Problem
At full speed, Hal travels 600 miles in 2 hours
with the wind. The same distance against
the wind takes 3 hours.
What's the maximum speed of Hal's airplane
in still air? What's the speed of the wind?​

Final answer:

The volume of the core of the golf ball from Great Drive, with a diameter of 1.68 inches, is approximately 2.48 cubic inches. This is calculated using the formula for the volume of a sphere with the radius derived from the given diameter. The correct answer is 2.48 in³, which is option A.

Explanation:

The volume of a sphere is given by the formula V = (4/3) πr3, where π is pi (approximately 3.14159) and r is the sphere's radius. The diameter of the golf ball's core is given as 1.68 inches, so the radius is half of that, which is 0.84 inches. Plugging this into the formula gives us:

V = (4/3) π (0.84 inches)3 = (4/3) π (0.84 inches × 0.84 inches × 0.84 inches)

Doing the math, we find that:

V ≈ (4/3) π (0.592704 inches3) ≈ 2.48 in3

Therefore, the volume of the core of the ball rounded to the nearest hundredth is 2.48 cubic inches.

The correct answer is option A.

Answer:

The standard deviation of the age is 6.16

Step-by-step explanation:

* Lets talk about the variance and the standard deviation

- The variance is the measure of how much values in a set of data are

 likely to differ from the mean value of the same data

- The steps to find the variance are:

1- Find the mean of the data  

2- Subtract the mean from each value and square the answer

3- Add all of these squared answer and divide the sum by the number

  of the values

- The answer of the step 3 is The variance (σ²)

- The standard deviation (σ) is the square root of the variance

* Now lets solve the problem

∵ The variance of the ages of the people who attended a rock

  concert is 38

∴ σ² = 38

∵ The standard deviation is the square root of the variance

∴ σ = √38 = 6.16

* The standard deviation of the age is 6.16

Answer:

[tex]\sigma=6.16[/tex]

Step-by-step explanation:

By definition, the variance V of a population is defined as:

[tex]V = \sigma^2[/tex]

Where [tex]\sigma[/tex] is the standard deviation

We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]

[tex]38 = \sigma^2[/tex]

[tex]\sigma^2=38[/tex]

[tex]\sigma=\sqrt{38}[/tex]

[tex]\sigma=6.16[/tex]

Finally  the standard deviation is: [tex]\sigma=6.16[/tex]

Answer: -2,0 0,4

Step-by-step explanation:

let me know if you need help still UwU

Answer:

The function is positive from (-∞,-2) and (0,4).

Explanation:

To find the intervals where the function is positive, note where the line of the graph is above the x-axis.

As the functions goes toward negative infinity, the arrow of the graph is pointed up, so the function is positive starting from -∞ until x = -2, where it becomes negative.

The function once again goes above the x-axis at x = 0 and stays positive until x = 4. After this point, the function decreases forever, so (-∞,-2) and (0,4) are the only intervals where the function is positive.

Answer:

16x² + 56x + 49

Step-by-step explanation:

First, expand:

(4x + 7)² = (4x + 7)(4x + 7)

Follow the FOIL method. FOIL = First, Outside, Inside, Last.

(4x)(4x) = 16x²

(4x)(7) = 28x

(7)(4x) = 28x

(7)(7) = 49

16x² + 28x + 28x + 49

Combine like terms:

16x² + (28x + 28x) + 49

16x² + (56x) + 49

16x² + 56x + 49 is your answer.

~

Answer:

288 square units

Step-by-step explanation:

The formula for the area of a square when you know its diagonal is: [tex]\frac{1}{2} d^2[/tex]

So, since we know the half diagonal is 12, we need to multiply that by 2 to get the diagonal, which is 24.

