Fifty percent of the gases making up the atmosphere are found below ________. 10 miles (16.2 km) 6 â½ miles (10.4 km) 3 â½ miles (5.6 km) 8 miles (12.8 km)

Answer:  The correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:  Given that the segment AB is being dilated to A''B'' with the center at the origin. The image of A, point A" has coordinates of (3.2, 6.4).

We are to find the scale factor of the dilation and the co-ordinates of the point B''.

From the given graph, we note that

the co-ordinates of point A are (4, 8).

Now, If S is the scale factor of dilation, then we must have

[tex]S\times (4,8)=(3.2,6.4)\\\\\Rightarrow (4S,8S)=(3.2,6.4)\\\\\Rightarrow S=\dfrac{3.2}{4}=\dfrac{6.4}{8}=0.8.[/tex]

So, the scale factor is 0.8.

Now, the co-ordinates of point B are (-4, -6). So, the co-ordinates of B'' will be

[tex](-4\times 0.8,-6\times 0.8)=(-3.2,-4.8).[/tex]

Thus, the correct option is

(A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Answer:

A) The scale factor is 0.8 and the coordinates of point B" are (–3.2, –4.8).

Step-by-step explanation:

Answer:

 The direction angle of vector v is equal to  [tex]9.5\°[/tex]

Step-by-step explanation:

Let

[tex]A(-5,0),B(7,2)[/tex]

The vector v is given by

[tex]v=B-A[/tex]

[tex]v=(7, 2) - (-5, 0)[/tex]

[tex]v=((7 - (- 5)), (2-0))[/tex]

[tex]v=(12, 2)[/tex]

 Remember that

The direction angle of the vector is equal to

 [tex]tan (\theta) =\frac{y}{x}[/tex]

substitute the values

 [tex]tan (\theta) =\frac{2}{12}[/tex]

 [tex]\theta=arctan(\frac{2}{12})=9.5\°[/tex]

Answer:

The direction angle of vector v is equal to  9.5\°

Step-by-step explanation:

Let

A(-5,0),B(7,2)

The vector v is given by

v=B-A

v=(7, 2) - (-5, 0)

v=((7 - (- 5)), (2-0))

v=(12, 2)

Remember that

The direction angle of the vector is equal to

tan (\theta) =\frac{y}{x}

substitute the values

tan (\theta) =\frac{2}{12}

\theta=arctan(\frac{2}{12})=9.5\°

Step-by-step explanation:

put that in a computer calc and  it shoud give u the awnser

Answer:

sec Ф = 13/12

Step-by-step explanation:

If tan Ф = 5 / 12, we can find the third side of this triangle (that is, the hypotenuse) by applying the Pythagorean Theorem:  

hyp² = 5² + 12² = 169.  Thus, the hyp is 13.

Thus, cos Ф = adj / hyp = 12/13.

The secant function is the reciprocal of the cosine function, so

sec Ф = 13/12.

Answer:

She will owe $16987.35 when she begins making payments

Step-by-step explanation:

* Lets explain how to solve the problem

- The loan is $16,000

- The loan at a 4.8% APR compounded monthly

- She will begin paying off the loan in 15 months

- The rule of the future money is [tex]A=P(1 + \frac{r}{n})^{nt}[/tex], where

# A is the future value of the loan

# P is the principal value of the loan

# r is the rate in decimal

# n is the number of times that interest is compounded per unit t

# t = the time in years the money is borrowed for

∵ P = $16,000

∵ r = 4.8/100 = 0.048

∵ n = 12 ⇒ compounded monthly

∵ t = 15/12 = 1.25 years

∴ [tex]A=16000(1+\frac{0.048}{12})^{12(1.25)}=16987.35[/tex]

* She will owe $16987.35 when she begins making payments

Answer:

xy = 1

k = 79

Step-by-step explanation:

Question One

The first and third frames look to me to be the same. I'll treat them that way.

y = x^2                        Equate y = x^2 to the result of 2y + 6 = 2x + 6

2y + 6 = 2(x + 3)         Remove the brackets

2y + 6 = 2x + 6           Subtract 6 from both sides

2y = 2x                       Divide by 2

y = x

Now solve these two equations.

so x^2 = x                  

x > 0

1 solution is x = 0 from which y = 0. This won't work. x must be greater than 0. So the other is

x(x) = x                           Divide both sides by x            

x = 1                            

y = x^2                           Put x = 1 into x^2

y = 1^2                           Solve

y = 1                      

The second solution is

(1,1)

xy = 1*1

xy = 1

Answer: A

Question Two

square root(k + 2) - x = 0

Subtract x from both sides

sqrt(k + 2) = x                Square both sides

k + 2 = x^2                    Let x = 9

k + 2 = 9^2                    Square 9

k + 2 = 81

k = 81 - 2

k = 79

Conditional probability means that an event happening only happened because another even had already occurred , Mean while independent probabilitty is like if two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

The addition is a Conditional probability.

