A dragon flew 300 miles from his castle to visit a friend. Flying with the wind, his trip took 2 hours. His return trip against the wind took 3 hours. What was the speed of the wind and the speed of the dragon in still air?


Please help me. I WILL mark brainliest and give lots of points.

Answer:

Step-by-step explanation:

To solve for y, isolate it on one side of the equation.

First, switch sides.

c=y+a

y+a=c

Then, you subtract by a from both sides.

y+a-a=c-a

Solve.

[tex]\Longrightarrow:\boxed{\sf{y=c-a}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

0.8L = red

0.64L = yellow

0.06L = white

Step-by-step explanation:

R : Y : W

20 : 16 : 1.5

20 + 16 + 1.5 = 37.5

1.5 ÷ 37.5 = 0.04

0.04 × 20 = 0.8L = red

0.04 × 16 = 0.64L = yellow

0.04 × 1.5 = 0.06L = white

The recursive definition of the geometric sequence is given by:

A. [tex]a_n = (0.8)a_{n-1}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The basic recursive relation is given as follows:

[tex]a_n = qa_{n-1}[/tex]

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, considering the given sequence, the common ratio is given by:

[tex]q = \frac{6144}{7680} = \frac{7680}{9600} = \frac{9600}{12000} = 0.8[/tex]

Hence option A is correct.

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The values of the motorcycle follows a geometric sequence

The recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

The values are given as:

$12,000 $9,600, $7,680, $6,144

Calculate the common ratio using:

r = a2/a1

So, we have:

r = 9600/12000

Divide

r = 0.8

Recall that:

r = a2/a1

So, we have:

a2/a1 = 0.8

Multiply both sides by a1

a2 = 0.8a1

Rewrite as:

[tex]a_{2} = 0.8a_{2-1[/tex]

Substitute n for 2

[tex]a_{n} = 0.8a_{n-1[/tex]

Hence, the recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

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Answer:

Step-by-step explanation:

(a). 5.33 m

(b). 41.65 m²

Answer:

32

Step-by-step explanation:

Answer:

14.3

Step-by-step explanation:

Formula: a^2 + b^2 = c^2

9+196= 205 then find the square root of 205, approximate then use tenths.

Answer:

14.3

Step-by-step explanation:

Use the following equation:

a² + b² = c² , in which the variable c = hypotenuse, and a & b are the other legs.

It is given that the legs measure 3 and 14 respectively. Plug in the given numbers to the given leg variables:

a² + b² = c²

3² + 14² = c²

Simplify. First, solve the powers, and then combine like terms:

(3 * 3) + (14 * 14) = c²

9 + 196 = c²

c² = 205

Next, root both sides of the equation:

√c² = √205

c = √205 = 14.3178

c = 14.3 (Rounded to the nearest tenth).

14.3 is your answer.

~

Answer:

327.5 feet²

Step-by-step explanation:

Let's divide the figure into multiple shapes (Refer to image). To determine the area of the figure, we need to find the area of the divided shapes, then sum it up to obtain the area of the figure.

Determining the area of the triangle:

Given dimensions:

Determining the base of the triangle:

[tex]22 + b + 5 = 7 + 8 + 17[/tex]

[tex]27 + b = 32[/tex]

[tex]b = 32 - 27[/tex]

[tex]b = 5 \ \text{ft}[/tex]

Substituting the base and the height:

[tex]\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}[/tex]

[tex]\text{Area of triangle} = \frac{1}{2} \times 5\times11[/tex]

Simplifying the R.H.S to determine the area:

[tex]\text{Area of triangle} = 5\times5.5[/tex]

[tex]\text{Area of triangle} = 27.5 \ \text{ft}^{2}[/tex]

Determining the area of rectangle₁

Given dimensions:

Substitute the length and the breadth:

[tex]\text{Area of rectangle}_{1}} = LB[/tex]

[tex]\text{Area of rectangle}_{1}} = (5)(17)[/tex]

Simplify the R.H.S to determine the area:

[tex]\text{Area of rectangle}_{1}} = 85 \ \text{feet}[/tex]

Determining the area of rectangle₂

Given dimensions:

Substitute the length and the breadth:

[tex]\text{Area of rectangle}_{2} = LB[/tex]

[tex]\text{Area of rectangle}_{2} = (7 + 5)(8)[/tex]

Simplify the R.H.S to determine the area

[tex]\text{Area of rectangle}_{2} = (7 \times 8) + (5 \times 8)[/tex]

[tex]\text{Area of rectangle}_{2} = 56+ 40[/tex]

[tex]\text{Area of rectangle}_{2} = 96 \ \text{feet}^{2}[/tex]

Determining the area of rectangle₃

Given dimensions:

Substitute the length and the breadth:

[tex]\text{Area of rectangle}_{2} = LB[/tex]

[tex]\text{Area of rectangle}_{2} = (17)(7)[/tex]

Simplify the R.H.S to determing the area:

[tex]\text{Area of rectangle}_{2} = 119\ \text{feet}^{2}[/tex]

Determining the area of the figure:

A (Figure) = A (Triangle) + A (Rectangle₁) + A (Rectangle₂) + A(Rectangle₃)

                 =     27.5 + 85 + 96 + 119

                 =     327.5 feet²

Answer:

False

Step-by-step explanation:

Vertical angles are not always adjacent, but they are always congruent.