Put 24 into the formula. [tex]\frac{1}{2} * 24^2[/tex]

Simplify the exponent. [tex]\frac{1}{2} * 576[/tex]

Finally, multiply. [tex]288[/tex]

Answer: i think C

Step-by-step explanation:

Answer:

4,-2 and 1

Step-by-step explanation:

These are all quantities greater than -5

-5 < 4

-5 < -2

-5 < 1

So C, D and E

[tex]y=\dfrac{k}{x}[/tex]

1.

[tex]12=\dfrac{k}{13}\\\\k=156[/tex]

2.

[tex]y=\dfrac{156}{x}[/tex]

3.

[tex]y=\dfrac{156}{44}=\dfrac{39}{11}[/tex]

Answer:

[tex]\large\boxed{y=4(x-3)^2+2\ \bold{vertex\ form}}\\\boxed{y=4x^2-24x+38\ \bold{standard\ form}}[/tex]

Step-by-step explanation:

The vertex form of a parabola:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

We have the vertex at (3, 2) → h = 3 and k = 2.

Substitute:

[tex]y=a(x-3)^2+2[/tex]

The point (4, 6) is on athe parabola. Put the coordinates of this point to the equation:

[tex]6=a(4-3)^2+2[/tex]       subtract 2 from both sides

[tex]6-2=a(1)^2+2-2[/tex]

[tex]4=a\to a=4[/tex]

Finally:

[tex]y=4(x-3)^2+2[/tex]          vertex form

use (a - b)² = a² - 2ab + b²

[tex]y=4(x^2-6x+9)+2[/tex]          use the distributive property

[tex]y=4x^2-24x+36+2[/tex]

[tex]y=4x^2-24x+38[/tex]             standard form

Answer:

y=4(x-3)^2+2

Step-by-step explanation:

Hopefully this helps :)

Answer:

31 seats

Step-by-step explanation:

Let x be the smaller van, and y be the larger one.

We know that y = x + 14

We also know that 2x + y = 65

If we replace y by its value in the second equation we have:

2x + (x + 14) = 65, then we solve

2x + x + 14 = 65

3x + 14 = 65

3x = 51

x = 17

We now know the smaller van has 17 seats.

To find how many seats are in the big one, we take the first equation:

y = x + 14

y = 17 + 14

y = 31

Answer: [tex]\sqrt{32}\text{ mi}[/tex]

Step-by-step explanation:

The Pythagoras theorem of right triangle says that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

From the given figure , the hypotenuse of the right triangle = [tex]\sqrt{113}\text{ mi}[/tex]

Then According to Pythagoras theorem , we have

[tex](\sqrt{113})^2=x^2+(9)^2\\\\\Rightarrow\ x^2=113-81\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}\text{ mi}[/tex]

Answer:

A and B are the solutions....

Step-by-step explanation:

7 and 12 are smaller than 17.

Answer:

A. [tex]x=7[/tex]

B. [tex]x=12[/tex]

Step-by-step explanation:

Check each option individually.

A. [tex]17>7[/tex] is true, so it is a correct choice.

B. [tex]17>12[/tex] is true, so it is a correct choice.

C. [tex]17>17[/tex] is false, so it is an incorrect choice.

Using Heron's formula where s = 9 ...... and a = b = c = the side lengths .....we have......

A = √[s(s -a)^3] = √[4*3^3] = √[4*27] = √[4*9*3] = √[36*3) = 9√3 sq. in.

Answer:

4

Step-by-step explanation:

[tex]f(x)=-2x+3, 0<x<=4[/tex]

Answer:

4

Step-by-step explanation:

The domain is the inputs (or the x values)

We start at -6 (but do not include it) and end at +4 (we include it)

-6 < x ≤4

The value that is included is 4

Answer:

The LCM of 8 and 9 is 72.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

This question is not complete.

