Rashawn and Jessie are playing a game where they lose the same number of points that they would have earned for each incorrect answer. Rashawn answers two 3-point questions incorrectly, and Jessie answers four 2-point questions incorrectly. If neither player has answered a question correctly, who is ahead? Explain.

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

Answer:

4/9, 11/13, 6/5

Step-by-step explanation:

About -$10.15 that is, on average you lose about 15 cents.

Using the principle of discrete probability, the expected value, which is a measure of the mean amount after many plays is - 2/13

Calculating the required probabilities :

P(winning) = P(drawing an Ace) = 4/52 = 1/13

Hence, P(losing) = 1 - 1/13 = 12/13

X :____ 10 _____ - 1

P(X) : _ 1/13_____ 12/13

The expected value :

E(X) = 10 × (1/13) + - 1(12/13)

E(X) = 10/13 - 12/13

E(X) = - 2/13

Hence, the measure of the mean amount is -2/13.

The victory value is $10, and the loss value is $-1.

Out of a total of 52 cards, this deck has 4 aces.

The probability can then be defined as the ratio of the number of desirable outcomes to the number of possible outcomes.

P(win) = number of favorable outcome/number of the possible outcome

= 4/52

= 1/13

P(loss) = number of favorable outcome/number of the possible outcome

= 48/52

= 12/13

Then we have

$10x1/13 + (-1)x12/13

= 10/13-12/13

= -2/13 dollars

= -$0.15

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Answer:

$20.44

Step-by-step explanation:

The average of a set of numbers is defined as:

\(\dfrac{\textrm{sum of values}}{\textrm{number of values}}\)

In this problem, we are shown a table where each row has a coupon value in the left column and the number of that coupon value in the right column (e.g., if we look at the top row, we can see there are 70 coupons each valued at $10).

So, the sum of values in this problem (i.e., the total number of dollars given out by the store in the form of coupons) is defined as the sum of the product of each row.

\(\textrm{sum of values} = (\$10 \times 70) + (\$20 \times 40) + (\$40 \times 20) + (\$60 \times 4) + (\$120 \times 2)\)

\(\textrm{sum of values} = \$700 + \$800 + \$800 + \$240 + \$240\)

\(\textrm{sum of values} = \$2780\)

The number of values in this problem is just the sum of the numbers in the right column (i.e., the number of coupons given out).

\(\textrm{number of values} = 70 + 40 + 20 + 4 + 2\)

\(\textrm{number of values} = 136\)

Finally, to answer the problem, we can plug the two numbers that we just solved for into the formula for the average of a set.

\(\textrm{average savings} = \dfrac{\textrm{value of all tickets}}{\textrm{number of tickets}}\)

\(\textrm{average savings} = \dfrac{\$2780}{136}\)

\(\textrm{average savings} \approx \$20.44\)

The position of A on the number line is

Number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line.

As seen of the number line above , it is numbered in the sequence, 1,.. 2,...3 and the intervals are indicated.

Between 0 and 1 there are 5 lines, these means that each line will be 4/5

If 1 line is 4/5 , therefore ;

4 lines will be 4 × 4/5

= 16/5 = 3 1/2

Therefore the position of A on the number line is 3 1/2

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Answer: The value of the limit of the function may not be equal to the value of the function evaluated at a particular x-value. In other words, just because a function takes on a certain value at a particular x-value doesn't mean that the limit of the function at that x-value is equal to that value. To determine the limit of the function, you may need to use different methods such as L'Hopital's Rule or other limit laws. Additionally, it's important to keep in mind that the limit of the function may not exist, in which case it wouldn't be equal to any specific value.