Hope that helps!

Answer:

False

Step-by-step explanation:

Hope it will help you*

[tex]b = 2[/tex]

Step-by-step explanation:

[tex]bx= 20[/tex]

insert x=10

[tex]b(10) = 20[/tex]

divide both sides by 10

[tex]b(10) \div 10 = 20 \div 10[/tex]

[tex]b = 20 \div 10[/tex]

simplify

[tex]b = 2[/tex]

Answer:

Range of x:  [tex]0\leq x < 12[/tex]    or    [tex]0\leq x\leq 11[/tex]

Largest possible value of [tex]x[/tex] is 19

Mean mark = 11.41 (nearest hundredth)

Step-by-step explanation:

The mode is the number that appears the most, so if the mode is 10, [tex]x[/tex] has to be smaller than 10.

We can say this in two ways:

[tex]0\leq x < 12[/tex]    or    [tex]0\leq x\leq 11[/tex]
since the number of points and players are positive integers.

The median is the middle value when the values in the data set are placed in order from smallest to largest.

If 10 is the median mark, to find the maximum number of 15s, sum the number of players scoring 5 and 10 points and subtract 1:

8 + 11 = 19

Therefore, the largest possible value of [tex]x[/tex] is 19.

The mean is the total of the numbers divided by how many numbers there are.  

To find the total marks, multiply the number of points by the number of players, and sum (using x = 19):

[tex]\textsf{Total points}=5 \times 8+10\times12+15 \times 19=445[/tex]

Total number of players = 8 + 12 + 19 = 39

[tex]\textsf{mean mark}=\dfrac{445}{39}=11.41\:\textsf{(nearest hundredth)}[/tex]

Answer:

y-intercept is 2

x- intercept(s) are -4 and 2

Step-by-step explanation:

y-intercept is where the line crosses the y line (vertical)

x- intercept is where the line crosses the x line (horizontal)

Answer:

5.291 x 10⁶

Step-by-step explanation:

Why is 5,291,000 written as 5.291 x 106 in scientific notation?

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10b

Follow the steps below to see how 5,291,000 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

Original Number: 5,291,000

New Number: 5.291000

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number: 5 . 2 9 1 0 0 0

Decimal Count: 1 2 3 4 5 6

There are 6 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10b

a = 5.291 (Please notice any zeroes on the end have been removed)

b = 6

Now the whole thing:

5.291 x 10⁶

Step 4

Check your work:

10⁶ = 1,000,000 x 5.291 = 5,291,000

Answer:

0.6%

Step-by-step explanation:

40% is the percentange of how many students play an instrument. (the whole) 20% is how many freshmen play. (part)

30% are the freshmen. 30% is over 100%.

20 x 100= 2000 and 40 x 30= 1200.

With the answers we got (2000 and 1200) we divide!!

2000÷1200=0.6

Which means the probabillity that the student is a random freshmen is 0.6% :)

Answer:

238

Step-by-step explanation:

First, you have to figure out the area for each of the boxes, and then you add all of the areas together

Answer:

false

Step-by-step explanation:

false

Answer: Number 11 is       21/5

Number 10 is  35/96

Step-by-step explanation:

Answer:

There is sufficient evidence to conclude that the distribution of responses is different now than it was historically.

Step-by-step explanation:

Since the p-value is less than the alpha significance level you reject the null hypothesis that the histrocial data matches the current.

We don't have enough evidence to conclude that the distribution of responses is different now than it was historically.

Human resources are the people who make up an organization's, business sector's, industry's, or economy's workforce.

A more specific concept is human capital, which refers to the knowledge and skills that individuals possess.

The chi-square goodness-of-fit test has a p-value of 0.089 at a significance level of 0.10. We cannot reject the null hypothesis because the p-value is greater than 0.10.

As a result, we lack sufficient evidence to conclude that the distribution of responses is different now than it was previously.

"We don't have enough evidence to conclude that the distribution of responses is different now than it was historically," is the correct answer.

Thus, this can be concluded regarding the given scenario.

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Your question seems incomplete, the probable complete question is:

Transcribed image text: Inference for categorical data (chi-square tests); Unit test The human resources department at a large company regularly conducts an employee satisfaction survey. One them on the survey presents employees with the statement, "I am happy overall at work. Based on historical data, here is the distribution of responses to this item Response Strongly Agree agree Disagree Strongly disagree 70% 15% 5% 10% Historical distribution The human resources department wants to test if the most recent responses fit the historical distribution. Here is a sample of 150 of the most recent responses to the statement along with a chi-square goodness-of-fit test. Response Strongly agree Agree Disagree Strongly disagree Inference for categorical data (chi-square tests): Unit test Response Strongly Agree Disagree Strongly agree disagree Observed 104 20 12 Expected 105 22.5 7.5 15 Components 0.01 0.28 5.63 0.6 x 6.52, DF - 3 P-value=0.089 Assume that all conditions for inference were met. At the a = 0.10 significance level, what should the human resources department conclude about the distribution of responses? Choose 1 answer: There is sufficient evidence to conclude that the distribution of responses is different now than it was Inference for categorical data (chi-square tests: Unit test Assume that all conditions for inference were met At the a 0.10 significance level, what should the human resources department conclude about the distribution of responses? Choose 1 answer: There is sufficient evidence to conclude that the distribution of responses is different now than it was historically We don't have enough evidence to conclude that the distribution of responses is different now than it was historically There is sufficient evidence to conclude that the distribution of responses is the same as it was historically No conclusions can be made from this test, because O expected counts cannot include decimals. There must have been a mistake in the calculations.

