The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2, the fraction is now equal to. If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem? 5n = 3d and 3n 6 = 2d 4 5n = 3d and 4n 4 = 3d 6 3n = 5d and 3n 6 = 2d 4.

Answer:

< and >

Step-by-step explanation:

If it doesnt have the line under it, it means the number is  not included

an open circle means the number is not included

closed circle means its included

Hope this helps ^-^

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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Answer:

A ~ 50.27

D ~ 8

Step-by-step explanation:

Step-by-step explanation:

50.24 sq mm

\(\pi {r}^{2} \)

3.14(4)^2

3.14*16

= 50.24sq mm

Answer:

Coupon second discount = 200 off

Step-by-step explanation:

Given:

Price of laptop = $1,313

Coupon first discount = 15% off

Coupon second discount = 200 off

Find:

Choose coupon get the bigger discount

Computation:

Coupon first discount = 15% off

Coupon first discount = 1,313 x 15%

Coupon first discount = $196.95

So,

Coupon second, for get the bigger discount

Answer:

\(\displaystyle \sin\theta=\frac{12}{13}\)

Step-by-step explanation:

Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:

\(\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)

We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:

\(a^2+b^2=c^2\)

Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.

Substitute:

\((5)^2+b^2=(13)^2\)

Solve for b:

\(b=\sqrt{169-25}=\sqrt{144}=12\)

So, the opposite side measures 12.

Then sine will be:

\(\displaystyle \sin\theta=\frac{12}{13}\)

Answer:

Newton's second law is the real law of motion and the other two laws can be deduced from 2nd law.

Answer: \(55,811.91\)

Step-by-step explanation:

Given

Principal amount is 25,000

Time Period is \(t=15\ yr\)

Rate of interest \(r=5.5\%\)

Amount in compound interest is given by

\(\Rightarrow A=P\left(1+r\%\right)^t\)

Insert the values

\(\Rightarrow A=25,000(1+\dfrac{5.5}{100})^{15}\\\\\Rightarrow A=25,000(1.055)^{15}\\\Rightarrow A=55,811.91\)

Therefore, \(55,811.91\) must be paid back

Answer:

○ \(\displaystyle 12,9\)

Step-by-step explanation:

Use the Law of Sines to find the length of the second edge:

Solving for Angles

\(\displaystyle \frac{sin\angle{C}}{c} = \frac{sin\angle{B}}{b} = \frac{sin\angle{A}}{a}\)

Use \(\displaystyle sin^{-1}\)towards the end or you will throw your result off!

Solving for Edges

\(\displaystyle \frac{c}{sin\angle{C}} = \frac{b}{sin\angle{B}} = \frac{a}{sin\angle{A}}\)

Let us get to wourk:

\(\displaystyle \frac{a}{sin\:40} = \frac{10}{sin\:30} \hookrightarrow \frac{10sin\:40}{sin\:30} = x; 12,855752194... \\ \\ \boxed{12,9 \approx x}\)

I am joyous to assist you at any time.

Answer:

x=-3

Step-by-step explanation:

The values of y with respect to the points created is constant, hence the two points will have the same y values but difference their respective x values

The value of the inequality is ( 45/4 , 19/4 )

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

According to the given information

Number of hours spent in washing cars = x

Number of hours spent in clearing tables = y

Amount paid per hour for washing the car = $7

Amount paid per hour for clearing the tables = $15

Earnings

7x + 15y ≥ 150

x + y ≤ 16

7x + 15y = 150 ........ (i)

x + y = 16 ........(ii)

Multiply (ii) by 7

7x + 7y = 112 ..... (iii)

Subtract (i) and (iii)

8y = 38

y = 19/4

Putting the value of y in (ii)

x + 19/4 = 16

x = 16 - 19/4

x = 45/4

The value of the inequality is ( 45/4 , 19/4 )

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Answer:

Step-by-step explanation:

I think you mean

x² - 49.

If so it factors to (x +7)(x - 7)

The combination of a gentle slope and Type 1 soil resulted in the most infiltration of rainwater.

The most significant factor leading to the greatest infiltration of rainwater is the combination of a gentle slope and Type 1 soil. This specific combination allows for optimal water absorption and percolation into the ground. Type 1 soil, which is characterized by its high permeability and water-holding capacity, facilitates the efficient movement of water through its pore spaces. Meanwhile, the gentle slope helps to minimize surface runoff and allows rainwater to gradually seep into the soil, reducing the risk of erosion. By considering these two elements together, the combination of a gentle slope and Type 1 soil proves to be the most effective in maximizing rainwater infiltration.

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The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

Here,

The slope of line perpendicular to the line y +6=-2/5(x-1)

m1=5/2

point=(4,-7)

y-y1=m(x-x1)

y+7=5/2(x-4)

2y+14=5x-20

5x-2y=34

The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.

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The statement that is not true of the test data approach in a test of a computerized accounting system is B) Test data should consist of data related to all controls prevalent in the organization.

