(Solve for v) 2v − 6 = 4

there are 5 ways for 1st place, then there would be 4 ways for 2nd place, then 3 ways for third

5*4*3 = 60 different ways

Answer:  The required number of ways is 60.

Step-by-step explanation:  Given that there are five automobiles entered in a race and there are no ties.

We are to find the number of ways in which the first three finishers come in.

Since there are 5 automobiles entered in the race, so the number of ways in which first finisher come in is 5.

Now, there are no ties, so the number of ways in which second and third finisher come in are 4 and 3 respectively.

Therefore, the total number of ways in which the first three finishers come in is

[tex]n=5\times4\times3=60.[/tex]

Thus, the required number of ways is 60.

Answer:

The value of k is 4.

Step-by-step explanation:

Given,

f of x equals 1 over 3 x minus 3,

[tex]\implies f(x)=\frac{1}{3}x-3[/tex]

Also, g of x equals 1 over 3 x plus 1,

[tex]\implies g(x)=\frac{1}{3}x+1[/tex]

Since, g(x) = f(x) + k,

By substituting the values,

[tex]\frac{1}{3}x+1=\frac{1}{3}x-3+k[/tex]

[tex]1=k-3[/tex]

[tex]\implies k = 1+3 = 4[/tex]

Hence, the value of k is 4.

Answer: Volume of cylinder is 1152.38 m³.

Step-by-step explanation:

Since we have given that

Radius of cylinder = 10 m

Height of cylinder = 11 m

Using Cavalieri's principle , volume of an oblique cylinder is equal to volume of cone.

So, Volume of an oblique cylinder is given by

[tex]V=\frac{1}{3}\pi r^2h\\\\V=\frac{1}{3}\frac{22}{7}\times 10\times 10\times 11\\\\V=1152.38\ m^3[/tex]

Hence, Volume of cylinder is 1152.38 m³.

Answer:

35.5 mph

Step-by-step explanation:

We are given that Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding.

Speed limit =65 mph

Sally traveled distance  97 km in 102 minutes

We have to find the Sally's average speed in mph

Time =102 minutes

We know that 1 hour =60 minutes

[tex]102 minutes=\frac{102}{60}=1.7 [/tex]hours

We know that 1 km=0.621371

97 km=[tex]0.621371 \times 97=60.272987[/tex]miles

Average speed =[tex]\frac{60.272987}{1.7}=35.45 mph[/tex]

Average speed  of Sally's =35.5 mph

Hence, average speed of Sally is less than 65 mph .Therefore, she was not fast speeding and she deserves a ticket.

[tex]4(x+2)=2(x+3)+2(x-1)\\\\use\ the\ distributive\ property:\ a(b\pm c)=ab\pm ac\\\\(4)(x)+(4)(2)=(2)(x)+(2)(3)+(2)(x)-(2)(1)\\\\4x+8=2x+6+2x-2\ \ \ \ |simplify\\\\4x+8=(2x+2x)+(6-2)\\\\4x+8=4x+4\ \ \ \ |-4x\\\\8=4\ FALSE!!!\\\\Answer:\ NO\ SOLUTION\ (x\in\O)[/tex]

perimeter = 4s

56=4s

s=56/4 = 14

diagonal = sqrt (s^2 x 2)= sqrt(14^2 x 2) = sqrt(392) = 19.7989 cm

round answer as needed

Answer:

The approximate length of diagonal is:

19.796 cm.

Step-by-step explanation:

We are given the perimeter of a square as 56 cm.

Let 's' be the side of the square.

We know that the perimeter of square is given as:

[tex]Perimeter=4\times s\\\\56=4s\\\\s=\dfrac{56}{4}\\\\s=14[/tex]

Hence, the side of square is 14 cm.

Now, the length of a diagonal(D) is given as:[tex]D=\sqrt{2}s[/tex]

( Since it could be proved with the help of Pythagorean Theorem )

Hence, as s=14 cm

Hence, the length of diagonal is:

[tex]D=\sqrt{2}\times 12\\\\D=1.414\times 14\\\\D=19.796\ cm[/tex]

Hence, the approximate length of diagonal is:

19.796 cm.

Answer:

f(-2 ) =2

f(0) = 3

f(4) = -1

Step-by-step explanation:

Clearly by looking at the graph of the given function f(x) we could observe that the function f(x) is increasing in the interval (-∞,0] and then decreasing in the interval (0,∞).

Also, the function is discontinuous at x=0.

( Since, there is a break in a graph and also the left and right hand limit of the function are not equal at x=0)

Hence, from the graph we could directly say that:

                 f(-2 ) =2

                 f(0) = 3

                  f(4) = -1

The values of the function values are:

f(-2 ) =2, f(0) = 3 and f(4) = -1

On the graph, the value of the function when x = -2 is 2

Hence, the value of f(-2) is 2

On the graph, the values of the function when x = 0 are 1 and 3.

However, the line that has a closed circle (i.e f(0) = 3) will take precedence over the line that has an open circle (i.e f(0) = 1)

Hence, the value of f(0) is 3

On the graph, the value of the function when x = 4 is -1

Hence, the value of f(4) is -1

Read more about functions and graphs at:

https://brainly.com/question/13136492

Answer:

a

Step-by-step explanation:

To cover 50 windows with coverings that are 15 windows long, at least 4 window coverings are needed to span all the windows.