Step-by-step explanation:

Hi, The question is not complete but i think the question was this:

Which of the following is the correct factorization of the polynomial below?

x^3 - 12

A. (x + 3)(x - 4)

B. (x - 3)(x + 4)

C. (x + 3)(x^2 - 4x + 4)

D. The polynomial is irreducible.

in which case, the answer will be this:

D as this polynomial can't be reduced

Answer:

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

Step-by-step explanation:

Question is incomplete (options are missing);

However, I'll factorize the polynomial using identity

Given

x³ - 12

This can be factorized using the following identity

a³ - b³ = (a - b)(a² + ab + b²)

By comparison,

a³ = x³ and b³ = 12

a = x and b = ∛12

Replace a with x and b with ∛12 in the above equation

a³ - b³ = (a - b)(a² + ab + b²) becomes

x³ - 12 = (x - ∛12)(x² + x∛12 + ∛12²)

x³ - 12 = (x - ∛12)(x² + x∛12 + 12²/³)

This is as far as it can be factorized

So, the factorization of x³ - 12 using identity is (x - ∛12)(x² + x∛12 + 12²/³)

Answer:

l

Step-by-step explanation:

Answer: [tex]\frac{1}{(x+1)(x+y)}[/tex]

Step-by-step explanation:

Given the expression:

[tex](\frac{x-y}{x^2-1})(\frac{x-1}{x^2-y^2})[/tex]

The first step is to multiply the numerator of the first fraction by the numerator of the second fraction and the denominator of the first fraction by the denominator of the second fraction. Then:

[tex]=\frac{(x-y)(x-1)}{(x^2-1)(x^2-y^2)}[/tex]

Since [tex](x^2-1)[/tex] and [tex](x^2-y^2)[/tex] are perfect squares, you can factorize them in the form:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Then:

[tex]=\frac{(x-y)(x-1)}{(x+1)(x-1)(x+y)(x-y)}[/tex]

Simplifying, you get:

[tex]=\frac{1}{(x+1)(x+y)}[/tex]

Answer:

x = -8

Step-by-step explanation:

-2x-2=14

We want to solve for x

Add 2 to each side

-2x-2+2 = 14+2

-2x=16

Divide each side by -2

-2x/-2 =16/-2

x = -8

Answer:

1.Area of Porch =2.5m²

2.Number of people =3 people

Step-by-step explanation:

The porch area from the diagram has a dimension of 4 units by 10 units

One units =1cm

Thus the porch is drawn with dimensions of 4cm by 10 cm

Taking length is 10 cm and width as 4 cm, convert these dimensions according to the scale.

The scale is 1cm=0.25m

The width will be= 0.25×4=1 m

The length will be=0.25×10= 2.5m

Area of the porch is given by the formula;

length×width because its has a shape of a rectangle

Area of porch will be

=1m ×2.5m =2.5m²

2.

Find the dimensions of the tent

14 units by 10 units

Applying the scale on the dimensions by multiplying by 0.25

14×0.25=3.5m

10×0.25=2.5m

Width=2.5m

length=3.5m

Subtract the edge distance on both the length and width

Length will be=3.5-(0.25×2)=3.0m

Width will be=2.5-(0.25×2)=2.0m

Find the area remaining to be covered by the people while sleeping

=3.0×2.0=6m²

Area covered by sleeping bag and a ground mat

2m×1m=2m²

Number of people that can sleep in the tent

6m²÷2m²=3 people

Answer: Area of porch in metres [tex]= 2.5 m^{2}[/tex]

No. of people that can sleep in the tent = 0 (according to the given conditions)

Step-by-step explanation:

In the given figure we have the scale of 1 cm : 0.25 m which denotes that we have 0.25 m length in actual for every 1 cm on the figure. Also, each square in the figure measures 1 cm on each side.

From the fig. the dimensions of tent porch area are:

Length = 10 cm = [tex]10 \times 0.25[/tex]

[tex]= 2.5 m[/tex] on ground

Breadth= 4 cm = [tex]4 \times 0.25[/tex]

[tex]= 1 m[/tex] on ground

∴ Area of porch in metres = [tex]1\times 2.5[/tex]

Area of porch in metres [tex]= 2.5 m^{2}[/tex]

Answer: [tex]y=(x-1)^2-4[/tex]

Step-by-step explanation:

The vertex form of the equation of a parabola is:

[tex]y=a(x-h)^2+k[/tex]

Where (h,k) is the vertex.

