2( x + 2) = 4x+ 1- 2x

The cargo plane's speed is 576.7 km /hour.

Given, the cargo plane flew away 9 hours before an air force plane.

The air force plane is in the opposite direction.

speed of the air force plane is : 260 km/hr

time = 3 hours

distance for which plane's are apart = 5970 km

therefore, 9x + 3(260) = 5970

9x + 780 = 5970

9x = 5970 - 780

9x = 5190

x = 5190/9

x = 576.7 km

hence the speed of the cargo plane is 576.7 km.

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The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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Answer:

55x + 35y = 200

Step-by-step explanation:

Answer:

55 x+ 35 y = 200

Step-by-step explanation:

When x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

1)  We are aware that only when x is positive is a logarithmic function, log x, defined. i.e., x>0 . Therefore, when x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

2) Order from smallest to largest:

     \(log^{200}_{20} < log 100 < log^{5}_{40} < log^{3}_{60} < log^{2}_{16}\)

3)

           \(\(2A=A(1+\frac{0.09}{52})^{n}\\\\ 2=(1+\frac{0.09}{52})^{n}\\\\ log2=log(1+\frac{0.09}{52})^{n}\\\\ log2=nlog(1+\frac{0.09}{52})\\\\ n=log2\div log(1+\frac{0.09}{52})\\\)\)

log(2)/log(1+0.09/52 = 400.831511360387616 weeks

400.831511360387616/52 = 7.708298295392069538

7.7 years

Hence, It take 7.7 years for deposit to double.

4)

a)

          \(S= 86 \ log d+112\\\\S= 86 log 50 +112\\\\S = 86*1.7+112\\\\S= 258.2\)

          S = 258.2 mph

b)

S = 258.2 mph ;  find d

258 =86 log10 (d) + 112

146 = 86 log10 (d)

 1.7 = log10 (d)

 d = 50.118

Change from Log Form to Exponential Form

50.118 miles = d   Rounded is 181 miles

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a. The system of equations that represents this scenario is : D + n = 29 and 0.1D + 0.05n = 2.15.

b. The numbers of nickels and dimes are 15 and 14, respectively.

We have a total of 29 coins in our piggy bank. All the coins are either nickels or dimes. The value of the coins is $2.15. We have to find out the equation that represents this scenario. We have to find out the number of nickels and dimes that we have in the piggy bank.

Let the number of dimes and nickels be represented by the variables "D" and "n", respectively. The value of a dime is $0.1. The value of a nickel is $0.05. The equations are given below.

D + n = 29

0.1D + 0.05n = 2.15

We will substitute the value of "D" from the first equation into the second equation.

D = 29 - n

0.1D + 0.05n = 2.15

0.1(29 - n) + 0.05n = 2.15

2.9 - 0.1n + 0.05n = 2.15

0.05n = 0.75

n = 15

Hence, the number of nickels is 15. We will substitute this value into the first equation.

D = 29 - n

D = 29 - 15

D = 14

Hence, the number of dimes is 14.

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The prediction of demand for December using the four-period moving average is 211.

This is option c.

To predict the demand for December using the 4-period moving average, the first step is to calculate the average of the demand in each four-month period. Here is how to calculate it:

Month Demand Average

Jan 141

Feb 276

Mar 216

Apr 156 179.75

May 261

June 141 186

Jul 246

Aug 246

Seperti 216 233.25

Oct 156

Nov 216 196.25

We then take the average of the last four months' average demands, which are the averages from September to November:

Average of the last four-month demand average = (233.25 + 196.25 + 216) / 3 = 215.5

Therefore, the prediction of demand for December using the four-period moving average is approximately 216. The answer is option (c) 211 (Approx)

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Answer:

So for..

a. from: 2   to: 4

b. from: 0   to: 2      ( I believe this one, may be incorrect- sorry if so)

c. from: 6   to: 10      ( I believe also for this one, sorry if incorrect)

d. from: 5   to: 6       ( I beleive- that is what it looks like- sorry if incorrect)

e.  They are staying at a constant rate, not changing, at rest...

Hope this helps!

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

LINE 1 : 3x + 4y = 20

rearranging : 4y = -3x + 20

y= -3/4 + 5 (y =mx + b)

therefore, m1 (slope) = -3/4

slopes of perpendicular lines are negative reciprocals of each other

m1 = -1 / m2 and m2 = -1/ m1

slope of line 2 (m2) = -1 / m1 = -1 / (-3/4) = 4/3

LINE 2 :

POINT - SLOPE FORM : y- y1 = m2 (x-x1)

point (3, -2); x1 = 3 and y1 = -2

m2 = 4/3

substituting the values in the point-slope form

y-y1 = m2 (x-x1)

y-(-2) = (4/3) (x-3)

y+2 = 4/3 (x) - 4/3(3)

y+2 = 4/3 x - 4

y = 4/3 x -4 - 2

y= 4/3 x -6

multiplying both sides of the equation by 3

3y = 4x -18

transposing,

4x-3y-18 = 0

answer: 4x - 3y -18 = 0

win / total = 6 /9

For 15 games:

x / 15

Where x is the number of wins in 15 games.