This statement is incorrect because the test data approach aims to test specific controls that the auditor wishes to rely on rather than all controls prevalent in the organization. The test data approach involves the creation of a set of test transactions that are processed by the client's computer program under the auditor's control.

The results of the test data are used to determine whether the application and general controls are functioning properly. By using this approach, the auditor can gain assurance that the system is functioning as intended and identify any control weaknesses that need to be addressed.

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¬ 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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The strongest influence on your behavior of taking home company supplies is the norm of social conformity within the workplace.

Social conformity refers to the tendency of individuals to adjust their behavior, thoughts, and actions to match the perceived norms of a particular social group. In the workplace, employees often observe the behavior of their peers and conform to their actions to fit in and be accepted.

When you witness your fellow employees regularly taking home company supplies, it creates a perceived norm that this behavior is acceptable or tolerated within the organization.

As a result, you may feel compelled to engage in similar behavior to conform and avoid standing out or facing social disapproval. The influence of social conformity can be strong, leading individuals to adopt behaviors they may otherwise consider wrong or unethical.

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The series you're referring to is the sum from n=1 to infinity of (n⁸)/(3n⁹). To determine if it is convergent or divergent, we can use the Ratio Test.

Step 1: Compute the ratio of consecutive terms: (a_(n+1))/a_n = ((n+1)⁸)/(3(n+1)⁹) * (3n⁹)/(n⁸).

Step 2: Simplify the ratio: ((n+1)⁸)/(3(n+1)⁹) * (3n⁹)/(n⁸) = (n+1)⁸/(n+1)⁹ * (n⁹)/(n⁸) = 1/((n+1)(n)).

Step 3: Take the limit as n approaches infinity: lim (n→∞) 1/((n+1)(n)) = 0.

Since the limit is less than 1, the series converges by the Ratio Test.

In summary, the series ∑(n=1 to ∞) (n⁸)/(3n⁹) is convergent. The Ratio Test is used to determine this, by finding the limit of the ratio of consecutive terms, which is less than 1.

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The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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Answer: 2

Step-by-step explanation:

The range of possible distances from the beach to the theater is 2 km to 16 km, calculated by subtracting the distance between the theater and the house (7 km) from the distance between the beach and the house (9 km), and adding it back.

To calculate the range of possible distances from the beach to the theater, we can use the information provided

Start with the distance between the beach and the house: 9 km.

Subtract the distance between the theater and the house: 7 km.

9 km - 7 km = 2 km.

This gives us the minimum possible distance from the beach to the theater: 2 km.

Add the distance between the theater and the house: 7 km.

9 km + 7 km = 16 km.

This gives us the maximum possible distance from the beach to the theater: 16 km.

Therefore, the range of possible distances is from 2 km to 16 km.

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--The given question is incomplete, the complete question is given below " Describe the range of possible distances from the beach to the theater "--

Step-by-step explanation:

least value is q

greatest value is n-q

close to zero is q-n

to get the equation of any straight line, we simply need two points off of it, let's use the provided ones

\(f(5)=-1\implies \underline{(\stackrel{x}{5}~~,~~\stackrel{y}{-1})}\hspace{5em}f(0)=-5\implies \underline{(\stackrel{x}{0}~~,~~\stackrel{y}{-5})} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{5}}} \implies \cfrac{-5 +1}{-5} \implies \cfrac{ -4 }{ -5 } \implies \cfrac{4 }{ 5 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{4 }{ 5 }}(x-\stackrel{x_1}{5}) \implies y +1 = \cfrac{4 }{ 5 } ( x -5) \\\\\\ y-1=\cfrac{4 }{ 5 }x-4\implies {\Large \begin{array}{llll} y=\cfrac{4 }{ 5 }x-3 \end{array}}\)

Answer:

5s^2 - 4s - 12

Step-by-step explanation:

Answer:

5s^2+4-12

Step-by-step explanation:

The types of triangles which can be used as a counterexample to the statement " all angles in a triangle are acute " are:

Obtuse

Right

Counter example in math's is defined as an attempt at showing that a mathematical statement is false.

Now, in this case we want to find the counter example that all angles in a triangle are acute angles.

Now, an acute angle is defined as an angle that is less than 90 degrees.

Now, A right angle fits the counter example statement because at least one angle is not less than 90 degrees.

Similarly, an Isosceles triangle does not fit the counter example argument because in an isosceles triangle, two angles are equal and it is possible for three of the angles to be less than 90 degrees.

An obtuse triangle means that one of the angles are greater than 90 degrees and as such this fits our counter example.

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Right triangles ABC and DEF are drawn to measure the slope of the line is:

a) run = 2 rise = 3 slope = 3/2

b) run = 6 rise = 9 slope = 9/6 = 3/2

c) Yes, they are similar because the 2 triangles are similar.

Two triangles are similar if they meet one of the following criteria. : Two pairs of corresponding angles are equal.

What is Right triangles?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

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