An airplane takes 9 hours to travel a distance of 8424 kilometers against the wind. The return trip takes 8 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

Answer:

C)  30 and 38

Step-by-step explanation:

In a normal distribution, 95% of the data points fall within two standard deviations of the mean.

Given:

To find the two values between which 95% of the data lies, subtract and add two standard deviations to the mean:

⇒ μ - 2σ = 34 - 2(2) = 34 - 4 = 30

⇒ μ + 2σ = 34 + 2(2) = 34 + 4 = 38

Therefore, 95% of the data lies between the values:

Answer:

43 °

Step-by-step explanation:

In the statement they mention the height and in addition to that the horizontal distance where a right triangle is formed, therefore we can apply a trigonometric ratio to calculate the angle, in this case it is the tangent, which relates the two legs of the angle:

Tan A ° = opposite / adjacent

opposite = 66, adjacent = 72, replacing we have:

Tan A ° = 66/72 = 0.9166

A ° = arc tan (0.9166)

A ° = 42.51

That is, the angle of elevation is 43 °

Answer:

Step-by-step explanation:

A=2(xy+xz+yz) where x,y,z are its dimensions

A=2(9(15)+9(8)+15(8))

A=2(135+72+120)

A=2(327)

A=654ft^2

V=xyz

V=9(15)8

V=1080ft^3

Answer:

A = 832 m²

Step-by-step explanation:

using the formula of a regular polygon with,

n = number of sides

s = Side length

a = apothem

Area = ½ × ans

Where n = 10, a = 16 and s = 10.4

A = ½ × 16 × 10 × 10.4

A = ½ × 1664

A = 832 m²

Answer:

area = 832 m²

Step-by-step explanation:

the area (A) is calculated as

A = \(\frac{1}{2}\) pa ( p is the perimeter and a the apothem )

a decagon has 10 sides , then

p = 10 × 10.4 = 104 m

A = \(\frac{1}{2}\) × 104 × 16 = 52 × 16 = 832 m²

The differentiation of \(e\x^{x}\) is \(e\x^{x}\) proved using the first law of differentiation or limit law.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

\(\frac{d}{dx}e\x^{x}\) using first order or limits to differentiate we get

for \(\lim_{h \to0} \frac{f(x+h) - f(x)}{h} = \frac{d}{dx}f(x)\)

therefore,

\(\lim_{h \to 0} \frac{e\x^{(x +h)}- e\x^{x} }{h} \\\) = \(\lim_{h \to 0} \frac{e\x^{x}(e\x^{h}-1 ) }{h}\) = \(\lim_{h \to 0} \frac{e\x^{x}*e\x^{h} }{1} \\\) ( using L-Hospital)

\(\lim_{h \to 0} e\x^{x} * e\x^{h} = e\x^{x} (proved)\)

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Step-by-step explanation:

13113x+1665
_____________________________
Rewrite 13113 as 9 .  1457

Rewrite 1665 as 9 .  185
= 9 .  1457x + 9 .  185
=9(1457x + 185)

Answer:16

Step-by-step explanation:

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

A: f(t) = t2(4t) - 14

B: It is a maximum because it continues redistributing forever.

C: Assuming you plotted this on a 0/0 grid, your axis of symetry would be at 18/28

Hope this helps, please mark brainliest

Step-by-step explanation:

A: it is simple really, your just redistributing each T to itself, which is what makes a square / vertex.

This one is pretty simple actually,

Starting from zero to get to 1.5 you add 1.5.

Same with -1.5 you just start from zero and go in reverse rather than going forward.

Hope this is helpful in some way.

Answer:

The correct answer is "$159 and $175".

Step-by-step explanation:

The give values are:

Mean,

= $167

Standard deviation,

\(\sigma\) = $40

Number of commuters,

n = 100

Now,

⇒ \(SE=\frac{\sigma}{\sqrt{n} }\)

On putting the given values, we get

⇒       \(=\frac{40}{\sqrt{100} }\)

⇒       \(=\frac{40}{10}\)

⇒       \(=4\)

By using the 2 SE rule of thumb, we get

= \($(167 - 2\times 4)\)

= \(167-8\)

= \(159\) ($)

Or,

= \((167 + 2\times 4)\)

= \(167+8\)

= \(175\) ($)

i.e,

$159 and $175

Answer:

c

Step-by-step explanation:

The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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The equivalent equation to the given one is:

h = A*t/(b - c)

We want to find an equation equivalent to the one below:

A = h*(b - c)/t

If we solve the equation for t, we would get:

t  = h*(b - c)/A

If we solve the equation for h, we will get:

h = A*t/(b - c)

If we solve the equation for b, we will get:

A = h*(b - c)/t

A*t/h = b - c

A*t/h + c = b

And if we solve it for c, we will get:

c = b - A*t/h

Then the correct option is the last one;

h = A*t/(b - c)

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Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

f(x) = x^3 - 6x^2 + 12x the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. The critical value that will give you a relative maximum is x = 4. The critical value that will give you a relative minimum is x = -2.

