Un oiseau se nourrit de poissons en plon-
geant dans l'eau depuis une falaise. Soit
h(r) la hauteur de l'oiseau au dessus du
niveau de l'eau en fonction de la distance x,
à l'horizontale, le séparant de la rive.
L'oiseau décrit une parabole et on trouve :
h(x) = r²-6r+5 pour r appartenant à [0; 6].

Answer: 8x^2 + xy - 15y^2

Step-by-step explanation:

first do the FOIL method than add 3xy to the equation after

Answer:

\(8x^2+xy-15y^2\)

Step-by-step explanation:

\((4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2\)

If the correlation between the independent variables is less than 0.7, we usually conclude that multicollinearity is not an issue.

The estimated regression equation that predicts the selling price of a used Honda Accord given the mileage and age of the car is: 20385.25 - 0.03739(mileage) - 686.3368(age) (to decimals). To determine if multicollinearity is an issue for this model, we need to find the correlation between the independent variables (mileage and age). The correlation between age and mileage is not provided in the question, so we cannot determine if multicollinearity is an issue or not.  Based on your provided information, I can help answer your questions.
a. The estimated regression equation to predict the selling price of a used Honda Accord given the mileage and age of the car is:
Selling Price = 20385.25 - (0.03739 * Mileage) - (686.3368 * Age)
b. To determine if multicollinearity is an issue, we need to look at the correlation between the independent variables (mileage and age). Unfortunately, you haven't provided the correlation value in your question. However, if the correlation between age and mileage is less than 0.7 (or -0.7), we can conclude that multicollinearity is not an issue. If it is higher than 0.7 (or -0.7), then multicollinearity would be an issue in this model.

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The dollar interval would be ± 6.70 to present in order to obtain a probability of 0.500.

What is probability?

Probability is a branch of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of error in research by using probability.

z value for the probability of 0.5  is 0.67

standard error = sd/√n = 80/√64 =10

dollar interval = z*se

                      = 0.67*10

                       =6.70

Hence, the dollar interval would be ±6.70.

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For a linear time sorting, any array of integers x[1,...n] can be sorted in O(n+M) time where M = max(x) - min(x) and Ω(nlogn) lower bound doesn't apply in this case because it does not involve comparing and merging the items, thus eliminating the need for recursion

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Answer:

They all come out to be infinity

Answer:

C

Step-by-step explanation:

Its C because it is 6+4 times a number n and parenthesis means to multiply, therefore the answer is (6+4)n=18

Answer:

both of you are wrong

Step-by-step explanation:

Answer: x=9

Step-by-step explanation: 2(x+5+)=3x+1 or 2x+10=3x+1

Answer:

x =  9

Step-by-step explanation:

2(x + 5) = 3x + 1  Distribute the 2

2x + 10 = 3x + 1  Subtract 2x from both sides

10 = x + 1  Subtract from both sides

9 = x

Check:

2(x + 5) = 3x + 1

2(9 + 5) = 3(9)+1

2(14) = 27 + 1

28 = 28

Answer:

6.06%

Step-by-step explanation:

198 + 6.06%=209.9988

9514 1404 393

Answer:

  c = -3; d = 5

Step-by-step explanation:

The function is differentiable if it is continuous and the derivative is continuous.

This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...

  5(3^2) +c = 45 +c

From the right, the limit is ...

  d(3^2) -3 = 9d -3

__

The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...

  f'(x) = 10x

  = 10(3) = 30

From the right, the limit is ...

  f'(x) = 2dx

  = 2d(3) = 6d

__

This gives us a pair of simultaneous equations in 'c' and 'd':

  45 +c = 9d -3

  6d = 30

The latter tells us d = 5. Then the former tells us ...

  45 +c = 9(5) -3   ⇒   c = -3

The function is differentiable if c = -3 and d = 5.

_____

Additional comment

With these values, the function becomes ...

  \(f(x)=\begin{cases}5x^2-3&\text{if }x\le 3\\5x^2-3&\text{if }x>3\end{cases}\)

Answer: Each transversal crossing a line generates 2 pairs of vertical angles and for 3 transversal crossing the same line it will be 3 x2 = 6 pairs (or 12 angles)

Step-by-step explanation:

(●'◡'●) ^_^

Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.

Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.

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The question is an illustration of fraction division and Adam's age as a fraction of Zara's age is 7/5

The ages are given as:

Adam = 3 years and 6 months

Zara = 2 years and 11 months

Rewrite the ages in months

Adam = 3 * 12 + 6 = 42 months

Zara = 2 * 12 + 11 = 35 months

Adam's age as a fraction of Zara's age is calculated using:

Fraction = Adam/Zara

This gives

Fraction = 42/35

Simplify

Fraction = 7/5

Hence, Adam's age as a fraction of Zara's age is 7/5

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Answer:

Sum of arithmetic series is \(2077\)

Step-by-step explanation:

We have \(n\)th term of arithmetic sequence

\(a+(n-1)d\)

Here

\(a+(n-1)d=127\\\\7+(31-1)d=127\\\\d=\frac{120}{30} \\\\=4\)

Sum of arithmetic sequence \(=\frac{n}{2} (2a+(n-1)d)\)

\(=\frac{31}{2} (2\times7+(31-1)4)\\\\=\frac{31}{2} (14+120)\\\\=31\times67\\\\=2077\)

Answer:

The sum of arithmetic series is 2077.

