Classify the following equation:H (x) = 2^(x/3)

The average speed of the plane in calm conditions is 619.35 miles/hour

Average:

Basically, an average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

A plane traveling from Phoenix to Washington, D. C with a tailwind of 20 miles per hour takes 3 hours. The return trip in the same wind, which is now a headwind, takes the same plane 3 hours and 12 minutes.

Here we need to find the average speed of the plane in calm conditions

While we looking into the given question, we have identified that,

Here we have the two timings

They are from time and to time.

The value of the from time 3 hours

And the value of to time 3 hours 12 minutes

So, in order to find the average is calculated as,

=> 3(s+20) = 3.20(s-20)

=> s = 620

=> 3*640 = 1920

=> 3840/(3 + 3.20) = 619.35

So, the average speed of the plane is 619.35 miles/hour

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Answer:

Looking at the given points we know that it is going to be a triangle because it only have 3 points.  Therefore the figure is a triangle and the area formula would be \(A=\frac{1}{2}*b*h\).

You can look at the attached graph and what we see is that our height of the triangle is from \(y=-3\) to \(y=4\) which means that our height is 7 units high.  We can also see that our base starts at \(x=-4\) and ends at \(x=4\) making us have a base of 8 units.

We then plug in the values and solve

\(A = \frac{1}{2}*7\ units * 8\ units\)

\(A = \frac{1}{2}*56\ units^2\)

\(A = 28\ units^2\)

Therefore, the area of our triangle is \(28\ units^2\)

Hope this helps!  Let me know if you have any questions

Answer: 50

Step-by-step explanation:

Answer:

5x(3x+7)

15x+35x

Answer= 50x

Step-by-step explanation:

First, distribute the 5X to both values in the parentheses. Then, because they have the same variable, add them together to get your final answer.  

First, subtract 4 from both sides:

\(5t\geq 15\)

Now, divide both sides of the equation by 5 to isolate variable t:

\(t\geq 3\)

Therefore, we know that t must be greater than or equal to 3 for this inequality to be true!

Curt and Melanie should use 0.45 quarts (or 0.45 * 32 = 14.4 ounces) of yellow paint to make seafoam green paint in a 1.5 quarts bucket.

To find out how much yellow paint Curt and Melanie should use, we need to determine the percentage of yellow paint in the seafoam green paint.

Since seafoam green paint is a mixture of 70% blue paint and 30% yellow paint, the remaining percentage will be the percentage of yellow paint.

Let's calculate it:

Percentage of yellow paint = 100% - Percentage of blue paint

Percentage of yellow paint = 100% - 70%

Percentage of yellow paint = 30%

Now we can use the percent equation to find out how much yellow paint should be used in a 1.5 quarts bucket.

Let "x" represent the amount of yellow paint to be used in quarts.

30% of 1.5 quarts = x quarts

0.30 * 1.5 = x

0.45 = x

Therefore, Curt and Melanie should use 0.45 quarts (or 0.45 * 32 = 14.4 ounces) of yellow paint to make seafoam green paint in a 1.5 quarts bucket.

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Answer: y=7x^2−42x+69

Step-by-step explanation:

Suppose a fair die is tossed twice, and X1 and X2 denote the scores obtained for the two tosses, respectively. Then, the probability distribution of the scores of the two tosses is given by P(X=k)=1/6 for k=1,2,3,4,5,6.

a)  Calculating E[X1] and var(X1)E[X1] is given by E[X1] = ∑k k P(X1 = k) = 1/6(1 + 2 + 3 + 4 + 5 + 6) = 7/2As we know that var (X1) = E[X1^2] - (E[X1])^2Now, E[X1^2] = ∑k k^2 P(X1 = k) = 1/6(1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2) = 91/6 and (E[X1])^2 = (7/2)^2 = 49/4. Therefore, var(X1) = 91/6 - 49/4 = 35/12

b) Probability distribution of Y = |X1 - X2| and [Y].The possible values of Y are 0, 1, 2, 3, 4, and 5. When Y = 0, it means X1 = X2, which can occur in 6 ways. When Y = 1, it means that (X1, X2) can be (1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (4, 3), (4, 5), (5, 4), (5, 6), or (6, 5). Thus, there are ten ways.

When Y = 2, it means that (X1, X2) can be (1, 3), (3, 1), (2, 4), (4, 2), (3, 5), (5, 3), (4, 6), or (6, 4). Thus, there are 8 ways. When Y = 3, it means that (X1, X2) can be (1, 4), (4, 1), (2, 5), (5, 2), (3, 6), or (6, 3). Thus, there are 6 ways.

