Can somone help me with this will mark u brainliest

The measures given form 2 triangles.

Each triangle has a hypotenuse of 37 inch and a side length of 12 inches ( right triangle)

So, we have to find the measure of the missing side of the right triangle_

Apply Pythagorean theorem:

c^2= a^2+b^2

Where c is the hypotenuse (37) and a and b are the other legs of the triangle:

37^2 = a^2+12^2

Solve for a

1,369= a^2+144

1,369-144 = a^2

1,225 = a^2

√1225 = a

35=a

The TV is 35 inches tall.

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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Answer:

c = f + 2

Step-by-step explanation:

Each time there is a new figure ( f ), two circles ( c ) are added.

The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Two norms on a linear space X are equivalent if they define the same topology, meaning they have the same open sets. To show ||x||p and ||x||[infinity] are equivalent in Rⁿ, use the inequalities max |xi| ≤ (Σ \(|xi|p)^{1/p}\) ≤ \(n^{1/p}\) max |xi|.

To show that two norms on a linear space X are equivalent if and only if they have the same open sets,

If two norms on X are equivalent, then they have the same open sets.

Let ||·|| and ||·||' be two equivalent norms on X, meaning that there exist positive constants c1 and c2 such that for any x in X,

c1||x|| <= ||x||' <= c2||x||

To show that ||·|| and ||·||' have the same open sets, we need to prove that a set U is open with respect to ||·|| if and only if it is open with respect to ||·||'.

Suppose U is open with respect to ||·||. Let x be any point in U, and let r be a positive real number such that the open ball B(x, r) = {y in X : ||y - x|| < r} is contained in U. We want to show that there exists a positive real number r' such that the open ball B'(x, r') = {y in X : ||y - x||' < r'} is also contained in U.

Let c = c2/c1, and choose r' = r/c2. Then, for any y in B'(x, r'), we have

||y - x||' <= c2||y - x||/c2 = ||y - x||

Therefore, y is also in B(x, r), which implies that y is in U. Hence, U is open with respect to ||·||'.

Conversely, suppose U is open with respect to ||·||'. Let x be any point in U, and let r' be a positive real number such that the open ball B'(x, r') = {y in X : ||y - x||' < r'} is contained in U. We want to show that there exists a positive real number r such that the open ball B(x, r) = {y in X : ||y - x|| < r} is also contained in U.

Let c = c2/c1, and choose r = c1r'. Then, for any y in B(x, r), we have

||y - x||' <= c2||y - x||/c1 <= c2r/c1 = r'

Therefore, y is also in B'(x, r'), which implies that y is in U. Hence, U is open with respect to ||·||.

In Rⁿ, show that the following norms are equivalent

||x||p = (Σ\(|xi|^p)^{1/p}\) and ||x||[infinity]: = max |xi|

i=1 1≤i≤n

To show that the two norms are equivalent, we need to show that there exist positive constants c1 and c2 such that c1||x||[infinity] ≤ ||x||p ≤ c2||x||[infinity] for all x in Rⁿ.

First, we will show that c1||x||[infinity] ≤ ||x||p. Let x be any element in Rⁿ. Then,

||x||[infinity] = max{|x1|, |x2|, ..., |xn|} ≤\(|x1|^p + |x2|^p + ... + |xn|^p\) = Σ\(|xi|^p\)

Since p > 0, we can take the p-th root of both sides to get

||x||[infinity] ≤ (Σ\(|xi|^ \infty)^{1/p}\) = ||x||p

Therefore, c1 = 1 is a valid constant.

Next, we will show that ||x||p ≤ c2||x||[infinity]. Let x be any element in R^n. Then,

||x||p = (Σ\(|xi|^p)^{1/p}\) ≤ (Σ\(|xi|^ \infty)^{1/p}\)=\(n^{1/p}\) ||x||[infinity]

Therefore, c2 = \(n^{1/p}\) is a valid constant.

Since we have found positive constants c1 and c2 such that c1||x||[infinity] ≤ ||x||p ≤ c2||x||[infinity], we have shown that the two norms are equivalent.

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Question 13.

The estimated monthly cost of an energy-efficient refrigerator is $57, meaning the yearly cost is

Question 14.

The least energy-efficient refrigerator costs $72 per month, meaning the annual cost is

Therefore, the amount you will save on an energy-efficient refrigerator be

Hence, the amount saved on an energy-efficient refrigerator will be $180.

Answer:

y = x + 3

Step-by-step explanation:

In point slope form, the equation of line is,

\(y - b = m(x - a)\)

where a and b correspond to the x and y coordinates of the given point and m is the slope

Since the line is parallel to y = x+4, it has the same slope so m = 1 since the slope of y = x+4 is 1

and putting the values of the point (-1,2), we get,

y - 2 = x - (-1)

y-2 = x + 1

y = x + 3

All the values of other trigonometric functions are,

cos θ = -4/5.

sec θ = -5/4.

tan θ  = 3/4.

cot θ = 4/3.

Since, We have to given that;

sin θ = -3/5 and csc θ = -5/3

We know that;

⇒ sin² θ + cos² θ = 1

Substitute the given values, we get;

⇒ (-3/5)² + cos² θ = 1

⇒ cos² θ = 1 - 9/25

⇒ cos² θ = 16/25

⇒ cos θ = -4/5

(negative because it is in Quadrant 3).

And, sec θ = 1 / cos θ

sec θ = -5/4.

And, tan θ = sin θ / cos θ

tan θ = -3/5 / - 4/5

= -3/5 × -5/4

=  3/4.

And, cot θ =  1 / tan θ

cot θ = 4/3.