Cross multiply:

Divide both sides by 9

They will win 10 games.

Answer:

first one is x = -1

Step-by-step explanation:

if you want me to do all of them ( which I can) then ima need more points then just 5 :)

Answer:  Juste.

Step-by-step explanation:

Il a raison. Les numeos ne sont pas corrects.

Il n'ya pas de signe entre le 100 et 001. C'est l'addition ou la multiplication?

Et que veux dire 1,000 02 x 1010?  

1.00002 × 10¹⁰ ?

Il vaut mieux avoir 1,00001 × 10⁵

To express the given system of differential equation as an almost linear system, we need to find the partial derivatives of the given functions with respect to x and y.

∂f/∂x = -ex
∂f/∂y = 2
∂g/∂x = -1
∂g/∂y = -4cosy

Now, substituting these values in the general form of an almost linear system,

x′(t) = ax + by + r(x,y)
y′(t) = cx + dy + s(x,y)

we get,

x′(t) = -ex + 2y
y′(t) = -x - 4cosy

So,

a = -e, b = 2, c = -1, d = 0

At the critical point (0,0), the Jacobian matrix is

J(0,0) = ⎡⎣⎢⎢⎢-1 2⎤⎦⎥⎥⎥

The eigenvalues of this matrix can be found by solving the characteristic equation,

det(J - λI) = 0

where I is the identity matrix of the same size as J.

det ⎡⎣⎢⎢⎢-1-λ 2⎤⎦⎥⎥⎥ = (-1-λ)(-λ) - 2(2) = λ^2 + λ - 4

Using the quadratic formula, we get the eigenvalues as

λ1 = (-1 + sqrt(17))/2 ≈ 0.56
λ2 = (-1 - sqrt(17))/2 ≈ -2.56

Since the eigenvalues have opposite signs, the critical point is a saddle.

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Logistic Regression is preferred over Linear Regression for classification problems for several reasons.

Firstly, the predicted values in Logistic Regression are much more interpretable as they lie in the range of 0 to 1, which represents the probability of a certain outcome occurring. In contrast, Linear Regression predicts continuous values which are difficult to interpret as probabilities.
Secondly, the sigmoid curve used in Logistic Regression fits the data better than a straight line used in Linear Regression. This is because the sigmoid curve captures the non-linear relationships between the input variables and the output variable, which is often the case in classification problems.
Lastly, Logistic Regression uses maximum likelihood estimation to estimate parameters, whereas Linear Regression minimizes the mean squared error. Maximum likelihood estimation is a more appropriate method for estimating parameters in classification problems as it takes into account the binary nature of the output variable. Linear Regression, on the other hand, does not consider this binary nature and may not produce accurate results in classification problems.

In summary, Logistic Regression is preferred over Linear Regression for classification problems because of its interpretable predicted values, better fit to non-linear relationships, and appropriate method of estimating parameters using maximum likelihood estimation.

We prefer Logistic Regression over Linear Regression for classification problems for the following reasons:

1) Predicted values in Logistic Regression are more interpretable as they lie in the range of 0 to 1, representing probabilities of class membership, while Linear Regression predicts continuous values which may not directly indicate class membership.

2) The sigmoid curve in Logistic Regression fits the data better for classification problems, as it represents a natural threshold between classes, while a straight line from Linear Regression may not provide clear separation between classes.

3) Logistic Regression uses maximum likelihood estimation to estimate parameters, which makes it more suitable for classification problems as it finds the best fit for the probability of class membership. Linear Regression minimizes the mean squared error, which focuses on minimizing the distance between predicted and actual values, but does not directly optimize for class membership probabilities.

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Answer:

$11838.7

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Simple Interest Rate Formula: \(\displaystyle A = P(1 + r)^t\)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 9500

r = 4.5% = 0.045

t = 5

Step 2: Find A

Answer:

Completing the square: \((x^2+4x)-5=0\)

Factored form: \((x+5)(x-1)=0\)

Step-by-step explanation:

1.

Completing the square is a method used to rewrite a quadratic equation in vertex form. First one groups the linear and the quadratic terms. Then one will factor out the coefficient of the quadratic term. After doing so, one makes the grouped equation a perfect square trinomial by introducing a term, don't forget to balance the equation. Finally one simplifies the equation. The result is a quadratic equation in vertex form.