The Addition Rule, used for calculating the probability of either event A or B occurring, applies to both independent and dependent events, requiring adjustment for overlapping probabilities.

The difference between independent and conditional probability is that independent events do not affect each other's occurrence, whereas conditional probability is the likelihood of one event given that another has occurred. The Addition Rule of probability is used with either independent or dependent events when you are calculating the probability of either event A or event B occurring (denoted as P(A OR B)). However, the rule requires an adjustment in the case of dependent events. The Addition Rule is P(A OR B) = P(A) + P(B) - P(A AND B). It is used to make sure that the probability of the intersection of A and B (which is counted in both P(A) and P(B)) is not counted twice.

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Answer:

D. The graph of d(x) is 25 units below the graph of f(x)

ANSWER

D. the graph of d(x) will be 25 units below the graph of f(x).

EXPLANATION

The graph of

[tex]f(x) = {x}^{2} [/tex]

is the base function.

The graph of

[tex]d(x) = {x}^{2} - 25[/tex]

is a vertical translation of the base function 25 units down.

This implies that, the graph of d(x) will be 25 units below the graph of f(x).

Therefore the correct answer is D.

Answer:

  D(4, 1)

Step-by-step explanation:

The two diagonals have the same midpoint, so ...

  (A+C)/2 = (B+D)/2

  A+C = B+D . . . . multiply by 2

  A+C-B = D . . . . . subtract B

  D = (1, 1) + (5, 3) - (2, 3) = (1+5-2, 1+3-3)

 D = (4, 1)

Answer:

D(4 ; 1)

Step-by-step explanation:

vector(AB)=(2-1 ; 3-1) = (1 ; 2)

vector(DC)=(5-x ; 3-y)  and D(x ; y )

ABCD  parallelogram :vector(AB)=vector(DC)

you have the system : 5-x =1

                                       3-y =2

so : x=4 and y=1

D(4 ; 1)

Answer: 1 out of 5 for the first box and 1 out of 7 for the second box

( in simplest form)

Step-by-step explanation:

Answer:

The area of the circle is [tex]78.5\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=31.4\ units[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values

[tex]31.4=2(3.14)r[/tex]

[tex]r=31.4/[2(3.14)]=5\ units[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

substitute the values

[tex]A=(3.14)(5)^{2}[/tex]

[tex]A=78.5\ units^{2}[/tex]

Answer:

78.5

Step-by-step explanation:

Answer: d) 2.5

Step-by-step explanation:

The mean is 16 so it has a z-score is 0

The standard deviation is 4 so:

Notice that 26 is between the z-scores of 2 and 3 = 2.5

Algebraically: [tex]\dfrac{26-16}{4}=\dfrac{10}{4}=2.5[/tex]

the expanded form of (3x + 4)(2x − 5) is 6x² - 7x - 20. The third option is the correct option.

The simplified form of (3x + 2y) - (x + 2y) is 2x. The correct option is the third option.

3x + 4y equals 36. The third option is the correct option.

To evaluate f(x) = 4x + 3x² - 5, f(x) evaluates to -1. The last option is the correct option.

The Breakdown

To expand the expression (3x + 4)(2x − 5), you can use the distributive property:

(3x + 4)(2x − 5) = 3x(2x) + 3x(-5) + 4(2x) + 4(-5)

Now, simplify each term:

= 6x² - 15x + 8x - 20

Combine like terms:

= 6x² - 7x - 20

So, the expanded form is 6x² - 7x - 20.

To simplify the expression (3x + 2y) - (x + 2y), we can remove the parentheses and combine like terms:

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

The terms "2y" and "-2y" cancel each other out:

= 3x - x

Simplifying further:

= 2x

Therefore, the simplified form of (3x + 2y) - (x + 2y) is 2x.

To find the value of 3x + 4y, we need to solve the given equation and then substitute the values into the expression.

Given: 1/2x + 2/3y = 6

To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 6:

6 × (1/2x + 2/3y) = 6 × 6

This simplifies to:

3x + 4y = 36

Therefore, 3x + 4y equals 36.

To evaluate f(x) = 4x + 3x² - 5 when x = -2, we substitute -2 for x in the expression:

f(-2) = 4(-2) + 3(-2)² - 5

Simplifying:

f(-2) = -8 + 3(4) - 5

f(-2) = -8 + 12 - 5

f(-2) = -1

Therefore, when x = -2, f(x) evaluates to -1.