Hence, All the values of other trigonometric functions are,

cos θ = -4/5.

sec θ = -5/4.

tan θ  = 3/4.

cot θ = 4/3.

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Answer:

No Solution.

Step-by-step explanation:

To solve for x in this equation, we need to simplify both sides of the equation and make them equal.

Starting with the left-hand side:

5 + x - 14 = x - 7

Adding 14 to both sides:

5 + x = x + 7

Subtracting x from both sides:

5 = 7

5 does not equal 7.

Therefore, the value of x is no solution.

Answer:

there is no solution for this, if you solve you will get 0=2 (This is also called a contradiction)

Step-by-step explanation:

5+x-14=x-7

5-14 = -9

-9+x=x-7

x-9=x-7

+9     +9

x=x+2

-x  -x

0 = 2

We have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\). This is the linearized equation.

To linearize the given ordinary differential equation (ODE) \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\), we need to rewrite it in a linear form. One common approach is to introduce a new variable that relates to the derivative of \(\( y \)\).

Let's define a new variable \(\( v = \sqrt{x} \)\). Taking the derivative of both sides with respect to \(\( t \)\), we have:

\(\[ \frac{{dv}}{{dt}} = \frac{{d}}{{dt}} \left( \sqrt{x} \right) \]\)

Using the chain rule, we can express \(\( \frac{{dv}}{{dt}} \)\) in terms of \(\( \frac{{dx}}{{dt}} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \frac{{dx}}{{dt}} \]\)

Now, we need to substitute \(\( \frac{{dx}}{{dt}} \)\) using the given equation \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \left( 5 \sqrt{x} \right) \]\)

Simplifying the right-hand side:

\(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

Thus, we have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

The linearized equation is much simpler compared to the original non-linear equation.

Note: The complete question is:

Linearize the ODE below;

\(\(\frac{{dy}}{{dt}} = 5\sqrt{x}\)\)

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The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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Answer:

Subtraction

Step-by-step explanation:

(4x^(5) - 8x) - (3x^(2) - 8x + 9) = 4 x^( 5) - 3 x^ (2)  - 9

Answer:

The answer is letter F po

Step-by-step explanation:

Use the formula

(b2)2 in order to create a new term. Solve for x

by using this term to complete the square.

Exact Form:x=±√17+5

The number of tickets that can be bought with $40 is 4 tickets

It costs $9.50 to buy 1 tickets

The number of tickets that will be bought with $40 can be calculated as follows

= 40/9.50

= 4.2

Hence 4 tickets will be bought with $40

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Step-by-step explanation:

we know the area of a rectangle is

length × width.

so,

3(n - 1)(n + 2) = 54

3(n² + 2n - n - 2) = 54

3(n² + n - 2) = 54

3n² + 3n - 6 = 54

3n² + 3n - 60 = 0

now we could simply divide everything by 3

n² + n - 20 = 0

but based on the listed drop-downs this simplification is seemingly not desired.

so, the right answer remains

3n² + 3n - 60 = 0

and the drop-downs are therefore

3

3

-60

\(\huge \bf༆ Answer ༄\)

Let's solve ~

Hence,

Answer:

Less = 0.24

More = 0.76

Step-by-step explanation:

Given that:

Numbers drawn by Carmen :

4, 7, 6, 0, and 2

To make a decimal less than 1 from the numbers drawn:

First digit would be always be 0 since we aren't considering negative numbers

If they are playing for less; then the least 2 digits will be used in ascending order after the decimal point as;

2, 4

0.24

If they are playing for more; then the highest 2 digits will be used in descending order after the decimal point as;

7, 6

0.76

Answer:

try using photo math it will give you the answer and show you how to work it out

Step-by-step explanation:

hope this helps

Answer:

-2x+4

Step-by-step explanation:

The word that best fits the definition of identifying which books have romantic or heroic themes is "genre."

In literature, the term "genre" refers to a category or classification of literary works based on their content, style, and themes. It helps to categorize books into different types or groups, making it easier for readers to find the kind of books they enjoy. One such genre that encompasses romantic or heroic themes is "romance" or "adventure."

Romance novels typically revolve around romantic relationships and often feature passionate love stories. These books explore themes of love, desire, and emotional connections between characters. On the other hand, adventure novels often involve daring and heroic actions, with protagonists embarking on thrilling quests or facing challenges that require bravery and determination. These books often highlight themes of heroism, courage, and the triumph of good over evil.

By identifying the genre of a book as romance or adventure, readers can easily find and select books that align with their preference for stories with romantic or heroic themes

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Here is the answer :

people who like both the songs is 35 and

people who like only folk songs is 100.

If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

The answer is -300 because he owes -225 and then when he spends they subtract the amount he spent so the equation would be -225-75= the answer of -300

Answer:

rise/rum so it would be 1,2?

Step-by-step explanation:

Answer:Over-specifying the model refers to option B.

Step-by-step explanation:

Over-specifying the model means including one or more independent variables in the model that have no partial effect on y. This results in a model that is too complex and has more variables than necessary. Over-specification can lead to problems such as multicollinearity, which occurs when two or more independent variables are highly correlated, making it difficult to determine the individual effect of each variable on y.

On the other hand, under-specification of the model means excluding one or more independent variables that have a partial effect on y. This results in a model that is too simple and does not capture all the important factors that affect y. Under-specification can lead to omitted variable bias, which occurs when the effect of an important variable is not captured in the model, leading to biased estimates of the effects of other variables in the model.

A well-specified model includes all the important independent variables that have a partial effect on y, while excluding variables that have no partial effect on y. The population coefficient is the true coefficient that would be obtained if the entire population were studied. A population coefficient of one does not necessarily indicate over-specification of the model.

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