The bumper car ride at the state fair has 3 red cars, 4 green cars, and 5 blue cars. Michelle is first in line for the ride and is assigned a car at random. Garth is next in line and is randomly assigned a car. What is the probability that both Michelle and Garth will drive a red bumper car? Express your answer as a percent. If necessary, round your answer to the nearest tenth.

Answer:

[tex]x = - 5 [/tex]

Step-by-step explanation:

To work out this question you have to first cross multiply.

[tex] \frac{2}{5} = \frac{(x - 3)} {(7x + 15)} \\ \\ 2(7x + 15) = 5(x - 3)[/tex]

When you cross multiply you will get the equation above. Therefore

[tex](2 \times 7x) + (2 \times 15) = (5 \times x) \\ - (5 \times 3) \\ \\ 14x + 30 = 5x - 15 \\ \\ 14x - 5x = - 30 - 15 \\ \\ 9x = - 45[/tex]

Therefore

[tex] \frac{9}{9} x = \frac{ - 45}{9} \\ \\ x = - 5[/tex]

Answer:

x = -5

Step by step:

multiply both side by 7x + 15.

2/5 (7x+15)= x − 3

Simplify 2)5 (7x+15) to 2(7x+15)/5.

2(7x+15)/5= x - 3

multiply both sides by 5.

2(7x+15)= 5x - 15

Expand.

14x+30= 5x - 15

subtract 5x from both sides.

14x+30−5x= − 15

Simplify 14x + 30 - 5x14x + 30−5x to 9x + 309x + 30.

9x+30= - 15

Subtract 30 from both sides.

simplify

x = -5

The length of Seneca between Mesa and La Paz Dr is = 144ft.

The driver of the Seneca Street was driving at 0.75 mi/hr therefore he was with the speed limits.

The maximum length of the skid marks left of Seneca Street by a car that travels within the speed limit is = 144ft

Length of Mesa (a)= 308ft

Length of La Paz Dr (c)= 340ft

Length of Seneca =b

Using Pythagorean theorem,

c²= a² + b²

340²= 308² + b²

make b the subject formula,

b² = 340² - 308²

b² = 115,600 - 94,864

b²= 20736

b = √20736

b = 144ft.

The speed limit within the Seneca road(s) = 50mi/h

The coefficient of friction (f) based on the surface material = 0.7 (asphalt).

The distance covered by the car = 144ft to miles = 144/5280 = 0.027.

Therefore the speed of car(s)

=√30fd

= √30 × 0.7× 0.027

= √0.567

=0.75 mi/hr

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Answer:

2:292

Step-by-step explanation:

They sold 292 in total

290 were board games and the rest were cards

so,

292-290=2

2 card games

Answer: 2:292

Step-by-step explanation:

They sold 292 in total

290 were board games and the rest were cards

so,

292-290=2

2 card games

The segment area of the circle that's given in the envision geometry is 2.568.

It should be noted that the segment area is given as:

= (a/360)π × R² - Area of triangle

= (90/360)π × 3² - (1/2 × 3²)

= 9π/4 - 9/2

= 2.568

In conclusion, the segment area of the circle that's given in the envision geometry is 2.568.

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He will reach the dance before time if he leaves at 16:40.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Given distance= 120 Km, speed= 100 km/h

For this speed,

time= distance/ speed

       = 120/100

        = 1.2 hours

If the guest leave at 4:40 p.m. then by the speed of 100 km/h he will reach the venue at 06:00 p.m.

Hence, he will reach before the time at wedding.

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The number of the grass squares of 1 square foot will be 480.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called as the area of the rectangle.

The total area covered by the grass will be:-

A  =  L  x   W

A  =  24  x  20 = 480 square feet

Number of the grass squares having an area of 1 square foot:-

N   =   Total area / area of one grass square

N   =  480 square feet   /   1 square feet

N   =  480

Therefore the number of the grass squares of 1 square foot will be 480.

