a report stated that the average number of times a cat returns to its food bowl during the day is 38. assuming the variable is normally distributed with a standard deviation of 3, what is the probability that a cat would return to its dish between 35 and 39 times a day? round the final answer to four decimal places and intermediate-value calculations to 2 decimal places.

The best least squares approximation to\(x^{1/3\)on [-1,1] by a linear function l(x) = c_1 1 + c_2 x is given by: \(l(x) = (2/5)^{(3/2)\)

To show that 1 and x are orthogonal, we need to show that their inner product is zero:

\((1, x) = \int^1_1 1\times x dx = [x^{2/2}]^{1_1 }= 0\)

Therefore, 1 and x are orthogonal.

To compute ||1||, we use the norm formula:

\(||1|| = (1, 1)^{1/2 }= \int^1_1 1\times 1 dx = [x]^1_1 = 0\)

Similarly, to compute ||x||, we use the norm formula:

\(||x|| = (x, x)^1/2 = \int^1_1 x\times x dx = [x^3/3]^1_1 = 2/3\)

To find the best least squares approximation to\(x^{1/3\) on [-1,1] by a linear function l(x) = c_1 1 + c_2 x, we need to minimize the squared error:

\(||x^{1/3 }- l(x)||^2 = \int^1_-1 (x^1/3 - c_1 - c_2 x)^2 dx\)

Taking partial derivatives with respect to c_1 and c_2 and setting them to zero, we get the normal equations:

\(c_1 = (2/5)^{(3/2)} and c_2 = 0\)

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Answer:

f(-9) = -119

Step-by-step explanation:

Hello!

You can evaluate for f(-9) by substituting -9 for x in the equation f(x) = -11 + 12x.

The evaluated value is -119.

Answer:

15/12

Step-by-step explanation:

\(x = \frac{31}{12} - \frac{8}{6} = \frac{15}{12} \)

and it says don't reduce otherwise u could also say 5/4

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The number of frogs among the four amphibians is \($\boxed{\textbf{(C)}\ 2}$.\)

If Brian is a toad, then Mike must be a frog, and vice versa. Therefore, Brian and Mike cannot be of different species. Hence, Brian is a frog. Since Chris is a frog if and only if LeRoy is a toad, and since Chris's statement is false, we know that LeRoy is a frog. This implies that Chris's statement is true, which is a contradiction.

Therefore, Chris is also a frog. Finally, Mike's statement implies that there are at least two toads among the four amphibians. Since Brian and Mike are both frogs, the other two amphibians, Chris and LeRoy, must both be toads. Therefore, the number of frogs among the four amphibians is \($\boxed{\textbf{(C)}\ 2}$.\)

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Answer:

y = -5x - 7

Step-by-step explanation:

(Change in y) / (Change in x)

(3-8) / (-2 - (-3))

-5 / 1

-5 is the slope

So far we have y = -5x

Plug in a set of values and find the difference

3 = -5(-2)

3 = 10

This is false

We need to subtract 7

Our equation therefore is

y = -5x - 7

Answer:

Step-by-step explanation:

Let the first angle = x

Let the second angle = y

They are complementary so

x + y = 90

x = y + 30

Substitute for x

y + 30 + y = 90

2y + 30 = 90             Subtract 30 from each side

2y = 90 - 30

2y = 60                     Divide by 2

2y/2 = 60/2          

y = 30

x = y + 30

x = 30 + 30

x = 60

a) The concavity of R, For q < 150, concavity down in this interval. For q > 150. concavity up in this interval. At q = 150, there is an inflection point where the concavity changes.

b) If the retailer wants to consider increasing the amount spent on advertising, they should evaluate the impact on revenue. If the revenue starts to increase, it may advantageous to increase the advertising amount and vice versa.

To determine the concavity of the revenue function

\(R(q) = -0.003q^3 + 1.35q^2 + 2q + 80000,\)

we need to analyze the second derivative of the function.

The second derivative will help us identify whether the function is concave up or concave down and determine the presence of any inflection points.

Let's start by finding the first and second derivatives of the revenue function:

\(R'(q) = -0.009q^2 + 2.7q + 2\) (first derivative)

R''(q) = -0.018q + 2.7 (second derivative)

To determine the concavity, we need to examine the sign of the second derivative. If R''(q) > 0, the function is concave up. If R''(q) < 0, the function is concave down.

Setting R''(q) = 0 and solving for q:

-0.018q + 2.7 = 0

q = 150

Now, let's evaluate the sign of R''(q) in different intervals:

For q < 150:

R''(q) = -0.018q + 2.7 < 0, indicating concavity down in this interval.

