At a high school,18% of the students play football and 6% of the students play afoot all and baseball. What is the probability that a student plays baseball given that he plays football

Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

∴ a14 = a + (14 - 1)d

∴ a14 = a + 13d

∵ a14 = -33

∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

* Lets subtract equation (2) from equation (1)

∴ (a - a) + (13 - 14)d = (-33 - 9)

∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

- Substitute this value of d in equation (1) or (2)

∵ a + 13d = -33

∵ d = 42

∴ a + 13(42) = -33

∴ a + 546 = -33 ⇒ subtract 546 from both sides

∴ a = -579

* Now lets write the equation of the nth term

∵ an = a + (n - 1)d

∵ a = -579 and d = 42

∴ an = -579 + (n - 1) 42 ⇒ open the bracket

∴ an = -579 + 42n - 42

∴ an = -621 + 42n

* The equation of the nth term is an = -621 + 42n

Answer:

I want to say that the answer is C.

Hope this helps!

Answer:

C. [tex]490 \textrm{ units}^{2}[/tex]

Step-by-step explanation:

The formula for surface area is

LA + 2B

LA indicated Lateral Area and can be found multiplying perimeter of base by the height.

7 + 7 + 14 + 14 = 42 * 7 = 294

Multiply the LA from above with the area of base times 2.

98 * 2 = 196

294 + 196 = 490, so the surface area of the rectangular prism is 490 units.

To find the surface area of a rectangular prism, add up the areas of all six faces by multiplying length by width.

To find the surface area of a rectangular prism, you need to add up the areas of all six faces. Each face is a rectangle, so to find the area, you multiply the length by the width. Then, you add up the areas of all the faces to get the total surface area.

For example, if the length of one side is 4 units, the width is 2 units, and the height is 3 units, the surface area would be:
Face 1: 4 units x 2 units = 8 square units
Face 2: 4 units x 2 units = 8 square units
Face 3: 4 units x 3 units = 12 square units
Face 4: 4 units x 3 units = 12 square units
Face 5: 2 units x 3 units = 6 square units
Face 6: 2 units x 3 units = 6 square units
Total surface area: 8 + 8 + 12 + 12 + 6 + 6 = 52 square units.

https://brainly.com/question/36027675

#SPJ3

Answer:

its one

Step-by-step explanation:

ape x legends

Answer:

x=7 satisfy the equation, so it is the solution.

x=4 doesn't satisfy the equation so it is extraneous solution.

Step-by-step explanation:

The equation given is:

[tex]\sqrt{x-3}+5=x[/tex]

Adding -5 on both sides

[tex]\sqrt{x-3}=x-5[/tex]

Taking square on both sides

[tex](\sqrt{x-3})^2=(x-5)^2[/tex]

Now solving

[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]

Verifying solutions:

Putting x=4 in the equation

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{4-3}+5=4[/tex]

[tex]\sqrt{1}+5=4[/tex]

[tex]1+5=4[/tex]

[tex]6\neq 4[/tex]

So, x=4 doesn't satisfy the equation so it is extraneous solution.

Now Putting x=7 and verifying

[tex]\sqrt{x-3}+5=x[/tex]

[tex]\sqrt{7-3}+5=7[/tex]

[tex]\sqrt{4}+5=7[/tex]

[tex]2+5=7[/tex]

[tex]7=7[/tex]

x=7 satisfy the equation, so it is the solution.

Answer:

= 7

Step-by-step explanation:

Answer:

[tex]AB =3 \sqrt{5} = 6.708203932...[/tex]

Step-by-step explanation:

[tex]A( - 1,6) \:,\: B(5,3)\\ AB = \sqrt{{(x1 - x2)}^{2} + {(y1 - y2)}^{2} } \\ AB = \sqrt{ {( - 1 - 5)}^{2} + {(6 - 3)}^{2} } \\ AB = \sqrt{ {( - 6)}^{2} + {(3)}^{2} } \\ AB = \sqrt{36 + 9} \\ AB = \sqrt{45} = 3 \sqrt{5} = 6.708203932...[/tex]

The distance between A and B to 3 significant figure is 6.71

The formula for calculating the distance between two points is expressed as:

[tex]D =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given the coordinate points (-1, 6) and (5, 3)

Substitute the given coordinates into the formula;

[tex]D =\sqrt{5+1)^2+(3-6)^2}\\D =\sqrt{(6^2+(-3)^2}\\D=\sqrt{36+9}\\D=\sqrt{45}\\D= 6.71\\[/tex]

Hence the distance between A and B to 3 significant figure is 6.71

Learn more here: https://brainly.com/question/22624745

Answer:

  84.8 in³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...