Step-by-step explanation:

Solution :

Here we have provided that :

We need to find :

Here's the required formula to find the sum of arithmetic series :

\(\longrightarrow{\pmb{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}\)

Substituting all the given values in the formula to find the sum of arithmetic series :

\({\longrightarrow{\sf S = \dfrac{n}{2} \Big(a_1 + a_n \Big)}}\)

\({\longrightarrow{\sf S = \dfrac{31}{2} \Big(7 + 127 \Big)}}\)

\({\longrightarrow{\sf S = \dfrac{31}{2} \Big(134 \Big)}}\)

\({\longrightarrow{\sf S = \dfrac{31}{2} \times 134 }}\)

\({\longrightarrow{\sf S = \dfrac{31}{\cancel{2}} \times \cancel{134 }}}\)

\({\longrightarrow{\sf S = 31 \times 67}}\)

\({\longrightarrow{\sf S = 2077}}\)

\(\star \: {\underline{\boxed{\sf{\red{S = 2077}}}}}\)

Hence, the sum of arithmetic series is 2077.

\(\rule{300}{1.5}\)

The characteristic polynomial of the block triangular matrix A coincides with det(a - λI) det(b - λI).

To show that the characteristic polynomial of a block triangular matrix, A = [a, 0; 0, b], where a and b are square matrices, coincides with det(a - λI) det(b - λI), we can follow these steps:
1. Recall that the characteristic polynomial of a matrix A is given by det(A - λI), where λ is an eigenvalue and I is the identity matrix.
2. In this case, our matrix A is block triangular, so it can be written as:
  A = [a, 0;
       0, b]
3. To find the characteristic polynomial, we need to compute the determinant of (A - λI):
  A - λI = [(a - λI), 0;
                0, (b - λI)]
4. Since the matrix (A - λI) is also block triangular, we can use Exercise 3.11 from Chapter 3, which states that the determinant of a block triangular matrix is the product of the determinants of the diagonal blocks.
5. Hence, det(A - λI) = det(a - λI) * det(b - λI).
So, the characteristic polynomial of the block triangular matrix A coincides with det(a - λI) det(b - λI).

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The rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

What is volume?

Volume refers to the amount of three-dimensional space occupied by an object or a substance.

To find the rate of increase in the volume V of a sphere when the surface area S becomes 100π square inches, we need to use the formulas relating the surface area and volume of a sphere to its radius.

The surface area S of a sphere is given by the formula:

\(S = 4\pi r^2,\)

where r is the radius of the sphere.

The volume V of a sphere is given by the formula:

\(V = (4/3)\pi r^3.\)

To find the rate of increase in volume with respect to time, we need to differentiate the volume formula with respect to time.

Given that the radius r is increasing at a uniform rate of 0.3 inches per second, we can write:

dr/dt = 0.3 inches per second.

Now, let's differentiate the volume formula with respect to time:

\(dV/dt = d/dt [(4/3)\pi r^3].\)

Using the power rule of differentiation, we get:

\(dV/dt = (4/3)\pi * 3r^2 * (dr/dt).\)

Simplifying further, we have:

\(dV/dt = 4\pi r^2 * (dr/dt).\)

Since we want to find the rate of increase in cubic inches per second, we need to express the volume in cubic inches.

Substituting the value of the surface area S = 100π square inches into the surface area formula:

\(100\pi = 4\pi r^2.\)

Dividing both sides by 4π, we get:

\(r^2 = 25.\)

Taking the square root of both sides, we find:

r = 5.

Now, we can substitute the value of r into the rate of increase formula:

\(dV/dt = 4\pi(5^2) * (0.3).\)

Simplifying the expression:

dV/dt = 4π(25) * 0.3.

dV/dt = 30π cubic inches per second.

Therefore, the rate of increase in the volume V is 30π cubic inches per second when the surface area S becomes 100π square inches.

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Answer:

statement not complete

Halpert Corporation's overall equipment effectiveness (OEE) was approximately 0.51.

OEE is a measure of how effectively a machine or equipment is utilized in producing quality output. It takes into account three factors: availability, performance, and quality.
To calculate OEE, we need to consider the following formula:
OEE = Availability * Performance * Quality
Availability: This is the ratio of actual run time to machine time available. In this case, the availability is 2,500 minutes / 3,125 minutes = 0.8.
Performance: This is the ratio of actual run rate to ideal run rate. Here, the performance is 2.4 units per minute / 3.2 units per minute = 0.75.
Quality: This is the ratio of defect-free output to total output. In this case, the quality is 5,100 units / 6,000 units = 0.85.
Now, we can calculate the overall equipment effectiveness (OEE):
OEE = 0.8 * 0.75 * 0.85 = 0.51
Therefore, Halpert Corporation's OEE is approximately 0.51, indicating that their machine utilization is at 51% efficiency.