For q > 150:

R''(q) = -0.018q + 2.7 > 0, indicating concavity up in this interval.

Therefore, at q = 150, there is an inflection point where the concavity changes.

Now, let's address part (b) of the question. If the retailer currently spends 140,000 on advertising, we can substitute this value into the revenue function to determine the revenue:

\(R(140) = -0.003(140)^3 + 1.35(140)^2 + 2(140) + 80000\)

≈ 287,700

If the retailer wants to consider increasing the amount spent on advertising, they should evaluate the impact on revenue. By calculating the revenue at different spending levels, they can determine if increasing the advertising budget would lead to a higher revenue.

For example, they can calculate R(150), R(160), R(170), and so on, to observe the trend in revenue. If the revenue continues to increase with higher advertising spending, it may be beneficial for the retailer to consider increasing their budget.

However, if the revenue starts to decrease or plateau, it may not be advantageous to increase the advertising amount.

Note that the given revenue function is an approximation, so the retailer should also consider other factors, such as the cost of advertising and the potential market response, in making a well-informed decision about increasing the advertising budget.

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When testing differences between the mean scores of more than two unconnected groups, the appropriate statistical technique to select is analysis of variance ANOVA.

When comparing the means of more than two unconnected groups, ANOVA is the appropriate statistical technique to use. ANOVA allows for the analysis of variance between multiple groups simultaneously. It tests whether there are significant differences in means among the groups based on the variability within and between the groups. ANOVA provides an F-statistic and associated p-value to determine if there are significant differences in means.

The dependent samples t-test (option b) is used when comparing the means of two related groups, where the same subjects are measured under different conditions or at different times. Regression (option c) is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. The independent samples t-test (option d) is appropriate when comparing the means of two independent groups. However, when dealing with more than two groups, ANOVA is the preferred method as it allows for a comprehensive analysis of variance across all groups simultaneously.

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Answer:

the answer 6.5

........

The distance between the points R(0, 1) and S(6, 3.5) is 6.5 units after using the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

It is given that:

Two points are:

R(0, 1) and S(6, 3.5)

To find the distance between points R and S we can use the distance formula.

\(\rm d=\sqrt{(6-0)^2+(3.5-1)^2}\\\)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

d = √(36 + 6.25)

d = √42.25

d = 6.5 units

Thus, the distance between the points R(0, 1) and S(6, 3.5) is 6.5 units after using the distance formula.

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Answer:

t ≥ 192

Step-by-step explanation:

To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)

The value of q is 16.

Collinear points are the points which are formed on a straight line, whether they are close or far away.

If three or more points are collinear, then they form on the same line.

The slope of each pair of points will be same.

Here if A, B and C are collinear,

Slope of AB = Slope of BC

(4 - 0) / (7 - 9) = (q - 4) / (1 - 7)

-2 = (q - 4) / -6

q - 4 = 12

q = 16

Hence the value of q is 16.

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Answer:

5√15cm or 19.36cm

Step-by-step explanation:

An isosceles triangle has two congruent sides.

The height of an isosceles triangle is also the median and the perpendicular bisector of the triangle dividing the base in half and forming two congruent right triangles.

a squared + b squared = c squared

5 squared + h squared = 20 squared

25 + h squared = 400

h squared = 375

h =√375

h = 5√15 cm

h = 19.36 cm

The amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

We should know that we have to deduct the tip for excellent driving g before adding up the tax to the total first.

The given parameters are

Bill =$65

Tax rate= 7%

Tip for excellent driving =20%

First deduct 0.2*65

=13

Balance = $(65-13)

Balance= $52.00

Tax = 0.07*65

Tax = 4.55

Then $(52.00+4.55)

= $56.55

In conclusion, the amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

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Answer:

Personally its a negative real‼️‼️

According to the Centroid Ratio Theorem , we have:

                    x = 37 , DG = 22,

                   AG = 44  and AD = 66

Centroid Ratio Theorem:

The Centroid ratio theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid point of the side.

according to the centroid ratio theorem, we have,

                        AG = 2/3 (AD)       ----------------------------- (1)

                        AG = x + 7

                        DG = x - 15

                        AD = x + 7 + x- 15 = 2x - 8

Putting the values in equation (1)

     x + 7 = 2/3 (2x - 8)

⇒ 3(x + 7) = 2( 2x - 8)

⇒3x + 21 = 4x - 16

⇒ -x = -37

⇒ x = 37

Putting the value of x= 37

DG = 37 - 15 = 22

AG = 37 +7 = 44

AD= 2×37 - 8 = 66

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Answer:

A. step 1

Step-by-step explanation:

I think its A , because a negative plus a negative is a postive

Answer:

step 2 is the incorrect step

The following functions are analytic:

1. f(z) = iz

2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)

4. f(z) = \(e^x(cosy - isiny)\)

5. f(z) = \(Re(z^2) - iIm(z^2)\)

8. f(z) = \(i/z^8\)

11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)

Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.