  V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³

_____

Comment on the answer

In more conventional units of measure, that is very nearly 3 pints of water.

Answer:

The last choice availablle

Step-by-step explanation:

The way you can tell the points the function has in common with the x-axis (also known as the solutions, roots, or zeros of the functiion) you have to factor it to solve for x.  When you throw this into the quadratic formula you get that there is a negative under the square root sign, which is indicative of imaginary solutions.  Imaginary solutions do NOT cross the x-axis.  So the answer to your problem is the last choice.

Answer:

21 jk

Step-by-step explanation:

Answer:

p = q

Step-by-step explanation:

There are 180 degrees in a triangle. If you subtract 50 and 60 from 180, you get 70. If you subtract 30 an 80 from 180, you get 70. therefore p = q.

14,776

/////////////////////////////////////////////////////////////

equation: 14494 + 282 = 14,776

(you convert the negative 282 to positive)

Add the highest elevation with the lowest elevation, to find the total difference. 14494 + 282 = 14,776. You convert the negative 282 to positive. The total difference in elevation between these two places is 14,776.

Answer:

d. -4.4​

Step-by-step explanation:

We know that log (a/b) = log a - log b

Since log a = 1.2 and log b = 5.6 , we can substitute these values into the equation.

                        log (a/b)  =   1.2 - 5.6

                                       = -4.4

Answer:

-6

Step-by-step explanation:

8,-6,-3,4,7 rearranged in ascending order produces -6, -3, 4, 7, 8.

-6 is the least of these scores (i. e., -6 is the lowest score).

Final answer:

Jack's least score from his last 5 card games is -6, as it is the smallest number in the set of his scores.

Explanation:

The question involves identifying the least score from a set of given numbers. To find the least score, Jack's scores from the last 5 card games are considered: 8, -6, -3, 4, 7.

Upon reviewing these numbers, it can be determined that -6 is the least because it is the smallest number and also it has a negative value, which makes it less than all the positive scores or any potential zero scores. Thus, the least of Jack’s scores is -6.

x = 30°.

The triangle drawn inside the circle is an equilateral and equiangular triangle which means that its three sides and its internal angles (that measure 60°) are equal.

To find x°:

First, we can see from the image that the tangent line to circle with arrows is formed a right angle, the angle of one side of the equilateral triangle, and the angle formed with the other side of the equilateral triangle, this three angles has to form 180° respect to the tangent line:

90° + 60° + y° = 180°

y° = 180° + 150°

y° = 30°

Second, the line in the right side of the equilateral triangle form an angle of 180°, so:

60° + z° = 180°

z° = 180° - 60°

z° = 120°

Finally, the triangle formed by this lines its internal angles are x°, y°, and z° and its sum is 180°, then:

x° + y° + z° = 180°

x° + 30° + 120° = 180°

x° + 150° = 180°

x° = 180° - 150°

x° = 30°  

Answer:

  -8

Step-by-step explanation:

For roots r and s, the quadratic can be factored ...

  f(x) = (x -r)(x -s) = x^2 -(r+s)x +rs

Then the value of r^2+s^2 can be determined from the coefficient of x (-(r+s)) and the constant (rs) by ...

  r^2 +s^2 = (-(r+s))^2 -2(rs) = (r^2 +2rs +s^2) -2rs = r^2 +s^2

Comparing this to your given equation, we have the coefficient of x as (-2m) and the constant term as (m^2+2m+3). Forming the expression ...

  (x-coefficient)^2 -2(constant term)

we get ...

  r^2 +s^2 = (-2m)^2 -2(m^2 +2m +3) = 2m^2 -4m -6

  r^2 +s^2 = 2(m -1)^2 -8

The minimum value of this quadratic expression is where m=1 and the squared term is zero. That minimum value is -8.