The derivative of the given function is f'(x) = 3x^2 - 12x + 12. Setting this equal to 0 gives us x = 0 and x = 4. By the first derivative test, we can determine that the function is increasing for x < -2, increasing for x > 4 and decreasing for -2 < x < 4. Therefore, the critical value that will give us a relative maximum is x = 4 and the critical value that will give us a relative minimum is x = -2. This can be verified by finding the second derivative of the function, which is f''(x) = 6x -12. Setting this equal to 0 gives us x = 2, which is between the two critical values. Since the second derivative is negative for x < 2, the critical value at x = -2 will give us a relative minimum and since it is positive for x > 2, the critical value at x = 4 will give us a relative maximum.

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Answer:

16

Step-by-step explanation:

18,903

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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The equation of L2 is y = 2x/3 + 23/3.

The equation of L3 is y = -3x/2 - 7.

The equation of L2 in standard form is 2x/3 - y = -23/3.

The x and y intercepts of L3 are (-4.667, 0) and (0, -7) respectively.

The point of intersection between L2 and L3 is (-6.769, 3.154).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about line 1 (L1) and line 2 (L2), we have the following equation;

Equation of line 1 (L1): 3x + 2y = 12

y = -3x/2 + 12

Since line L2 is perpendicular to L1 at (2, 9) and a slope of 2/3, the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y - 9 = 2/3(x - 2)

y = 2x/3 + 23/3

Since L3 is parallel to L1 and passes through point (-4, -1), the equation of L2 can be calculated as follows;

y - y₁ = m(x - x₁)

y + 1 = -3/2(x + 4)

y = -3x/2 - 6 - 1

y = -3x/2 - 7

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Answer:

  C)  (x, y) ⇒ (x -3, y -4), (5, -1)

Step-by-step explanation:

You know that the x-coordinate measures how far to the right of the y-axis a point is. If the point is moved 3 units left, it will be 3 fewer units to the right of the y-axis. That is, its x-coordinate will have changed from x to x-3.

Similarly, moving a point down 4 units reduces its y-coordinate by 4 units, so that y becomes y-4.

Together, these transformations are ...

  (x, y) ⇒ (x -3, y -4) . . . . . . matches choice C

Answer:

13) C= 95°, a= 0.157, c= 9.86

14) C= 165°, a= 3.35, b= 1.68

15) A= 40°, a= 2, c= 3.06

16) C= 50°, a= 11.8, c= 9.19

Step-by-step explanation:

Please see the attached pictures for the full solution.

Note:

sine rule

\( \textcolor{steelblue}{\boxed{{\frac{ \sin A}{a} = \frac{ \sin B }{b} = \frac{ \sin C}{c} }}}\)

∠ sum of ∆

The sum of the angles in a triangle is 180°.

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

\(A=b(b+\frac{5}{2} )\)

Step-by-step explanation:

hey there!!!

we know already that the area of a triangle is given as

\(A=\frac{1}{2}b *h\)

where b= base

and h= heigth

Given that the height is 5 times more than twice it base

let h= 2b+5

Now we substitute h=2b+5 in the area of the triangle

\(A=\frac{1}{2}b * (2b+5)\)

\(A= \frac{2b^2}{2} +\frac{5b}{2}\)

\(A= b^2+\frac{5b}{2}\\\\A=b(b+\frac{5}{2} )\)

The value of v in terms of i and j is v = 3i + 3j

We are given that;

P₁ = (-5,3), P₂ = (-2,6)

Now,

To find the component form of a vector, we need to subtract the coordinates of the initial point from the coordinates of the terminal point3.

We have P₁ = (-5,3) and P₂ = (-2,6).

v = P₂ - P₁ = (-2 - (-5), 6 - 3) = (3, 3). We can write v in terms of i and j as v = 3i + 3j.

Therefore, by vectors the answer will be v = 3i + 3j.

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Answer:  \(\textsf{285 total calories}\)

-------------------------------------------------------------------------------------------------------------

Given: \(\textsf{1 egg = 95 calories}\)

Find: \(\textsf{Calories in 3 eggs}\)

Solution: In order to determine the total amount of calories in 3 eggs we must multiply the amount of calories in one egg by 3.  So we do 95 * 3 which gives us 285 total calories.

"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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Answer:

(5+5)x2-12 = 8

Step-by-step explanation:

5+5=10, 10×2= 20-12 = 8

Answer:

.6

Step-by-step explanation:

Answer:

0.7

Step-by-step explanation:

0.66 shaded parts

round up to 0.70

take the 0 away

you get 0.7

On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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