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Step-by-step explanation:

best I could, hopefully this helps

right:wrong is 10:2 which can be reduced by 2 on both sides so you get 5:1

hope it helps comment if you have any questions and have an amazing day

The equation of the line is y = -6x - 19 in slope-intercept form.

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

In this case, the y-intercept is -19 and the slope is -6. So we can plug those values into the equation and simplify:

y = -6x - 19

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Answer:

\(y'= \frac{3x+2}{2\sqrt{x} }\)

General Formulas and Concepts:

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

Product Rule: \(\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)

Chain Rule: \(\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)

Step-by-step explanation:

Step 1: Define

\(y=\sqrt{x} (x+2)\)

Step 2: Rewrite

\(y=x^{\frac{1}{2} } (x+2)\)

Step 3: Differentiate

Answer:

Slope is -2

Step-by-step explanation:

(y2-y1) / (x2-x1)

(6-10) / (-10+12) = (-4)/(2) = -2

Step-by-step explanation:

You need to either graph the equation or manipulate the equation into the standard form for a circle  ( often requiring 'completing the square' procedure)

circle equation:

        (x-h)^2 + (y-k)^2  = r^2    where (h,l) is the center   r = radius

x^2  - 6x      +     y^2 + 10 y  = 2    'complete the square for x and y

x^2 -6x +9    +     y^2 +10y + 25   = 2  + 9   + 25      reduce both sides

(x-3)^2           +  (y+5)^2    = 36     (36 is 6^2   so r = 6)

   center is  3, -5

Answer:

if the center is a square, then x = 11

Adding a quadratic term to data that shows a curve in the scatterplot will provide a better fit but not affect the residual plot in any way, this statement is false

A scatterplot is a type of data display that shows the relationship between two numerical variables. Each member of the dataset gets plotted as a point whose x-y coordinates relates to its values for the two variables.

When on adding a quadratic term to  data, is illustrated on a scatter plot, a quadratic equation will form a “U” shape that is either concave down or concave up.

Therefore, adding a quadratic term to data that shows a curve in the scatterplot will provide a better fit but not affect the residual plot in any way, this statement is false.

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Answer:

Julia had 120 peas to start .

Answer:

  120 peas

Step-by-step explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

  (j -15) -(2/3j +15) = 10

  1/3j -30 = 10

  1/3j = 40

  j = 120

Julia had 120 peas at first.

__

Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

<95141404393>

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete. However, I will solve using the following assumptions.

Job A:

\(y = 2x + 5\)

Job B

\(\begin{array}{cccccc}x & {1} & {2} & {3} & {4} & {5} \ \\ y & {6} & {10} & {14} & {18} & {22} \ \end{array}\)

The first step is to calculate the rate of Job B using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where:

\((x_1,y_1) = (1,6)\)

\((x_2,y_2) = (2,10)\)

So, we have:

\(m = \frac{10 - 6}{2 - 1}\)

\(m = \frac{4}{1}\)

\(m = 4\)

So, the hourly rate of job B is $4/hr

For Job A:

\(y = 2x + 5\)

A linear equation has the form:

\(y = mx + b\)

Where m is the rate

By comparison:

\(m = 2\)

So, the hourly rate of Job A is $2/hr

Comparing both rates, we can draw the following conclusions;

Answer:

The race must be up to 29 meters for Dhvan to win.

Step-by-step explanation:

Since Shaan walks 2.5 meters per second, while his brother Dhvan walks 1 meter per second, and Dhvan wants to have a race, and Shaan knows that he walks faster, but he wants to give his brother a head start of 45 meters, so it doesn't seem that he is allowing him to win, to determine how many meters long should the race be in order for Dhvan to win the following calculation must be performed:

45 / (2.5 - 1) = X

45 / 1.5 = X

30 = X

Therefore, the race must be up to 29 meters for Dhvan to win.

Answer:

===========

The solution is one of the elements of the replacement set.

Answer:

The solution set is {9}.

Step-by-step explanation:

The replacement set for an equation is the set of values that may be substituted for the variable.

Given equation:

\(3(n+7)=48\)

Given replacement set:

The solution set is the set of all values that make the equation true.

To find the solution set from the replacement set, input each value from the replacement set and evaluate both sides of the equation. If the two sides are equal, the equation is true and the value is a solution.

\(\begin{aligned}n=8 \implies 3(8+7)&=48\\3(15)&=48\\45&=48\\\end{aligned}\)

As 45 ≠ 48, n=8 is not a solution.

\(\begin{aligned}n=9 \implies 3(9+7)&=48\\3(16)&=48\\48&=48\\\end{aligned}\)

As both sides are equal, the equation is true and n=9 is a solution.

\(\begin{aligned}n=10 \implies 3(10+7)&=48\\ 3(17)&=48\\51&=48\\\end{aligned}\)

As 51 ≠ 48, n=10 is not a solution.

Therefore, the solution set is {9}.