Step-by-step explanation:

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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Working with the right side,

(1 + sin(θ))/(1 - sin(θ)) - (1 - sin(θ))/(1 + sin(θ))

multiply the first term by (1 + sin(θ))/(1 + sin(θ)) and the second one by (1 - sin(θ))/(1 - sin(θ)). This gives

(1 + sin(θ))/(1 - sin(θ)) • (1 + sin(θ))/(1 + sin(θ)) = (1 + sin(θ))^2 / (1 - sin^2(θ))

… = (1 + sin(θ))^2 / cos^2(θ)

and

(1 - sin(θ))/(1 + sin(θ)) • (1 - sin(θ))/(1 - sin(θ)) = (1 - sin(θ))^2 / (1 - sin^2(θ))

… = (1 - sin(θ))^2 / cos^2(θ)

Now combine the fractions, expand the numerator, and simplify:

(1 + sin(θ))^2 / cos^2(θ) - (1 - sin(θ))^2 / cos^2(θ) = ((1 + sin(θ))^2 - (1 - sin(θ))^2) / cos^2(θ)

… = ((1 + 2 sin(θ) + sin^2(θ)) - (1 - 2 sin(θ) + sin^2(θ))) / cos^2(θ)

… = 4 sin(θ) / cos^2(θ)

… = 4 • sin(θ)/cos(θ) • 1/cos(θ)

… = 4 tan(θ) sec(θ)

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

Answer:

85

Step-by-step explanation:

the mean is equal to=99+66+90=255

255÷3=85

Answer:

Anna's test average would be 85%.

Step-by-step explanation:

To find the average, you have to do 66 + 90 + 99 to get an answer of 255. The next thing you do is divide 255 by 3 to get a final answer of 85%. :) I hope this helps! ^^

The three Pythagorean trigonometric identities, which I’m sure one can find in any Algebra-Trigonometry textbook, are as follows:

sin² θ + cos² θ = 1

tan² θ + 1 = sec² θ

1 + cot² θ = csc² θ

where angle θ is any angle in standard position in the xy-plane.

Consistent with the definition of an identity, the above identities are true for all values of the variable, in this case angle θ, for which the functions involved are defined.

The Pythagorean Identities are so named because they are ultimately derived from a utilization of the Pythagorean Theorem, i.e., c² = a² + b², where c is the length of the hypotenuse of a right triangle and a and b are the lengths of the other two sides.

This derivation can be easily seen when considering the special case of the unit circle (r = 1). For any angle θ in standard position in the xy-plane and whose terminal side intersects the unit circle at the point (x, y), that is a distance r = 1 from the origin, we can construct a right triangle with hypotenuse c = r, with height a = y and with base b = x so that:

c² = a² + b² becomes:

r² = y² + x² = 1²

y² + x² = 1

We also know from our study of the unit circle that x = r(cos θ) = (1)(cos θ) = cos θ and y = r(sin θ) = (1)(sin θ) = sin θ; therefore, substituting, we get:

(sin θ)² + (cos θ)² = 1

1.) sin² θ + cos² θ = 1 which is the first Pythagorean Identity.

Now, if we divide through equation 1.) by cos² θ, we get the second Pythagorean Identity as follows:

(sin² θ + cos² θ)/cos² θ = 1/cos² θ

(sin² θ/cos² θ) + (cos² θ/cos² θ) = 1/cos² θ

(sin θ/cos θ)² + 1 = (1/cos θ)²

(tan θ)² + 1 = (sec θ)²

2.) tan² θ + 1 = sec² θ

Now, if we divide through equation 1.) by sin² θ, we get the third Pythagorean Identity as follows:

(sin² θ + cos² θ)/sin² θ = 1/sin² θ

(sin² θ/sin² θ) + (cos² θ/sin² θ) = 1/sin² θ

1 + (cos θ/sin θ)² = (1/sin θ)²

1 + (cot θ)² = (csc θ)²

3.) 1 + cot² θ = csc² θ

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

20 blogs

Step-by-step explanation:

Step 1:  Determine the proportion of pop culture blogs:

First, we need to determine the proportion of pop culture blogs already written.  We can do this by dividing the number of pop culture blogs already written by the total number of blogs written:

The proportion of pop culture bloggers = Number of pop culture bloggers / Total number of bloggers

Proportion =  26 / (20 + 26 + 7 + 12)

Proportion = 26 / 65

Proportion = 0.4

Step 2:  Multiply the proportion of pop culture blogs by the number of upcoming blogs:

To determine the expected number of pop culture blogs that will be written given the data, we can multiply the proportion of pop culture blogs already written by the number of upcoming blogs:

Expected number of pop culture blogs = proportion of pop culture blogs *  number of upcoming blogs

Expected number = 0.4 * 50

Expected number = 20

Thus, you should expect 20 pop culture blogs to be written given the data.

