£10 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Gordon get?

The value of x, in the triangle shown is: C. 5.25.

In the image given, the triangles shown are similar to each other, which means that their corresponding side lengths are proportional to each other.

Therefore, we would have the following proportion:

x / 2 = 16.8 / 6.4

Cross multiply:

6.4 * x = 16.8 * 2

6.4x = 33.6

6.4x/6.4 = 33.6/6.4

x = 5.25

The correct value of x is: C. 5.25.

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From the calculation, all three inequalities are satisfied, which means that the given measurements produce one triangle.

To determine whether the given measurements produce one triangle, two triangles, or no triangle at all, we can use the Law of Sines and the Triangle Inequality Theorem.

Given:

a = 10

b = 13.6

A = 33°

Determine angle B:

Angle B can be found using the equation: B = 180° - A - C, where C is the remaining angle of the triangle.

B = 180° - 33° - C

B = 147° - C

Apply the Law of Sines:

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

a/sin(A) = b/sin(B) = c/sin(C)

We can rearrange the equation to solve for side c:

c = (a * sin(C)) / sin(A)

Substituting the given values:

c = (10 * sin(C)) / sin(33°)

Determine angle C:

We can use the equation: C = arcsin((c * sin(A)) / a)

C = arcsin((c * sin(33°)) / 10)

Apply the Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, we need to check if a + b > c, b + c > a, and c + a > b.

If all three inequalities are satisfied, it means that the measurements produce one triangle. If one of the inequalities is not satisfied, it means no triangle can be formed.

Now, let's perform the calculations:

B = 147° - C (from step 1)

c = (10 * sin(C)) / sin(33°) (from step 2)

C = arcsin((c * sin(33°)) / 10) (from step 3)

Using a calculator, we find that C ≈ 34.65° and c ≈ 6.16.

Now, let's check the Triangle Inequality Theorem:

a + b > c:

10 + 13.6 > 6.16

23.6 > 6.16 (True)

b + c > a:

13.6 + 6.16 > 10

19.76 > 10 (True)

c + a > b:

6.16 + 10 > 13.6

16.16 > 13.6 (True)

All three inequalities are satisfied, which means that the given measurements produce one triangle.

In summary, with the given measurements of a = 10, b = 13.6, and A = 33°, we can determine that one triangle can be formed. The measures of the angles are approximately A = 33°, B ≈ 147° - C, and C ≈ 34.65°, and the lengths of the sides are approximately a = 10, b = 13.6, and c ≈ 6.16.

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Answer: -17

Step-by-step explanation:

-2(7)-3=

-14-3=-17

Answer:

-94%, -.925, -9/10, -8/9

Step-by-step explanation:

-.94, -.8, -.925, -.9

-.94, −0.925, −0.9, -0.8

Answer: The answer is B.

Step-by-step explanation: This is because the x-axis is days, and the y-axis is pounds. The option B states that Winnie eats 5 pounds of dog food in 2 days, while actually the dog eats 2 pounds of dog food in 5 days.

Answer:

Its B!

Step-by-step explanation:

The X axis represents days and the Y axis represents pounds! 5 is the X axis and 2 is the Y axis! So to make the sentence true, it would be (2,5).

Hope this helps, and don't forget to follow!

a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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All three graphs (d), (e), and (f) have infinite connected components.

To determine the number of connected components in the given graphs, we need to analyze the connectivity of the vertices based on the given edge conditions.

(d) V(G) = Z×Z, Edges: (a, b) is adjacent to (c, d) if and only if (c−a, d−b) = (4, 2) or (c − a, d − b) = (−4, −2) or (c − a, d − b) = (1, 2) or (c − a, d − b) = (−1, −2).

This graph has infinite connected components since for any vertex (a, b), there will always be adjacent vertices satisfying the given edge conditions.

(e) V(G) = Z×Z, Edges: (a, b) is adjacent to (c, d) if and only if (c−a, d−b) = (5, 2) or (c − a, d − b) = (−5, −2) or (c − a, d − b) = (2, 3) or (c − a, d − b) = (−2, −3).

Similar to the previous graph, this graph also has infinite connected components since for any vertex (a, b), there will always be adjacent vertices satisfying the given edge conditions.

(f) V(G) = Z×Z, Edges: (a, b) is adjacent to (c, d) if and only if (c−a, d−b) = (7, 2) or (c − a, d − b) = (−7, −2) or (c − a, d − b) = (3, 1) or (c − a, d − b) = (−3, −1).

Similarly, this graph also has infinite connected components since for any vertex (a, b), there will always be adjacent vertices satisfying the given edge conditions.

In summary, all three graphs (d), (e), and (f) have infinite connected components.

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Answer:

50.27

Step-by-step explanation:

π-3.14 so...