When Y = 4, it means that (X1, X2) can be (1, 5), (5, 1), (2, 6), or (6, 2). Thus, there are 4 ways. When Y = 5, it means that (X1, X2) can be (1, 6) or (6, 1). Thus, there are two ways. Hence, the probability distribution of Y is given by,P(Y = 0) = 6/36P(Y = 1) = 10/36P(Y = 2) = 8/36P(Y = 3) = 6/36P(Y = 4) = 4/36P(Y = 5) = 2/36. Now, we have to find E[Y]E[Y] = ∑k k P(Y = k) = (0 x 6/36) + (1 x 10/36) + (2 x 8/36) + (3 x 6/36) + (4 x 4/36) + (5 x 2/36) = 35/18

c) (i) E(Z^2)=E(Y^2)We can obtain E(Y^2) by using the relation var(Y) = E(Y^2) - (E[Y])^2Now, E[Y^2] = var(Y) + (E[Y])^2 = 245/108Now, E(Z^2) = E[(X1 - X2)^2] = E[X1^2] + E[X2^2] - 2E[X1X2]As we know that E[X1^2] = 91/6 and E[X2^2] = 91/6andE[X1X2] = ∑i ∑j ij P(X1 = i and X2 = j) = ∑i ∑j ij(1/36) = 1/6(1 + 2 + 3 + 4 + 5 + 6)^2 = 49. Thus,E(Z^2) = 91/6 + 91/6 - 2(49) = 35/3 = 105/9. Therefore, E(Z^2) ≠ E(Y^2). So, the statement is False.

(ii) var(Z) = var(Y)We can find the variance of Z by using the relation var(Z) = E(Z^2) - (E[Z])^2. We know that E[Z] = E[X1 - X2] = E[X1] - E[X2] = 0Now, var(Z) = E(Z^2) - (E[Z])^2 = 35/3. Similarly, we know that var(Y) = E(Y^2) - (E[Y])^2 = 245/108 - (35/18)^2 = 455/324Now, var(Z) ≠ var(Y). So, the statement is False.

The expectation and variance of X1 is calculated to be E[X1] = 7/2 and var(X1) = 35/12. The probability distribution of Y = |X1 - X2| is tabulated and found to be P(Y = 0) = 6/36, P(Y = 1) = 10/36, P(Y = 2) = 8/36, P(Y = 3) = 6/36, P(Y = 4) = 4/36, P(Y = 5) = 2/36. The expectation of Y is calculated to be E[Y] = 35/18. Finally, it is shown that the statement E(Z^2) = E(Y^2) is False and the statement var(Z) = var(Y) is False.

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Answer:

\(\implies \footnotesize \text{ Average Speed} = \dfrac{ \text{Total Distance}}{ \text{Total time}} \\ \)

\(\implies \footnotesize \text{ Average Speed} = \dfrac{ 6.7 \: km}{ \frac{1}{2} \: hr }\)

\(\implies \footnotesize \text{ Average Speed} = 6.7 \times 2 \: km/h\)

\(\implies \footnotesize \textbf{ Average Speed = 13.4 \: km/h}\)

His rate is 13.4km/ hour

Data;

To solve this problem, we have to convert his speed from km/min to km/h

\(60min =1 hour\\\)

Since his rate is 6.7kmin 30 minutes, let's convert it to hour

\(6.7km = 30min\\x km = 1min\\x = \frac{6.7}{30} \\x = 0.223km/min\)

But to convert minutes to hours, we have to divide the time by 60

\(0.223\frac{km}{min}*60/1 = 13.4\)

From the calculation above, his rate is 13.4km/ hour

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The given statement is 1. Always true

2. Always true

3. Always true

4. Sometimes true

5. Never true

Statement 1: A line and a point are always coplanar.

Answer: Always true.

Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.

Statement 2: Congruent angles form vertical angles.

Answer: Always true.

Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.

Statement 3: Linear pairs that are congruent are right angles.

Answer: Always true.

Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.

Statement 4: The sum of angles that form a linear pair is less than 180 degrees.

Answer: Sometimes true.

Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.

Statement 5: Vertical angles are complementary.

Answer: Never true.

Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.

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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.

To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.

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Answer:

answers for the questions

Answer: 3.5

Step-by-step explanation:

It is an intersection of a tangent and a secant.

122=9(9+2a)
144=81+18a63= 18a3.5=a

Took test as well!

The numerical value of 'a' in the secant segment of the circle is 3.5.

The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment."

It is expressed as:

( tangent segment )² = External part of the secant segment × Secant segment.

From the diagram:

tangent segment = 12 ft

The external part of the secant-segment = 9 ft

Secant segment = ( a + a + 9 ) = 2a + 9

To determine the value of 'a', we use the secant-tangent power theorem.

12² = 9 × ( 2a + 9 )

Solve for 'a':

144 = 18a + 81

144 - 81 = 18a

63 = 18a

a = 63/18

a = 3.5

Therefore, 'a' has a value of 3.5.

Option C) 3.5 is the correct answer.

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Answer:

if i see the picture

i can probaly help

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

14 = 35% of x

35% = 0.35

So lets make an equation and solve for x:

14 = 0.35x

x = 14÷0.35

x = 40

To check our answer let's put it back into the question :

35% of 40 = 14

10% = 4 , 30% = 12 , 5% = 2

35% = 12+2 = 14 ✅

Hope this helped and have a good day

No, it's not a function

It is not a function because it doesnt pass the "vertical line test" and the "horizontal line test"

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer:

24$

Step-by-step explanation:

Answer:

Your answer would be $219.5

Step-by-step explanation:

9.75% of 200 is 19.5

19.5 + 200 = 219.5

Have a good day! - Zac

the equation of the horizontal line passing through (-3, 4) is y = 4.