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Note: Check the file attached below for the complete question

Answer:

Betty's monthly take home is $20 less

Step-by-step explanation:

Betty's monthly income = $2300

Betty's monthly savings = $200

Amount left after savings = $2300 - $200

Amount left after savings = $2100

Federal and State Income tax rate = 20% = 0.2

Tax amount paid = $420

Monthly take home = $2100 - $420

Monthly take home = $1680

Compared to $150 per month savings, Betty's monthly take home is $20 less

The required it will take 2 hours for the friends to put 7 km between them.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the number of hours it takes the friends to be "x". During that time, Rae will have traveled 2x km. And Dana will have traveled 3(x-1) km (since she left an hour later).

We can now set up an equation:

2x + 3(x-1) = 7

Expanding the second term:

2x + 3x - 3 = 7

Combining like terms:

5x - 3 = 7

Adding 3 to both sides:

5x = 10

Finally, dividing both sides by 5:

x = 2

So it will take 2 hours for the friends to put 7 km between them.

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A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.

The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.

The next step is to branch from the starting point and show the possible results of the first event. This includes taking out  the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.

After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.

The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.

The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome

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Answer:

Men: 18%

Women: 42%

Boys: 18%

Girls: 22%

Children: 40%

Step-by-step explanation:

Answer:

2/45+1/9=

7/45

Have a great day

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

  84 men

Step-by-step explanation:

The ratio of men to children is ...

  men/children = 35%/30% = 7/6

Given the number of children is 72, the number of men is ...

  men/children = 7/6 = men/72

  men = (7/6)(72) = 84

There are 84 men at the party.

_____

Additional comment

The fraction of women is 100% -30% -35% = 35%, the same as the number of men. There are 84 women at the party and 240 total people.

Angles and lines come in many distinct varieties in geometry.

Geometry has several different kinds of lines and angles. The six different types of angles include reflex angle, complete angle, straight angle, acute angle, and obtuse angle. The various sorts of lines are transverse, parallel, perpendicular, vertical, horizontal, and vertical lines.

There are three ways to name an angle: by the vertex, by the angle's three points (the middle point must be the vertex), or by a letter or number put inside the angle's aperture.

You can create your address block for letters, envelopes, and other mail merges using Label Lines, a collection of fields. Use Label Lines rather of Acknowledgement, Company, and Address lines to skip blank lines in your labels and address blocks.

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The speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.

We are given the speed of a plane on a bearing of N \(75^\circ\) E and its ground speed. We have to find its speed in miles per hour and the direction angle in degrees. We will apply the formula of projection for both the x-axis and y-axis.

As we know, projection, R = V + W

Now, the x-axis projection will be R cos\(15^\circ\) according to the angle given to us. Therefore, R cos \(15^\circ\) = V cos\(30^\circ\) + \(W_{x}\)

The y-axis projection,

R sin \(15^\circ\) = V sin \(30^\circ\) + \(W_{y}\)

From here, now we will find \(W_{x}{\) and \(W_{y}\)

\(W_{x}{\) = 330 cos\(15^\circ\) - 390 cos\(30^\circ\)

\(W_{x}\) = -19 miles/hour

\(W_{y}\) = 330 sin\(15^\circ\) - 390 sin\(30^\circ\)

\(W_{y}{\) = -109.6 miles per hour

Now, W = \(\sqrt{(W_{x})^{2} + (W_{y})^{2{}}\)

W = \(\sqrt{(-19.0)^{2} + (-109.6})^{2{}}\)

W = 111.2 miles/hour

Now, we will find the angle with the help of tan θ.

tan θ = \(\frac{W_{y}}{W_{x}}\)

tan θ = \(\frac{-109.6}{-19.0}\)

θ =  \(tan ^{-1} (\frac{109.6}{19.0})\)

θ = 260.\(2^\circ\)

Therefore, the speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.

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Answer: 155

Step-by-step explanation:

ok done. Thank to me :>