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Answer:

option 1, 2

Step-by-step explanation:

since R is between Q and S

____________________

Q    (3x+6)     R    (5x-2)    S

--------------(12x - 4)-------------

Q                                       S

so

QR + RS = QS

[tex](3x+6) + (5x - 2) = 12x - 4\\(3x + 5x) + (6 - 2) = 12x - 4\\(8x) + (4) = 12x - 4\\8x + 4 - 4 = 12x - 4 -4\\8x = 12x - 8\\8x - 12x = 12x - 12x - 8\\-4x = -8\\\frac{-4x}{-4} = \frac{-8}{-4}[/tex]

Answer:

2

Step-by-step explanation:

It mentions R is between points Q and S.

Hence, QR + RS = QS.

Based on the attached photo and explanation below, the price should not be increased at all.

Note: See the attached photo for the calculation of Revenues at Different Number of Customers and Prices.

Every other being equal, profit is maximized when revenue is at the maximum,

From the attached photo, it can be seen that revenue is at the maximum or the highest when the price is $10 and the number of customers is 1,000.

Increasing the price in increments of a dollar results in a fall in revenue progressively until it reaches $0.

Therefore, the price should not be increased at all.

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Answer: y = 1/2x + 1/2

Answer:

A=

[tex]3(3m + 1)(3m - 1)[/tex]

Step-by-step explanation:

[tex] {27m}^{2} - 3[/tex]

Factorise

[tex]3( {9m}^{2} - 1)[/tex]

Rewrite it

[tex]3(( {3m)}^{2} - {1}^{2} )[/tex]

[tex]3(3m + 1)(3m - 1)[/tex]

Answer:

24 and 16.

Step-by-step explanation:

They both are in between the sum of the two numbers.

Answer: 9,156.24 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is V = πr²h. The problem gives us both the radius and the height, so we have all necessary values to solve by substitution:

r = 9

h = 36

V = π(9)²×36

= 81 × 36 × π

= 2916π

= 9,156.24 ft³

Answer:

Step-by-step explanation:

Comment

The general formula for a tangent and secant is

tangent^2 = external segment * full length of the secant.

Givens

tangent length = x

external segment = 7

secant length = 7+ 21

Formula

x^2 = 7 * (7 + 21)                         Remove brackets

x^2 = 7 * 28                                Combine

x^2 = 196                                    Take the square root of both sides

√x^2 = √196

x = 14

Answer: x = 14

Answer:

21.6 units² (nearest tenth)

Step-by-step explanation:

[tex]\textsf{Area of a trapezoid}=\dfrac{1}{2}(a+b)h \quad \textsf{(where a and b are the bases and h is the height)}[/tex][tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]

Given:

[tex]\begin{aligned}\textsf{Area of figure} & =\textsf{area of trapezoid + area of semicircle}\\& = \dfrac{1}{2}(a+b)h+\dfrac{1}{2} \pi r^2\\& = \dfrac{1}{2}(2+8)(4)+\dfrac{1}{2} \pi (1)^2\\& = 20+\dfrac{1}{2} \pi\\& = 21.6\: \sf units^2 \:(nearest\:tenth)\end{aligned}[/tex]

Area of the trapezium

Area of semicircle

Total area

Answer:

F = 53.1°

Step-by-step explanation:

When you consider F as your angle

cos F = adjacent / hypotaneous

or, cos F = EF/DF

We do not have DF right now,

so DF² = DE² + EF²

DF = √ (12² + 9²)

DF = 15

cos F = adjacent / hypotaneous

or, cos F = EF/DF

cos F = 9 / 15

F = cos ⁻¹ (9/15)

F = 53.1°

Answer:

the inequality, b ≤ 0 has interval Notation of -∞,0

Step-by-step explanation:

the inequality, b ≤ 0 has interval Notation of -∞,0

Answer:

domain: x > 1; range: all real numbers

Step-by-step explanation:

Given function:    [tex]f(x)=\log(x-1)+2[/tex]

Logarithms are not defined for zero or negative numbers.

[tex]\implies (x-1) > 0 \implies x > 1[/tex]

Therefore:

Answer:

B on edge

Step-by-step explanation:

Just took the test :)

Answer:

y= -4x/9+4

Step-by-step explanation:

4x+9y=36 (move 4x)

9y=-4x+36 (divide by 9)

y= -4/9x+36/9

y= -4x/9+4

Answer:

11 h

Step-by-step explanation:

1/2 h

11h 1/2 will be need for a bike

Answer:

Approximately 0.3.