Answer:

20

Step-by-step explanation:

I think

sorry

The required Henry needs to score 18 points in his next game to have an average of 24 points per game.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
average = sum of all scores/number of scores

We know that Henry has played four games so far, and his scores are 30, 29, 22, and 21 points. Therefore, the sum of his scores is:

sum of scores = 30 + 29 + 22 + 21 = 102

Let's assume that Henry scores x points in his next game. Then, his total score for all five games will be,

total score = 102 + x

If his average is 24 points per game, we can set up the equation:

24 = (102 + x) / 5

120 = 102 + x

x = 18

Therefore, Henry needs to score 18 points in his next game to have an average of 24 points per game.

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Answer:

  f(-1) = 3

  f(5) = 20

Step-by-step explanation:

When evaluating a piecewise-defined function, the first step is to locate the argument value in the correct domain. Then the corresponding function is evaluated in the usual way.

__

For x=-1, the relevant piece is the one defined for x < 4:

  f(x) = x² +2

  f(-1) = (-1)² +2 = 3

__

For x=5, the relevant piece is the one defined for x > 4:

  f(x) = 2x +10

  f(5) = 2(5) +10 = 20

_____

Additional comment

The function written in this problem statement is "undefined" at x=4, so the graph would ordinarily show a "hole" there. We're not sure whether that is intentional.

4 X + z = 90- 35 = 55°

4X = 55 - Z

X= (55 - Z) / 4

Further cannot be done.

Answer:

x=7.1429 I think that's the answer and I think it's A

x²= 8²-5²

=39

x=V39

..........

Answer:

Step-by-step explanation:

Use the distributive property.

Use the foil method formula.

Distributive property:

⇒ A(B+C)=AB+AC

Foil method formula:

[tex]\Longrightarrow: \sf{(A+B)(C+D)=AC+AD+BC+BD}[/tex]

→ 2x*3x+2x*4-3*3x-3*4

Solve.

[tex]\Longrightarrow: \sf{2x*3x+2x*4-3*3x-3*4=\boxed{\sf{6x^2-x-12}}}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

12 inches

Step-by-step explanation:

This is a square of sidee length 3 inches.  As there are four (equal) sides, the perimeter of this square magnet is 4(3 inches), or 12 inches.

Answer:

B. 15 inches

Step-by-step explanation:

you multiply 6 x 5 since those are the dimensions of the triangles which equals 30 then you divide by 2 to get an answer of 15

Answer:

i would say A.  10in

Step-by-step explanation:

Answer:

Step-by-step explanation:

If an angle measures x degrees, the measure of its supplement is (180-x) degrees.

This means that x-62.4 = 180-x, meaning that x=121.2.

So, the angles are 121.2 and 58.8 degrees.

The sector angle formed by the cone when it is opened is: 54°.

Curved surface area of a cone = πrl, where l is the slant height and r is the radius of the cone.

Area of a sector in a circle = ∅/360 × πr², where ∅ is the sector angle.

Step 1: Find the height (h) of the cone using the volume formula, V= 1/3 x π x r² x h:

V = 95.4 cm³

r = 2.4 cm

Plug in the values:

95.4 = 1/3 x 3.14 x 2.4² x h

95.4 = 6.03 x h

h = 15.8 cm

Step 2: Use the pythagroean theorem to find the slant height (l) of the cone

l = √(h² + r²)

Plug in the values

l = √(15.8² + 2.4²)

l = 16 cm.

Step 3: Find the curved surface area of the cone

Curved surface area = πrl = π(2.4)(16) = 120.6 cm².

Step 4: Find the sector angle of the sector formed by the cone when opened

Curved surface area of the cone = area of the sector formed by the cone = 120.6 cm².

Area of a sector in a circle = ∅/360 × πr², therefore:

120.6 = ∅/360 × (3.14)(16²)

120.6 = ∅/360 × 803.84

(120.6)(360) = (∅)(803.84)

43,416 = (∅)(803.84)

43,416/803.84 = ∅

∅ = 54°

Therefore, the sector angle formed by the cone when it is opened is: 54°.

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Answer:

  113.1 m³

Step-by-step explanation:

In terms of diameter, the volume of a sphere is given by the formula ...

  V = (π/6)d³

For a diameter of 6 m, the volume is ...

  V = (π/6)(6 m)³ = 36π m³ ≈ 113.1 m³

The volume of the sphere is about 113.1 cubic meters.

Answer:

B

Step-by-step explanation:

four times as much;