3.14*r^2

\(area = π {r}^{2} = 3.14 \times {4}^{2} \)

\(area = 3.14 \times 16 = 50.24\)

Done.....♥️♥️♥️♥️♥️

The evaluated square root is 1, for the given function is\(f (x)= sin^{-1} (x)\)
We can use the chain rule to find f'(x) given function is\(f (x)= sin^{-1} (x)\) . The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x).

Let  us consider that h(x) = square root(3)/2.
Now,\(sin^{-1} (h(x)) = sin^-1(\sqrt{(3)/2} ).\)

So let take  sin(60°) = square root(3)/2 .
Then,
\(sin^{-1} (\sqrt{(3)/2)} )\)

= 60°.

Now let us implement the chain rule
f'(√(3)/2) = cos(60°) / \(\sqrt{(1 - (\sqrt{(3)/2} )^2)}\)

f'(√(3)/2) = cos(60°) / √(1/4)

f'√(3)/2) = cos(60°) * 2

f'(√(3)/2) = 1

The evaluated square root is 1, for the given function is\(f (x)= sin^{-1} (x)\)
We can use the chain rule to find f'(x) given function is\(f (x)= sin^{-1} (x)\) . The chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x).

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the parameters we are estimating using the OLS method must be themselves linear

What are the Gauss Markov assumptions?

Gauss Markov Assumptions

Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.

What are the properties of Gauss Markov Theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

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The probability that Juan loses his next tennis match is 48%

From the question, we have the following parameters

The proportion of tennis matches won

p = 52%

This proportion implies that the probability that the player will win his next tennis match

So, we have the following representations

Probability of winning, p = 52%

Express the percentage as decimal

So, we have the following representations

Probability of winning, p = 0.52

The probability of losing the next match is the complement of the probability of winning

This is represented as

Probability of losing = 1 - Probability of winning,

Substitute the known values in the above equation

So, we have the following equation

Probability of losing = 1 - 0.52

Evaluate

Probability of losing = 0.48

Hence, the probability is 0.48 or 48%

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An equation of the plane that contains all the points that are equidistant from (-7, 3, 1) and (6, - 2, 3) is,

⇒ 13x - 11y + 12z = 105

Now, Let (x, y, z) be a point on the plane that contains all the points that are equidistant from (-7, 3, 1) and (6, -2, 4).

Then, the distance from (x, y, z) to (-7, 3, 1) is equal to the distance from (x, y, z) to (6, -2, 4).

Hence, By Using the distance formula, we get:

√[(x - (-7))² + (y - 3)² + (z - 1)²]

= √[(x - 6)² + (y + 2)² + (z - 4)²]

Squaring both sides, we get:

(x - (-7))² + (y - 3)² + (z - 1)²

= (x - 6)² + (y + 2)² + (z - 4)²

Expanding and simplifying, we get:

13x - 11y + 12z = 105

Therefore, an equation of the plane that contains all the points that are equidistant from (-7, 3, 1) and (6, - 2, 3) is,

⇒ 13x - 11y + 12z = 105

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To find the general solution to the given differential equation, we start with the equation:

\(\[ y(x) = C1e^{-3x} + C2e^{4x} \]\)

We are given the initial conditions:

\(\[ y(0) = 13 \]\) and \(\[ y'(0) = -4 \]\)

Let's find the values of C1 and C2 using these initial conditions.

Substituting \(\( x = 0 \)\) into the equation \(\( y(x) \)\), we have:

\(\[ y(0) = C1e^{-3 \cdot 0} + C2e^{4 \cdot 0} = C1 + C2 = 13 \]\)

This gives us the first equation: \(\( C1 + C2 = 13 \)\).

Next, we differentiate \(\( y(x) \)\) with respect to \(\( x \)\):

\(\[ y'(x) = -3C1e^{-3x} + 4C2e^{4x} \]\)

Substituting \(\( x = 0 \)\) and \(\( y'(0) = -4 \)\) into the equation, we have:

\(\[ y'(0) = -3\)

\(C1e^{-3 \cdot 0} + 4C2e^{4 \cdot 0} = -3C1 + 4C2 = -4 \]\)

This gives us the second equation: \(\( -3C1 + 4C2 = -4 \)\).

We now have a system of two equations with two unknowns (C1 and C2):

\(\[C1 + C2 &= 13 \\-3C1 + 4C2 &= -4\]\)

Solving this system of equations, we can find the values of C1 and C2.

Multiplying the first equation by 3, we have:

\(\[ 3C1 + 3C2 = 39 \]\)

Adding this equation to the second equation, we \(\[ C2 = 5 \]\) C1:

\(\[ 3C1 + 3C2 + (-3C1 + 4C2) = 39 + (-4) \]\)

Simplifying the equation, we get:

\(\[ 7C2 = 35 \]\)

Dividing both sides by 7, we find:

\(\[ C2 = 5 \]\)

Substituting this value of C2 back into the first equation, we have:

\(\[ C1 + 5 = 13 \]\)

Subtracting 5 from both sides, we find:

\(\[ C1 = 8 \]\)

Therefore, the values of C1 and C2 are C1 = 8 and C2 = 5.