To obtain this form, we need to complete the square:

Move the 3 to the other side of the equation:

[tex]y+3=x^2-2x[/tex]

Add this value to both sides of the equation: [tex](\frac{-2}{2})^2=1[/tex]

[tex]y+3+1=x^2-2x+1[/tex]

[tex]y+4=x^2-2x+1[/tex]

Then, rewriting:

 [tex]y+4=(x-1)^2[/tex]

Finally, we must solve for "y", getting the equation of the parabola in vertex form:

 [tex]y=(x-1)^2-4[/tex]

Answer:

B

Step-by-step explanation:

We can solve this by finding the slope of the function that passes through the points (2,15) and (3,26). We can use the "formula" rise over run.

So we have:

(26-15)/(3-2) which gives us 11 as our slope. Now we must find the y intercept!

It is -7.

So the answer is B

Answer:

the equation is y = 11x - 7

B is correct option.

Step-by-step explanation:

The function passes through the points (2, 15) and (3, 26)

Slope can be calculated by the formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

using this formula, the slope is given by

[tex]m=\frac{26-15}{3-2}\\\\m=\frac{11}{1}\\\\m=11[/tex]

The slope intercept form of line is y = mx+b

here, m = 11

hence, the equation is  y = 11x +b

Now, using the point (2,15) to find b

15=11(2)+b

15 = 22 +b

b = -7

Hence, the equation is y = 11x - 7

B is correct option.

Answer:

A.) ∠3, ∠6, and∠7

If you have a protractor, that would help you alot :) but I hope this help you!

Answer:

A. ∠3, ∠6 and ∠7.

Step-by-step explanation:

Given,

r ║ s

Also, t is the common transversal of parallel lines r and s,

By the given diagram,

∠2 and ∠3 are vertical angles,

By vertically opposite angle theorem,

∠2 ≅ ∠3,

∠2 and ∠6 are corresponding angle,

By the corresponding angle theorem,

∠2 ≅ ∠6,

∠2 and ∠7 are alternate exterior angles,

By the alternate exterior angle theorem,

∠2 ≅ ∠7

Hence, Option 'A' is correct.

The sum of all the angles of a triangle is 180 degrees. To solve for y you can make a formula of the sum of the angles equal to 180 like so...

y + y + 60 = 180

Now you must combine like terms. This means that first numbers with the same variables (y) must be combined...

y + y + 60 = 180

y + y = 2y

2y + 60 = 180

Now bring 60 to the left side by subtracting 60 to both sides (what you do on one side you must do to the other). Since 60 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

2y + 60 - 60 = 180 - 60

2y + 0 = 120

2y = 120

Next divide 2 to both sides to finish isolating y. Since 2 is being multiplied by y, division (the opposite of multiplication) will cancel 2 out (in this case it will make 2 one) from the left side and bring it over to the right side.

2y / 2 = 120 / 2

y = 60

C. 60

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

F

Step-by-step explanation:

F

zero

Anytime you have zero as a possible answer, you have to consider it carefully. Part of the whole number system is 0. They go up from there. No fraction is a whole number. No decimal is a whole number except those that are equal to  a whole number.

The rest are all decimals so they are not whole numbers. Note I just noticed that the other numbers have periods after the choice. There are other whole numbers there if that is the case.

C D E and F are all whole numbers if that is a period after their choice letters.

Answer:

7.81 dollars

Step-by-step explanation:

20 which was given to

take away the cost of the bill of 12.19

which will give you how much change you will need to give back

Plug 14 in for a and 12 in for b like so...

14 + 7(12)

14 + 84

98

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

60 degrees-30 = 90

50'-40'= 10

40"-50"= 10

Please mark brainliest and have a great day!