The inverse of the function f(x) = x + 2 is found by swapping the variables and solving for y, resulting in f^-1(x) = x - 2.

The function f(x) = x + 2 is a simple linear function in Mathematics. The inverse of any function can be found by swapping the x and the y, and then solving for y. In this case, step-by-step, it would work like this:

So the inverse of the function f(x) = x + 2 is f^-1(x) = x - 2.

https://brainly.com/question/17872426

#SPJ12

The inverse of the function f(x) = x + 2 is found by switching the roles of x and y and solving for y, resulting in the inverse function h(x) = x - 2. None of the provided options is correct.

To determine the inverse of the function f(x) = x + 2, you need to first replace f(x) with y, resulting in the equation y = x + 2. Next, swap x and y to get x = y + 2. Solve for y to find the inverse function: y = x - 2. Therefore, none of the options provided is the correct inverse of the function f(x) = x + 2. The correct inverse is h(x) = x - 2.

https://brainly.com/question/17872426

#SPJ12

Answer:

  7.5 ft

Step-by-step explanation:

The distance can be found using the Pythagorean theorem. The given distances form the legs of a right triangle, and the ending distance (d) between the players is its hypotenuse. The Pythagorean theorem tells you ...

  d² = (6 ft)² +(4.5 ft)² = 36 ft² +20.25 ft²

  d² = 56.25 ft² = (7.5 ft)² . . simplifying and rewriting as a square

  d = 7.5 ft . . . . . . . . . . . . . . . taking the positive square root

The ball must be passed a distance of 7.5 ft for it to reach between players.

_____

If you recognize the given numbers as having the ratio 3:4, then you may realize they are the legs of a 3-4-5 right triangle with a scale factor of 1.5. The distance between players will be 1.5×5 = 7.5 feet.

Answer:

[tex]\boxed{\text{7.5 ft}}[/tex]

Step-by-step explanation:

If the players are running perpendicular to each other, we have a right triangle, as in the diagram below.

We can apply Pythagoras' Theorem.

[tex]\begin{array}{rcl}a^{2} & = & b^{2} + c^{2}\\& = & 4.5^{2} + 6^{2}\\& = & 20.25 +36\\& = & 56.25\\a & = & \sqrt{56.25}\\& = & \mathbf{7.5}\\\end{array}\\\text{The distance between the two players will be } \boxed{\textbf{7.5 ft}}[/tex]

Answer:

see below

Step-by-step explanation:

Events are independent when the probability of one of them does not depend on the other one. That is, P(A|B) = P(A) and P(B|A) = P(B).

They are not independent if the above condition is not met.

A quick assessment of the given table shows ratios of one row to the next are different between columns, and vice versa. Hence the events are not indpendent.

Answer:

Step-by-step explanation:

the translation (x,y) --> (x+6,y-4):

(1, 5)--> (1+6,5-4)=(7,1)

(2, 2)--> (2+6,2-4)=(8,- 2)

(6, 3)--> (6+6,3-4)=(12,- 1)

the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :

the triangle has vertices of (7, 1), (8,- 2), and (12, -1)

Answer:

B. 10.

Step-by-step explanation:

This is the number of combinations of 3 from 5.

5C3  = 5! / 3! (5-3)!

= 5*4*3*2*1 / 3*2*1 * 2*1

= 5*4/2*1

= 10.

Answer: 10 i think

Step-by-step explanation:

Answer:

  16.5 ft by 25.5 ft

Step-by-step explanation:

Let w represent the width of the garden in feet. Then w+9 is the garden's length, and w(w+9) represents its area.

The surrounding walkway adds 8 feet to each dimension, so the total area of the garden with the walkway is ...

