Review the proof of tan (A-B) =
tanA-tanB/1+(tanA)(tanB) to complete step3, which expression must full in each blank space

Answer:

y=-16(t-7/2)squared + 198

Answer:

The answer will be B x=36 and y=18

Step-by-step explanation:

Hope this Helped

The exact solutions on the interval [0, 2) for the equation 2cos²(t) + 3cos(t) = -1 are t = 0.955 and t = 1.323.

To find the exact solutions for the equation 2cos²(t) + 3cos(t) = -1 on the interval [0, 2), we can rearrange the equation and solve for cos(t).

By substituting cos(t) with x, the equation becomes a quadratic equation: 2x² + 3x + 1 = 0. Solving this quadratic equation gives us two values for x: x = -1 and x = -0.5.

Since x represents cos(t), we can find the corresponding angles by taking the inverse cosine (cos⁻¹) of each value.

However, we need to consider the interval [0, 2). The inverse cosine function gives us values in the range [0, π], so we find the angles t = 0.955 and t = 1.323 that fall within the specified interval.

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Answer:

1. -14

2. v=10

Step-by-step explanation:

1.

- 22= - 8+k

-k-22=-8

-k=-8+22

-k=14/(-1)

k=-14

Answer:

Fifteen fifteen fifteen fifteen fifteen

Fifteen fifteen fifteen fifteen fifteeb

The answers are (a) The angular speed of the Ferris wheel is approximately 17.11 radians per minute and (b) The Ferris wheel makes approximately 163.15 revolutions per hour.

(a) To find the angular speed of the Ferris wheel in radians per minute, we need to convert the linear speed of the passengers from miles per hour to feet per minute.

Given that the passengers are travelling at 7 miles per hour, we can convert this to feet per minute:

7 miles/hour * 5280 feet/mile / 60 minutes/hour = 616 feet/minute.

The linear speed of a point on the Ferris wheel is equal to the product of the angular speed and the radius. In this case, the radius of the Ferris wheel is 36 feet. So we have:

616 feet/minute = angular speed * 36 feet.

Solving for the angular speed, we find:

angular speed = 616 feet/minute / 36 feet = 17.11 radians/minute.

Therefore, the angular speed of the Ferris wheel is approximately 17.11 radians per minute.

(b) To find the number of revolutions the wheel makes per hour, we can divide the linear speed by the circumference of the wheel. The circumference of the Ferris wheel is given by 2π times the radius:

circumference \(= 2\pi * 36 feet = 72\pi feet\).

The number of revolutions per minute is then:

revolutions per minute = linear speed / circumference = 616 feet/minute / (72π feet) = 2.719 revolutions/minute.

To find the number of revolutions per hour, we multiply the revolutions per minute by 60:

revolutions per hour = 2.719 revolutions/minute * 60 minutes/hour = 163.15 revolutions/hour.

Therefore, the Ferris wheel makes approximately 163.15 revolutions per hour.

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Congruent triangles have corresponding sides that are also congruent. As a result, we can say that side PC and side BQ are equal.

We can use the principle of parallel lines to demonstrate that side PC is equal to side BQ in an isosceles triangle ABC, where AB = AC and line PQ is parallel to BC.

Take the triangle ABC, where AB = AC, for example.

We can infer that angle BPC is congruent to angle BQC since line PQ is parallel to BC. This is because the parallel lines BC and PQ, as well as the transversal line PQ, produce congruent alternate interior angles.

The base angles of an isosceles triangle are similar. Angles ABC and ACB are therefore similar.

When we examine triangles BPC and BQC, we see the following:

Angle BPC and angle BQC are parallel, as was already established.

Angle AB is similar to Angle ABC (Isosceles property of triangle)

Triangles BPC and BQC can be said to be congruent using the angle-side-angle (ASA) principle.

Congruent triangles have corresponding sides that are also congruent. As a result, we can say that side PC and side BQ are equal.

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Answer:

d

Step-by-step explanation:

m= 6-10 / -1-(-5) = -2

Hope this Helps :)

Answer:

f is correct

Step-by-step explanation:

A weak negative correlation. Correct option is E.

A correlation between two variables tells the how the first variable will change, with change in second variable.

Given,

Value of y decreases as the value of x increases and vice versa.

Also, x and y are nearly linearly related.

But, there is still some deviation in the values and are not perfectly linear.

Hence, there is a weak negative correlation between x and y.

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Calculating percent error when the theoretical value is zero requires a slightly modified approach. The percent error formula can be adapted by using the absolute value of the difference between the measured value and zero as the numerator, divided by zero itself, and multiplied by 100.

The percent error formula is typically used to quantify the difference between a measured value and a theoretical or accepted value. However, when the theoretical value is zero, division by zero is undefined, and the formula cannot be applied directly.

To overcome this, a modified approach can be used. Instead of using the theoretical value as the denominator, zero is used. The numerator of the formula remains the absolute value of the difference between the measured value and zero.

The resulting expression is then multiplied by 100 to obtain the percent error.

The formula for calculating percent error when the theoretical value is zero is:

Percent Error = |Measured Value - 0| / 0 * 100

It's important to note that in cases where the theoretical value is zero, the percent error may not provide a meaningful measure of accuracy or deviation. This is because dividing by zero introduces uncertainty and makes it challenging to interpret the result in the traditional sense of percent error.

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Answer:

C

Step-by-step explanation:

7(3)-2=19

21-2=19

19=19

Answer: 1.8 mi.