Step-by-step explanation:

I can only estimate the value of the function when x = 2. it looks like it's about 2.4.

Average rate of change = [(f4) - f(2)] /  (4 - 2)

= (3 - 2.4) / 2

= 0.6/2

= 0.3.

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

That is representative of all possible outcomes from flipping the coin

Answer:

8 Answer is a) R

9 Answer is b) -4

Step-by-step explanation:

Answer of your Question bro and good evening and please mark me as brainliest and thank u

The critical points for the inequality x²-5x+6 is x= 2 and x = 3.

In calculus, a critical point of a function is a point where the derivative of the function is either zero or undefined.

These points are important in determining the maximum and minimum values of a function, and can also help identify points of inflection and other important features of a curve.

To find the critical points for the inequality x²-5x+6, we need to find the values of x that make the expression equal to zero (i.e., the roots of the quadratic equation).

We can factor the expression as (x-2)(x-3) and set each factor to zero to find the critical points:

x-2 = 0 or x-3 = 0

x = 2 or x = 3

So the critical points are x = 2 and x = 3.

Therefore, the answer is x= 2 and x = 3.

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Dexter is thinking of a number, x. Two more than three times his number is the same value as thirteen less than five times his number. The number which he is thinking is 7.5.

Two or more expressions with an equal sign is called as Equation.

Given that Dexter is thinking of a number, x. Two more than three times his number is the same value as thirteen less than five times his number.

Let the number which Dexter is thinking be x.

Two more than three times his number.

It means value two is added to the product of 3 and the number which he is thinking x.

3x+2

thirteen less than five times his number

It means value thirteen is subtracted from  the product of 5 and the number which he is thinking x.

5x-13.

It is given Two more than three times his number is the same value as thirteen less than five times his number

3x+2=5x-13

Take the like terms to one side

13+2=5x-3x

15=2x

Divide both sides by 2.

x=7.5

Hence the value of x is 7.5.

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Answer:

371/999

Step-by-step explanation:

all repeating numbers like that just go over nines. Two repeating? Over 99. Four repeating? Over 9,999

Solving as exponents

[tex]\\ \rm\Rrightarrow 9^{(x-8)}=3^{(4x-12)}[/tex]

[tex]\\ \rm\Rrightarrow 3^{2(x-8)}=3^{2(x-6)}[/tex]

[tex]\\ \rm\Rrightarrow 2(x-8)=2(x-6)[/tex]

[tex]\\ \rm\Rrightarrow 2x-16=4x-12[/tex]

[tex]\\ \rm\Rrightarrow -2x=4[/tex]

[tex]\\ \rm\Rrightarrow x=-2[/tex]

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]9^{x-8}=3^{4x-12}[/tex]

Rewrite 9 as 3²:

[tex]\implies (3^2)^{x-8}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{2(x-8)}=3^{4x-12}[/tex]

[tex]\implies 3^{2x-16}=3^{4x-12}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 2x-16=4x-12[/tex]

Subtract 2x from both sides:

[tex]\implies 2x-16-2x=4x-12-2x[/tex]

[tex]\implies -16=2x-12[/tex]

Add 12 to both sides:

[tex]\implies -16+12=2x-12+12[/tex]

[tex]\implies -4=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{-4}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies x=-2[/tex]

y=3x+3

Step-by-step explanation:

The m is 3 because it is rise over run. For every 3 up it goes one over (3/1) or just 3. The b is 3 because b is where x equals 0 and it is at 3.

If cos90 is equivalent to zero, hence the cos inverse of 0 is 90 degrees which is equivalent to pi/2 in radians

Inverse of a function are the opposite of the function. Given the inverse of cosine function as shown:

[tex]cos^{-1}x[/tex]

If x = 0, hence;

[tex]cos^{-1}{0[/tex]

If cos90 is equivalent to zero, hence the cos inverse of 0 is 90 degrees which is equivalent to pi/2 in radians

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