 40 hours per week)

= $17.75 per hour

Hourly wage for $650 per week:

= $650 / 40 hours per week

= $16.25 per hour

Hourly wage for $18 per hour.

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Being a girl and playing a sport are C. No, they are not independent events, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62.

Let's consider the probabilities:

P(girl) = (number of girls) / (total number of students) = 135 / 275 ≈ 0.49

P(girl plays a sport) = (number of girls playing a sport) / (total number of students) = 76 / 275 ≈ 0.276

If being a girl and playing a sport were independent events, the joint probability would be the product of the individual probabilities:

P(girl) × P(girl plays a sport) ≈ 0.49 × 0.276 ≈ 0.13524

However, the actual joint probability is different from the expected value:

P(girl, plays a sport) ≈ 76 / 275 ≈ 0.276

Since the joint probability does not match the product of the individual probabilities, we can conclude that being a girl and playing a sport are not independent events based on the given data.

Therefore, option C. No, they are not independent, because P(girl) 0.49 and P(girl plays a sport) ~ 0.62. is the correct answer.

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Answer:

\(f'(x) = \frac{1}{5}x\)

Step-by-step explanation:

Given

\(f(x) = 5x\) --- Nickel to Penny

Required

Determine the function that converts penny to nickel

This question implies that we determine the inverse of the function.

We have:

\(f(x) = 5x\)

Represent f(x) with y

\(y = 5x\)

Swap the positions of x and y

\(x = 5y\)

Make y the subject by dividing both sides by 5

\(\frac{1}{5}x = \frac{5y}{5}\)

\(\frac{1}{5}x = y\)

\(y =\frac{1}{5}x\)

Replace y with f'(x)

\(f'(x) = \frac{1}{5}x\)

Hence, the function that converts x pennies to nickels is \(f'(x) = \frac{1}{5}x\)

Answer: 17873.75 dollars

Step-by-step explanation:

We can use the equation: l = p x r x t (Total Interest = principal x interest rate x years/time)

9050 will be the principal; it's the amount you deposit in the first place.

7.5% is the interest rate. You can convert it to 0.075 as a decimal.

13 is the years/time. If Marcus's parents put the college fund in when he was 5 and now he's 18, there has been 13 years in between.

9050 x 0.075 x 13 = 8823.75

8823.75 + 9050 = $17873.75

So in Conclusion, the total amount in the account when Marcus is 18 is 17873.75 dollars.

Hope this helps!

Answer:

just looking for free point..

Step-by-step explanation:

Answer:

2nd one

Step-by-step explanation:

if you were to look on a grid the slope would point up

Using Jefferson’s method, the number of tutors  to allocate to each subject is = 8,8,3,2 tutors to each of the subjects

Subjects      students enrolment         tutors to assign      Aprx tutors

Maths                        355                              8.4                           8

English                       325                              7.7                           8

Chem                          135                               3.2                          3

Biology                        75                                 1.8                          2

Total                          890                                                               21

Total number of tutors to be allocated is = 21

Using ratios to divide we have

English = 355/890 * 21/1 = 8.476

Maths = 325/890 *21 = 7.668

chem = 135/890 * 21 = 3.185

Biology = 75/890 *21 = 1.76966

Approximate the total to get  8+8+3+2 = 21 tutors

the method division used here is ratio of number of students in each subject

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Answer:

x=4

Step-by-step explanation:

Square root of four equals 2 then +2 = 4

Answer:

The answer would be 50%

Step-by-step explanation:

You Would get this by dviding 36/72 which would give you .5 and then you convert that to a percentage

Answer:

50%

Step-by-step explanation:

The constant of proportionality is 2.5 and the cost of each pound of chocolates is  $2.5

The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. It is also known as unit rate and it is usually expressed by k.

Given that: A local candy store sells three pounds of chocolates for $15.75

This is a proportional relation between the weight of candy (W) and the price(P). So we can represent the relationship with:

P = kW    Where k is the constant of proportionality

k = P/W = 15.75/3 = 5.25

Given: y = 2.5x

constant of proportionality = 2.5

Since the constant of proportionality is defined as unit rate. Therefore, the cost of each pound of chocolate is $2.5

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The rate of the first athlete is greater than the rate of the second athlete.

To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.

The average speed of an athlete is calculated by dividing the distance traveled by the time taken.

For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:

Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.

For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:

Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.

To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:

Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.

Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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