The answer is:

The first option,

[tex]y=3.5[/tex]

To solve the problem, we need to follow the next steps:

- Set your calculator in degree mode to calculate Cos(64°)

- Isolate Y by multiplying each side of the equation by 8.

Solving we have:

[tex]Cos(64\°)=\frac{y}{8}\\\\0.44=\frac{y}{8}[/tex]

Multiplying each side of the equation by 8, we have:

[tex](0.44)*8=\frac{y}{8}*8\\3.52=y[/tex]

[tex]y=3.52[/tex]

Rounding to the nearest tenth, we have:

[tex]y=3.5[/tex]

Hence, the answer is the first option,

[tex]y=3.5[/tex]

Have a nice day!

[tex]\boxed{W=2ft}[/tex]

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. On the other hand, a rectangular prism is a solid whose base is a rectangle.  Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

[tex]V=L\times W\times H[/tex]

From the statement of the problem we know:

[tex]V=24ft^3 \\ \\ H=3ft \\ \\ W=W \\ \\ L=W+2[/tex]

So:

[tex]24=(W+2)(W)(3) \\ \\ 3W(W+2)=24 \\ \\ 3W^2+6W-24=0 \\ \\ From \ the \ Quadratic \ Formula: \\ \\ W_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{12}=\frac{-6 \pm \sqrt{6^2-4(3)(-24)}}{2(3)} \\ \\ W_{1}=2 \\ \\ W_{2}=-4[/tex]

Since we can't have negative distance, the only valid option is [tex]\boxed{W=2ft}[/tex]

Answer:

Step-by-step explanation:

X=15

Answer:

Step-by-step explanation:

[tex]log_6 6^{(x-8)} = log_6 730\\x-8 = log_6 730\\x= 8+log_6 730[/tex]

im pretty sure it's the first option.

Answer:

#1) is right

Step-by-step explanation:

I believe the correct answer is 4.33%.

Answer:

2.00%

Step-by-step explanation:

Answer:

[tex]a=9\ in\\b= 9\ in[/tex]

Step-by-step explanation:

This straight triangle has two angles equal to 45 ° and two equal sides.

We know that the side opposite the 90 degree angle is:

[tex]c =9\sqrt{2}\ in[/tex]

Since the triangle has two equal angles, then it is an iscoceles triangle.

This means that

[tex]a = b[/tex]

We use the Pythagorean theorem to find b

[tex]c^2 = a^2 + b^2\\\\c^2 = b^2 + b^2\\\\c^2 = 2b^2\\\\(9\sqrt{2})^2 =2b^2\\\\b^2=\frac{(9\sqrt{2})^2}{2}\\\\\sqrt{b^2}=\sqrt{\frac{(9\sqrt{2})^2}{2}}\\\\b=\frac{(9\sqrt{2})}{\sqrt{2}}\\\\b=a=9[/tex]

Answer:x=18

Step-by-step explanation:2x-9=x+9

Answer:

C. 6 feet

Step-by-step explanation:

The answer is:

The correct option is B. the string is 3.9 feet long.

To solve the problem, we need to use the given formula, substituting "T" equal to 2.2 seconds, and then, isolating "L".

Also, we need to remember the formula to calculate a simple pendulum:

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

Where,

T, is the period in seconds

L, is the longitud in meters or feet

g, is the acceleration of the gravity wich is equal to:

[tex]g=9.81\frac{m}{s^{2} }[/tex]

or

[tex]g=32\frac{feet}{s^{2} }[/tex]

We are given the formula:

[tex]T=2\pi \sqrt{\frac{L}{32} }[/tex]

Where,

T, is the period of the pendulum (in seconds).

L, is the length of the string.

32, is the acceleration of the gravity in feet.

So, substituting "T" and isolating "L", we have:

[tex]2.2seconds=2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}} }}\\\\2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=2.2seconds\\\\\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=\frac{2.2seconds}{2\pi }[/tex]

Then, squaring both sides of the equation, to cancel the square root, we have:

[tex]\sqrt{\frac{L}{32\frac{feet}{seconds^{2} }}}=\frac{2.2seconds}{2\pi}\\\\(\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}})^{2}=(\frac{2.2seconds}{2\pi})^{2}=(0.35seconds)^{2} }\\\\\frac{L}{32\frac{feet}{seconds^{2}}}}=0.123seconds^{2}\\\\L=32\frac{feet}{seconds^{2}}*0.123seconds^{2}\\\\L=3.94feet=3.9feet[/tex]

Hence, we have that the answer is:

B. the string is 3.9 feet long.

Have a nice day!