The equation of a horizontal line is of the form y = c, where c represents the y-coordinate of any point on the line. In this case, we are given that the line passes through the point (-3, 4). Since the line is horizontal, the y-coordinate remains constant for all points on the line.

Therefore, the equation of the horizontal line passing through (-3, 4) is y = 4. This means that no matter what x-value we choose, the y-value will always be 4.

In other words, all the points on this line will have a y-coordinate of 4.

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Complete question is below

Write the equation of the horizontal line that passes through (-3, 4).

The equation for the horizontal line that passes through a given point is y = b.

A horizontal line is a straight line that is parallel to the x-axis. The equation of a horizontal line is of the form y = c, where c is a constant. Since the line is horizontal, the value of y remains constant for all values of x. Therefore, the equation of a horizontal line passing through a given point (a, b) is y = b.

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Answer:

Step-by-step explanation:

(-5a²b⁷)⁷ = (-5)⁷*(a²)⁷*(b⁷)⁷            {(x*y)ⁿ = xⁿ yⁿ}

              = (-5)⁷a²ˣ⁷ b⁷ˣ⁷              { (xᵃ)ᵇ = xᵃˣᵇ}

              = (-5)⁷a¹⁴b⁴⁹

Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:

A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.

This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.

Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.

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Step-by-step explanation:

Let alpha be the unknown angle. We can set up our sine law as follows:

\( \frac{ \sin( \alpha ) }{5 \: m} = \frac{ \sin(42) }{3.6 \: m } \)

or

\( \sin( \alpha ) = \frac{5 \: m}{3.6 \: m} \times \sin(42) = 0.929\)

Solving for alpha,

\( \alpha = arcsin(0.929) = 68 \: degrees\)

Answer:

(x-3) (x+1)

Step-by-step explanation:

Factor

x^2 − 2x + 3

What two numbers multiply to 3 and add to -2

3 and -1

(x-3) (x+1)

Answer:

-2

Step-by-step explanation:

Answer:

x = 40°

Step-by-step explanation:

The base angles of the triangle are 71° and 69° ( vertical angles ) , then

x = 180° - (71 + 69)° = 180° - 140° = 40°

Answer:

Answer:

Step-by-step explanatinon:

percent is per hundred

4 dimes is  40 cents or $0.40 or 40/100 of a dollar which is40%

1 nickel and 3 pennies or 8 cents or $0.08 Or 8/100 or 8%

5 quarters and one dime is 135/100 or  $1.35 or 135/100 which is 135%

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

7 dimes and 1 nickel = 7*10 + 5 = 75 cents.

A dollar has 100 cents

75 cents * 1 dollar/100  cents  * 100 =

0.75 * 100 = 75%

The height of the rectangular prism can be calculated using the following formula:

Volume (V) = Length (L) * Width (W) * Height (H)

Therefore, rearranging the formula, we can calculate the height of the prism:

Height (H) = Volume (V) / (Length (L) * Width (W))

For this problem, plugging in the known values, we get:

Height (H) = 490 cm³ / (10 cm * 7 cm)

Therefore,

Height (H) = 8.14 cm

The time after which the planes will be 800 kilometers apart is: 3.2 hours

Let x be the time in hours taken for the planes be 800 km apart.

First plane would have travelled (200 ⋅ x) km in x hours.

Second plane would have travelled (400 ⋅ (x − 2)) km after x hours as it had started 2 hours behind.

Since first plane has left towards east and the second towards south, they moved in perpendicular directions and we can conveniently apply Pythagoras Theorem.

(200x)² + (400(x - 2))² = 800²

200²(x² + (2(x - 2))²) = 800²

x² + 4x² - 16x + 16 = 16

x² + 4x² - 16x = 0

5x²  = 16x

x = 16/5

x = 3.2 hours

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The solution to the system of equations is x = 3, y = 4, option C is correct.

To solve the system of equations using a graphing calculator, we first need to rewrite the equations in slope-intercept form:

y - 2x = -2 can be rewritten as y = 2x - 2

y - x = 1 can be rewritten as y = x + 1

From the graph, we can see that the lines intersect at the point (3, 4). Therefore, the solution to the system of equations is x = 3, y = 4

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Given,An investment of $50,000 in property taxes and rental income received of $800 per month, annual taxes of $1,500 paid monthly for four years.

We need to calculate the Return on Investment (ROI).Let us begin with calculating the total amount of rental income received by multiplying the monthly rental income by 12 and then multiplying the resultant by 4, as it is for 4 years. Rental income received= 12 × 4 × 800 = $38,400

Now, let us calculate the total amount of taxes paid by multiplying the annual taxes by 4. Annual taxes = $1,500Total taxes paid

= 4 × $1,500

= $6,000Now, let us calculate the ROI. ROI

= (Total rental income received − Total expenses)/Total investment

= (38,400 − 6,000)/50,000

= 32,400/50,000

= 0.648 or 64.8%

The ROI for the investment is 64.8%. Hence, e. 4.25% is the correct option.

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