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Answer:

x = 8cm

Step-by-step explanation:

17² = 15² + x²

289 = 225 + x²

- x² = 225 - 289

x² = 64

x = √64

x = 8

\({ \boxed{ \sf \color{blue}{answer}}}\)

x = 8 cm

Step-by-step explanation:

17² = 15² + x²

289 = 225 + x²

x² = 225 - 289

x² = 64

x = √64

x = 8

Teorema pythagoras

Ronnie's purchase is not an example of impulsive buying because he had an intention to buy electronic device Impulsive Buying

Impulsive buying is simply a situation buyers are faced with when they purchase items they do not really need or no intention prior to the time of purchase.

However, in this situation Ronnie purchase is not an example of impulsive buying because he had intention to purchase an electronic device, hence he walked into and electronic store.

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Answer

A = pi * r^2

= pi * (2x^-3)^2

= pi * 2^2 * (x^-3)^2

= pi * 4 * (x^-6)

= 4*pi * x^-6

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Since Seth pays $0.50 for each check he writes, he would write (let x be how many checks Seth wrote) "x" checks for $6.50. That means;

1 = 0.50

x = 6.50

Now let us set up a fraction:

\(\frac{0.5}{1}=\frac{6.5}{x}\)

Step 1: Cross multiply

\(0.5x=1\cdot \:6.5\)

\(0.5x=6.5\)

Step 2: Divide both sides by \(0.5\)

\(\frac{0.5x}{0.5}=\frac{6.5}{0.5}\)

Simplify

\(x=13\)

Therefore, Seth will write 13 checks for $6.50

To send Kred to a Krew member, you can follow the steps provided by the Kred platform. These steps typically involve accessing your Kred account, selecting the desired recipient, specifying the amount of Kred to send, and confirming the transaction.

Sending Kred to a Krew member usually requires using the features and functionalities provided by the specific Kred platform or service. The process may vary depending on the platform, so it is recommended to refer to the official documentation or guidelines provided by the platform. Typically, you would need to log in to your Kred account, navigate to the appropriate section for sending Kred, select the intended recipient from the list of Krew members, enter the desired amount of Kred to send, review the transaction details, and confirm the transfer. The platform may also offer additional options or settings for customizing the transfer process.

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Answer:

21.5

Step-by-step explanation:

square is 10x10 = 100

circle is A=πr2=π·5²≈78.54

100-78.54 = 21.46 = 21.5

Answer:

21.5 sq cm

Step-by-step explanation:

Area of Square:

A= LXW= 10x10= 100 sq cm

Area of Circle=

A=πr²

Radius= D/2= 10/2= 5 cm

A=3.14(5²)

A=3.14(25)= 78.5 sq cm

Shaded Region= 100-78.5= 21.5

The area of the shaded region is 21.5 sq cm.

Explanation:

To solve the equations by Elimination we can multiply the first equation by -2.5 as follows:

Now, we can add this equation to the second equation as follows:

- 5x - 20y = - 15

5x + 20y = 15

0 + 0 = 0

0 = 0

When we get 0=0, the system has infinite solutions

So, this system has solutions with the form:

(x, y) where 2x + 8y = 6

It also means that both equations, 2x + 8y = 6 and 5x + 20y = 15 are equivalent equations and the solutions of the first one are also the solutions of the second one.

If hose A takes x hours to fill the pool, hose B will take x+3 hours to fill the pool. So, each hour, A will fill \(\bf{\dfrac{1}{x}}\) parts of the pool and B will fill \(\bf{\dfrac{1}{x+3}}\) parts. Since using both hoses fills the pool completely, you have to:

                                                          \(\large\displaystyle\text{$\begin{gathered}\sf \bf{ 1= \frac{1}{x}+\frac{1}{x}+\frac{1}{x+3}+\frac{1}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2}{x}+\frac{2}{x+3} } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ =\frac{2x+2x+6}{x(x+3)} } \end{gathered}$}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+3x=4x+6\ \Longrightarrow\ \ 0=x^2-x-6=(x-3)(x+2) } \end{gathered}$}\)

Hose A takes 3 hours to fill the pool and Hose B takes 6 hours.