  (w+8)(w+9+8) = w^2 +25w +136

If we subtract the area of the garden itself, then the remaining area is that of the walkway:

  (w^2 +25w +136) - (w(w+9)) = 400

  16w + 136 = 400 . . .simplify

  16w = 264 . . . . . . . . subtract 136

  264/16 = w = 16.5 . . . . . width of the garden in feet

  w+9 = 25.5 . . . . . . . . . . .length of the garden in feet

Answer:

5.5% per year

Step-by-step explanation:

Using Formula A = P (1 + rt)

Where

A = Final amount = $10,000 + $6,600  = $16,600

P = Principal = Beginning Amount = $10,000

t = time = 12 years

r = rate in $/year (which we need to find)

Assembling the formula

A = P (1 + rt)

16,600 = 10,000 (1 + 12r)

[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r

1.66 = 1 + 12r

1.66 - 1 = 12r

0.66 = 12 r

r = 0.055 = 5.5%

Answer:

Step-by-step explanation:

The zeros are where the graph crosses the x-axis (y=0). They are x=-2 and x=4.

The factors are the binomials that are zero when x has the value of a zero:

  y = (x +2)(x -4)

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{\stackrel{30}{~~\begin{matrix} 60\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 2\pi\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }=r\implies 30=r \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} r=30\\ \theta =140 \end{cases}\implies s=\cfrac{\pi (140)(30)}{180}\implies s=\cfrac{70\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill s\approx 73.30~\hfill[/tex]

Answer:

x = 9

Step-by-step explanation:

Those are chords of a circle, and the theorem to find x is, in this context:

6(3) = 2(x) so

18 = 2x and

x = 9

Answer:

a 16

Step-by-step explanation:

16 x 12 = 192 plates

496 total plates - 192 = 304

304 packages of 8 plates

304 / 8 = 38 sets of 8 plates

38 + 16 = 54 packs of plates

Check the picture below.

The elm is 21 m tall.

Both the triangles are the same.

To find the height, by similarity we get

17 / h = 51 / 63

h = 63 * 17 / 51 = 21

The answer is 21 m.

If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar. Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

Learn more about triangles here: https://brainly.com/question/1675117

#SPJ2

Answer

x^3-15x^2+75x-125

Answer:

C) 4,850

Step-by-step explanation:

                  No. of

LED bulbs : CFL bulbs : Total

       2        :        3         :    5

   5000     :     7500     : 12 500

Percentage of non-defective LED bulbs = 100% - 3% = 97%

No. of non-defective LED bulbs = 97% x 5000 = 4850

Answer:

A = (1/2)(7 units)(5 units) = (35/2) units^2.

Step-by-step explanation:

Call AB "the base" and recognize that its length is 7 units.  Call BC "the height" and recognize that its length is 5 units.

Then apply the area-of-a-triangle formula A = (1/2)(base)(height):

A = (1/2)(7 units)(5 units) = (35/2) units^2.

The area of triangle ABC is A = (1/2)(7 units)(5 units) = (35/2) units^2.

Triangle's area is equal to 1/2 (b* h) square units.

where the triangle's base and height, respectively, are denoted by b and h.

Given

Call AB "the base" and recognize that its length is 7 units.  Call BC "the height" and recognize that its length is 5 units.

Then apply the area-of-a-triangle formula A = (1/2)(base)(height):

A = (1/2)(7 units)(5 units) = (35/2) units²

To know more about area of triangle refer  to:

https://brainly.com/question/10117243

#SPJ2

Answer:

Option A.Exponential decay, 55% decrease

Step-by-step explanation:

we have

[tex]f(x)=54(0.45)^{x}[/tex]

This is a exponential function of the form

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

where

a is the initial value

b is the base

b=(1+r)

r is the rate of change

In this problem

a=54

b=0.45

so

0.45=1+r

r=0.45-1

r=-0.55

Convert to percentage

r=-55% ------> is negative because is a exponential decay

Answer:

Exponential decay, 55% decrease

Step-by-step explanation:

[tex]f(x) = 54(0.45)^x[/tex]

General exponential growth function is [tex]y=a(1+r)^x[/tex]

exponential growth function is [tex]y=a(1-r)^x[/tex]

The value of 1-r is less than 1 then it is exponential decay

In the given f(x) , the 1-r is 0.45 that is less than 1

So it is exponential decay.

[tex]1-r= 0.45[/tex]

Subtract 1 on both sides

[tex]r=0.55[/tex]

Multiply by 100 to get %

r= 55%

Exponential decay, 55% decrease