The quadratic equation:

\(x^2+4x-5=0\)

Group the linear and quadratic terms:

\((x^2+4x)-5=0\)

The quadratic term doesn't have a coefficient, so one doesn't need to factor the group. Now, one has to add a term to make the group a perfect square trinomial. Remember to balance the equation:

\((x^4+4x-4)-5-4=0\)

Simplify,

\((x-2)^2-9=0\)

2.

Factoring a quadratic equation is a method of rewriting a quadratic equation as the product of two linear equations. One splits the constant term up into factors, such that the sum of the factors is equal to the coefficient of the linear term.

\(x^2+4x-5=0\)

Factor:

\((x+5)(x-1)=0\)

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{-8}-\underset{x_1}{4}}} \implies \cfrac{1 +2}{-8 -4} \implies \cfrac{ 3 }{ -12 } \implies - \cfrac{ 1 }{ 4 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{4}) \implies y +2 = - \cfrac{ 1 }{ 4 } ( x -4)\)

\(y+2=- \cfrac{ 1 }{ 4 }x+1\implies y=- \cfrac{ 1 }{ 4 }x-1 ~~ \impliedby ~~ \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

The obtained t-value is approximately (b) 3.46.

The obtained t-value can be calculated using the formula:

t = ΣD / (sD / √(n))

where ΣD is the sum of the differences between paired observations, sD is the standard deviation of the differences, and n is the sample size.

Given ΣD = 24, n = 8, and s₂D = 6, we can find sD by taking the square root of s₂D:

sD = √(s₂D) = √(6) ≈ 2.45

Substituting the given values, we get:

t = ΣD / (sD / √(n)) = 24 / (2.45 / √(8)) ≈ 3.46

Therefore, the obtained t-value is approximately (b) 3.46.

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The answer is B. 7x + 27 units.

Area is length multiplied by width, so to find the length, simply divide the expression 21x + 81 by the width --> 3.

21x becomes 7x, and 81 becomes 27.

Answer:

ANSWER

GIVEN:

OA= 3x-1 , OC= 5x-3, OD= 6x-5 , BO = 2x+1

AO/OC = BO/OD

[The diagonals of a Trapezium divide each other proportionally]

(3x-1)/(5x-3) =( 2x+1)/(6x-5)

(3x-1) (6x-5) = (5x-3) ( 2x+1)

3x(6x-5) -1 (6x-5) = 2x(5x-3)+1(5x-3)

18x² -15x -6x +5 = 10x² -6x +5x -3

18x² -21x +5 = 10x² - x -3

18x² -10x² -21x + x +5+3 =0

8x² - 20x +8= 0

4(2x² -5x +2) = 0

2x² -5x +2 = 0

2x² -4x -x +2= 0

[By factorization]

2x(x-2) -1(x-2)= 0

(2x-1) (x-2) = 0

(2x-1) = 0 or (x-2) = 0

x = ½ or x = 2

If we put x= ½ in OD , The value of OD is negative.

Hence, the value of is x = 2.

Step-by-step explanation:

1 =29 and 2=44...............

The degrees of freedom for a data table can be calculated using the formula:

Degrees of Freedom = (Number of Rows - 1) * (Number of Columns - 1)

In this case, the data table has 10 rows and 11 columns. Plugging these values into the formula:

Degrees of Freedom = (10 - 1) * (11 - 1) = 9 * 10 = 90

Therefore, the degrees of freedom for the given data table is 90.

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If the conditions for a binomial distribution are met, the variance, given the number of trials (n) and the probability of success(p) is given as:

Given:

n = 170

p = 0.7

Solution

By substituting the given values, the variance is:

Answer: 35.7

The average number of activations per 25 minutes is 3.333.

Average number is a measure of central tendency that represents the typical value in a set of data. It is calculated by summing all the values in the dataset and dividing by the total number of values.

First we can start by using the fact that there are 60 minutes in an hour to convert the rate of activations per 2 hours to a rate of activations per 25 minutes.

The average rate of activations per 2 hours is 16, so the average rate of activations per 1 hour is 8. Therefore, the average rate of activations per 1 minute is 8/60 = 0.1333.

To find the average number of activations per 25 minutes, we can multiply the average rate per minute by the number of minutes:

Average rate per 25 minutes = (0.1333 activations/minute) x (25 minutes) = 3.333

Therefore, the average number of activations per 25 minutes is 3.333

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Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Answer:

29- x=59

Step-by-step explanation:

The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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The Orthocentre is one of the four (4) most common centres of a triangle.

It is located at the point where the triangle's three(3) altitudes intersect called a point of concurrency.

The Orthocentre is located inside an acute triangle, on a right triangle and outside an Obtuse triangle.

Hence, the correct option is Option C

Answer:

This is your answer ☺️