The question asks how many window coverings are necessary to span 50 windows, given that each window covering is 15 windows long. To find out how many window coverings are required, you divide the total number of windows by the length of one window covering. So, we do 50 ÷ 15 which equals approximately 3.33. Since you can't have a fraction of a window covering, you'll need at least 4 full window coverings to span all 50 windows.

x = 50 * tan(60) = 50sqrt(3) =86.6 feet

tower is 93.6 feet tall

The true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Let's analyze each statement:

1. The graph of [tex]\(y - \log(x-4)\)[/tex] is the graph of [tex]\(y - \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y - \log(x-4)\)[/tex] is the result of shifting the graph of [tex]\(y = \log(x)\) 4[/tex] units to the right, not down.

2. The graph of [tex]\(y = \log(x) - 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units down.

  This statement is incorrect. The function [tex]\(y = \log(x) - 4\)[/tex] represents a vertical translation of 4 units down from the graph of [tex]\(y = \log(x)\)[/tex], not left.

3. The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of [tex]\(y = \log(x)\)[/tex] translated 4 units up.

  This statement is true. Adding a constant term to a function vertically shifts the graph of the function by that amount. So, adding 4 to [tex]\(y = \log(x)\)[/tex] shifts it 4 units up.

4. The graph of [tex]\(y = \log(x+4)\)[/tex] is the graph of [tex]\(y = \log_2(x)\)[/tex] translated 4 units right.

  This statement is incorrect. The function [tex]\(y = \log(x+4)\)[/tex] represents a horizontal translation of 4 units to the left from the graph of [tex]\(y = \log(x)\).[/tex]

Therefore, the true statement is: The graph of [tex]\(y = \log(x) + 4\)[/tex] is the graph of y = (log(x) translated 4 units up.

Question

Which statement is true?

The graph of Y - log(x-4) is the graph of y-log,(x) translated 4 units down.

The graph of Y = log: (x)-4 is the graph of y = log. (x) translated 4 units left.

The graph of y = log,(x)+4 is the graph of Y=log.(x) translated 4 units up.

The graph of y = log. (x+4) is the graph of y = log2 (x) translated 4 units right.

Answer:

d. Carrying a notebook and immediately recording all of her transactions in it.

Step-by-step explanation:

The correct answer is option D.

A bank statement is a document that is typically sent by the bank to the account holder every month, summarizing all the transactions of an account during the month.

Bank statements contain bank account information, such as account number and a detailed list of deposits and withdrawals.

Cassandra's best option would probably be carrying a notebook and immediately recording all of her transactions in it.

Since she does not like to do a lot of heavy thinking when she gets home, and tends to lose pieces of paper, this method is ideal because it would allow her to consolidate all her purchase records in one notebook, eliminating the need to carry receipts, and recording them immediately will make it so she can relax when she gets home.

Perhaps once a month, she can compile all of her notebook activity into a computer program and reconcile it to her bank statements. 

Hence, the correct option is D.

Learn more about bank statements click;

https://brainly.com/question/22786262

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Let the length of the rectangle = x

since the perimeter is 24m then the width of rectangle is (12-x)m.

the area of rectangle is:
 A=x*(12-x)

A=-x^2+12x

x=-12/-2 =6:

Since the length is 6m the width will be: 12-6=6m

We conclude that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :

Area = 6^2 =36M^2

Final answer:

A function is in simplified form when all unnecessary terms have been eliminated, subscripts are used appropriately, and it uses the most compact and standard notation possible. Always verify the reasonableness of the simplified function.

Explanation:

To determine when a function is in simplified form, several steps should be followed:

When you have eliminated all unnecessary terms and used standard conventions for simplification mentioned above, the function is considered to be in its simplest form. It is always good practice to check the answer to see if it is reasonable and does not violate any known principles or constraints.

The value of x is 13.

The problem at hand has a quadrilateral shape. The problem depicts four angles and sides, with the only known angle being X.

The graphic depicts four sides (quad), and the stick drawn in the center of each side explains the length relationship.

One stick is equal to two sticks, and two sticks are equal to one stick.

Angles Assumed:

X=102 deg

W=(7x+4) deg

Y=(5x-4) deg

Because angle X is 102 degrees, angle Z must also be 102 degrees. A quadrilateral has a total angle of 360 degrees.

So, to find x, do the following:

102 + 102 + 7x + 4 + 5x - 4 = 360

Add the constant terms: 102 + 102 + 4 - 4 = 204

Combine x terms: 7x + 5x = 12x

Substitute the combined terms:

204 + 12x = 360

Isolate x:

12x = 360 - 204

12x = 156

x = 156 / 12

Simplify:

x = 13

Therefore, the solution is x = 13.

L = lemon drops

J = jelly beans

L +J = 100

L=100-J

1.90L + 1.20J=1.48*100

1.90(100-j) +1.20J =148

190-1.90J+1.20J=148

190-0.7J=148

-0.7J=-42

J = 60

L=100-60 = 40

40 pounds of Lemon Drops are needed

Final answer:

40 pounds of lemon drops are needed.

Explanation:

To find out how many pounds of lemon drops are needed to make a 100-pound mix that costs $1.48 per pound, we can set up a system of equations. Let L represent the number of pounds of lemon drops and J represent the number of pounds of jelly beans.

Since the total weight of the mix is 100 pounds:

L + J = 100

Given the cost of lemon drops is $1.90 per pound and jelly beans cost $1.20 per pound, and the entire mix should cost $1.48 per pound:

1.90L + 1.20J = 100 * 1.48

We already have that L + J = 100, so J can be expressed as 100 - L. Substituting J in the second equation we get:

1.90L + 1.20(100 - L) = 148

Solving for L:

1.90L + 120 - 1.20L = 148

0.70L = 28

L = 28 / 0.70

L = 40

Therefore, 40 pounds of lemon drops are needed for the mix.