The specific solution to the differential equation is:

\(\[ y(x) = 8e^{-3x} + 5e^{4x} \]\)

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Answer:

$141.33

Step-by-step explanation:

He gave $100 to one fried and 158.67 to another

100+158.67=258.67

Answer:

$141.33

Step-by-step explanation:

25% of 400 is 100

$100 to his friend and $158.67 to the other friend

100+158.67= 258.67 to his friends all together

(His money before)--> $400-$258.67<---(The money he gave)

=$141.33

The statement "Despite their efforts, the shoguns were unable to prevent Japan from becoming a colony of a European power" is true.

During the late 19th and early 20th centuries, Japan faced increasing pressure from European powers to open up to foreign trade and influence. Despite the efforts of the shoguns to resist foreign control and maintain their independence, Japan eventually succumbed to colonization by a European power. This marked a significant shift in Japan's political and social landscape, leading to the transformation of its feudal system and the emergence of a centralized imperial government.

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Answer:

11.25

77.85

Step-by-step explanation:

1.6x + 3 = 21

use inverse operation (+ = -, x = ÷) by taking 3 to the opposite side and changing it's integer to negative

1.6x = 21 - 3

divide 2 sides by 1.6

1.6x = 18

1.6x/1.6 = 18/1.6

x = 11.25//

2.15(x-5)=75

inverse operation

x= 75 - 2.15 + 5

x= 77.85//

Answer:

1 muffin is 5.25 and 1 cup of coffee is 3.95

Step-by-step explanation:

32.85 - 22.35 is 10.5. 10.5 divided by 2 is 5.25 that is the cost of 1 muffin. 22.35 - 10.5 is 11.85. 11.85 divided by 3 is 3.95.

Answer:

2.22

Step-by-step explanation:

4/9 x 5

The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

34

Step-by-step explanation:

1 and 2 of sequence are both in 10s

so 67/2 = 33.5

closest to 33.5 = 34 that follows the sequence

We have that the equation of a line is:

y = m + bx

where, m is the slope, but to know the slope we have a formula that is:

m = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

We have 3 points of the line:

(2,8); (0,2); (3,-7)

When we want to know the slope we need two points and they can be any two points in any order, so we can say we are going to use:

Point 1:

(2,8)

Point 2:

(0,2)

\(y_{1}\) = 8 ;   \(y_{2}\) = 2

\(x_{1}\) =2 ;    \(x_{2}\) =0

Now we substitute the values in the formula for m:

m = \(\frac{(2-8)}{(0-2)}\)

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

m = 3

So, the slope is 3.

Using the power-reducing formula, the simplified tangent expression is given as follows:

tan^4(3x) = [3 – 4 cos (6x) + cos (12x)] / [3 + 4 cos (6x) + cos (12x)]

Power-reducing formulas are formulas for which the nth power of a trigonometric expression can be written using only trigonometric expressions of power 1.

For the fourth order of the tangent of an angle, the expression is given as follows:

tan^4(u) = [3 – 4 cos (2u) + cos (4u)] / [3 + 4 cos (2u) + cos (4u)]

For this problem, the expression is:

tan^4(3x).

Hence comparing to the standard formula, we have that u = 3x, hence the equivalent expression is given as follows:

tan^4(3x) = [3 – 4 cos (6x) + cos (12x)] / [3 + 4 cos (6x) + cos (12x)]

We just replaced each instance of u in the formula by 3x.

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Answer:

74

Step-by-step explanation:

answer: 74

explanation: hope it helped

The balance after 5 years when the interest is compounded quarterly is  $5,593.60

Compound Interest:

Compound interest is the principal plus interest on a loan or deposit, or in other words, principal plus interest. It is the result of reinvesting interest, or adding it to the principal borrowed instead of paying it, or demanding payment from the borrower so that the next installment of interest is principal plus previously accrued interest. Compound interest is the norm in finance and economics.

Lets use the compound interest formula provided to solve this:

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 2.25% into a decimal:

2.25% > 2.25/100 > 0.0225

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

      \(A = (1+\frac{0.0225}{4} )4(5)\\\)

Or, A = 5593.60

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Answer:

the answer is A and C

Step-by-step explanation:

to be an exponential decay the Y values should decrease as you increase x value, so from the graph, both B and D are increasing Y values, so they are incorrect

the answer is A and C

Answer:

300

Step-by-step explanation:

You simply multiply 50 and 6.  I hope you have a nice day.  :)

Answer:

300 :3

Step-by-step explanation:

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 50 = 300