Answer:

its B

Step-by-step explanation:

Answer:

(x + 5)² + (y + 7)² = 288

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)

r = [tex]\sqrt{(7+5)^2+(5+7)^2}[/tex] = [tex]\sqrt{12^2+12^2}[/tex] = [tex]\sqrt{288}[/tex]

Hence

(x - (- 5))² + (y - (- 7))² = ([tex]\sqrt{288}[/tex])², that is

(x + 5)² + (y + 7)² = 288

Answer:

  D)  168 ft^3

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = (1/3)πr^2·h

Putting your numbers in, we have ...

  V = (1/3)π(4 ft)^2·(10 ft) = (160π/3) ft^3 ≈ 168 ft^3

The answer is d 168ft3

Explanation:

(1/3)*(4^2)*10*pi

Answer:

84.463°

Step-by-step explanation:

Determine the x- and y-components of these two vectors.  Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:

x-comps:

5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83

y-comps:

5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562

Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°:  ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or

1.474 rad       180°

-------------- * -----------  =  84.463°

       1                π

Answer:

it's false

Step-by-step explanation:

If you have the equation of a parabola in vertex form y=a(x−h)^2+k, then the vertex is at (h,k) and the focus is (h,k+14a).

In this case, h = 0,k = 0 and a = 1/4

Then the focus is at (h, k +14a) = (0, 0 + 14*1/4) = ( 0, 1)

So, it's false.

Answer:

false

Step-by-step explanation:

Answer:

  D.  7 +11i

Step-by-step explanation:

In many situations, you can treat "i" as though it were a variable. Collect terms in the usual way.

  (2 +8i) -(-5-3i) = 2 +8i +5 +3i = (2+5) +(8+3)i

  = 7 +11i

ANSWER

[tex]( - \frac{23}{5} , - 4)[/tex]

EXPLANATION

Given the points P(2,-1) and Q(-9,-6),the coordinates of the point that partition the directed line segment PQ in the ratio 3:2 is given by

[tex]x = \frac{ mx_2+nx_1}{m + n} [/tex]

[tex]y= \frac{ my_2+ny_1}{m + n} [/tex]

Where m=3 and n=2

[tex]x = \frac{ 3 ( - 9)+2(2)}{3+ 2} [/tex]

[tex]x = \frac{ - 23}{5} [/tex]

[tex]y= \frac{ 3( - 6)+2( - 1)}{3 + 2} [/tex]

[tex]y= \frac{ - 20}{5} = - 4[/tex]

The point is

[tex]( - \frac{23}{5} , - 4)[/tex]

The coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2 are (-21/5, -17/5).

To find the coordinates of the point on the directed line segment PQ that partitions it in the ratio 3/2, we can use the section formula. The section formula states that the coordinates of a point dividing a line segment with endpoints (x1,y1) and (x2,y2) in the ratio m:n are given by:

x = (m*x2 + n*x1)/(m+n)

y = (m*y2 + n*y1)/(m+n)

Plugging in the values from the given points P(2,-1) and Q(-9,-6) into the formula, we get:

x = (3*(-9) + 2*2)/(3+2) = -21/5

y = (3*(-6) + 2*(-1))/(3+2) = -17/5

So, the coordinates of the point are (-21/5, -17/5).

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Answer:

C. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We have been given a table showing rates of time taken by Judy and Sam to complete a puzzle.

We can see from our given table that Sal's rate is r. We are told that Judy completes a puzzle by herself, it takes her 3 hours. working with Sal, it only takes them 2 hours.

Since Judy completes the puzzle in 3 hours, so part of puzzle completed by Judy in one hour would be [tex]\frac{1}{3}[/tex], therefore, correct choice is option C.

Answer:

C.

Step-by-step explanation:

Answer:

It's the first choice (20 degrees).

Step-by-step explanation:

These angles will be equal ( by The Alternate Angle Theorem).

5(x - 2) = x + 14

5x - 10 = x + 14

4x = 24

x = 6.

So the measure of each angle =  5(6 - 2) = 6 + 14 = 20 degrees.

The angles of elevation and depression are equal because they are alternate interior angles. Solving the given expressions yields x = 6. Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

First, let's set up the problem:

In any scenario involving angles of elevation and depression, these angles are equal because they are alternate interior angles formed by a horizontal line and a transversal.

Therefore, we can equate the two expressions:

5(x-2) = (x+14)

Now, solve for x:

Now substitute x back into the expressions to find the angle measures:

For the angle of elevation: 5(x-2) = 5(6-2) = 5*4 = 20 degrees

For the angle of depression: (x+14) = (6+14) = 20 degrees

Therefore, both the angle of elevation and the angle of depression measure 20 degrees.

This confirms that our setup and calculation are correct.

the answer would be 3 I believe

1-7=

-6

4-(-2)=

6

-6/6=

-1

The slope is -1