Step-by-step explanation:

Formula for distance, rate, time

d = rt                    >I think of dirt

x = r, rate

Trip up:

r= 45 min = .75 hr                  >convert by dividing by 60

d = x(.75)    This is in

d =  x

x = d/.75

Trip down:

r= 20 min = .333 hr

d = (x+3)(.333)            >distribute

d =  .333x + 1        

Substitute trip up into trip down equation and solve for d

d = .333(d/.75) +1

d = .444d +1                  >subtract .444d from both sides

.555d = 1                       >divide .555 to both sides

d = 1.8 mi

Answer:

4

Step-by-step explanation:

all the details can be found in the attachment.

The minimax regret criterion, also known as the minimax regret strategy, is an approach used in decision theory by economists. It aims to minimize the maximum regret that could be experienced when choosing a particular course of action.

The minimax regret criterion is a decision-making technique that takes into account the potential regret associated with each possible decision. It recognizes that decision-makers often face uncertainty and that their choices may lead to outcomes that are different from what was initially expected. By considering the worst-case scenario or maximum regret for each decision, the minimax regret criterion helps decision-makers select the option that minimizes the potential regret.

In this approach, decision-makers evaluate the consequences of their choices by comparing the actual outcome with the best outcome that could have been achieved if a different decision had been made. The minimax regret strategy focuses on minimizing the maximum regret across all possible decisions, aiming to choose the option that would result in the least regret, regardless of the actual outcome.

Economists often use the minimax regret criterion to analyze decision problems under uncertainty, particularly when the consequences of different actions cannot be precisely predicted. It provides a framework for decision-making that incorporates risk aversion and the desire to minimize the potential for regret. By considering the worst possible outcomes, decision-makers can make more informed choices that take into account the potential regrets associated with their decisions.

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No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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Answer:

Yes

Yes

No

Yes

Step-by-step explanation:

Check if 1/3 will make the equations TRUE.

5/8 + 1/3

(15 + 8) / 24 = 23 /24

5/12 + 1/3

(5 + 4) / 12 = 9/12 = 3/4

13/18 - 1/3

(13 - 6) / 18

7 / 18

8/15 - 1/3

(8 - 5) / 15

3/15 = 1/5

Answer: I= 480.00

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 4000 × 0.03 × 4 = 480

I = $ 480.00

The simple interest accumulated

on a principal of $ 4,000.00

at a rate of 3% per year

for 4 years is $ 480.00.

Answer:  -418, 728, 446, -429, 1159, -696

Step-by-step explanation:

1. \(n = -199 - 219 = \boxed{-418}\).

2. \(m = 438 - (-290) = 438 + 290 = \boxed{728}\).

3. \(128 - (-318) = 128 + 318 = \boxed{446}\).

4. The sum of 429 and 429 is \(429+429 = 858\). We need to subtract this from 429, so \(429 - 858 = \boxed{-429}\).

5. The sum of 510 and 319 is \(510+319 = 829\). Subtracting -330, we get \(829 - (-330) = 829 + 330 = \boxed{1159}\).

6. Call the unknown number "\(\star\)". Then \(\star + 298 = -398\), so \(\star = -398 - 298 = \boxed{-696}\). (Think about it.)

Answer: Two Postive solutions

Step-by-step explanation:

Answer: 24.75 x 1.5 x 1.5 inches

Step-by-step explanation: Hope this helps!

The solutions are;

1) m^6/2

2) a^4b^2/4

3) 27x^5y/4

4) 4x^12/9

5) 8y^9/27

6) x^4y^2/4

The simplify means to write is the lowest possible form of the expression.

Let us now simplify each expression;

1) (-2m^4)^2/8m^2

4m^8/8m^2

m^6/2

2) (2a^3b^4)^3/(2ab^2)^5

2^3a^9b^12/2^5a^5b^10

a^4b^2/4

3) (3x^5y^3)^5/(6x^10y^7)^2

243x^25y^15/36x^20y^14

27x^5y/4

4) (4x^7/6x)^2

16x^14/36x^2

4x^12/9

5) (2y^5/3y^2)^3

8y^15/27y^6

8y^9/27

6) (5x^6y^2/10x^4y)^2

25x^12y^4/100x^8y^2

x^4y^2/4

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Answer: square root of 9

Step-by-step explanation:

The answer is the square root of 9, which is 3.

Answer:

31.42 in

Step-by-step explanation:

C=πd=π·10≈31.41593in

AS given by the question

There are given that the 2 hours to 45 minutes.

Now

First, convert 2 hours to the minute

So,

For converting hours into minutes, multiply by 60.

So, 2 hours is 120 minutes

Then, the ratio will be:

Answer: y=2/5x+1

Step-by-step explanation: (5,3) 2/5

y=mx+b

3=2/5(5)+b 2/5x5=10/5=2

3=2+b

3-2=b

1=b

answer : y=2/5x+1

A direct relationship between two variables is reflected in a "POSITIVE" correlation coefficient.

Correlation is a statistical technique for measuring and describing the relationship between two variables.

The variables move in the same direction when they have a positive correlation. In other words, as one variable increases, so does the other, and conversely, as one variable decreases, so does the other.

Typically, the two variables are simply observed rather than manipulated. Two scores from the same individuals are required for the correlation.

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The correct answer of slope (A) 4\(\pi\).

To find the slope of the tangent line to the polar curve \(r=20^{2}\) at the point where θ \(=\pi\) we need to differentiate the equation with respect to θ and evaluate it at θ \(=\pi\).

Differentiating the polar equation \(r=20^{2}\) with respect to θ gives us:

\(\frac{dr}{dθ} =40\)

Now, let's substitute θ\(=\pi\) into this derivative:

\(\frac{dr}{dθ} θ=\pi =4\pi\)

Therefore, the slope of the tangent line to the polar curve \(r =20^{2}\) at θ \(=\pi\) is \(4\pi\)

So, the correct answer of slope (A) 4\(\pi\).

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Answer:

This might help u........

The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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