you are driving a 30 foot bus on a highway at 45 mph. the road is dry and visibility is good. a safe distance between you and the vehicle ahead of you should be at least:

Answer:

x = 7

Step-by-step explanation:

Using trigonometry, it is found that:

1. Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

2. The angles are θ = 157.38º and θ = 202.62º, as shown in Graph 1.

3. Graph 3 shows an angle of θ = 315º.

In item 1, it asks for an angle in which both the sine and the cosine of the angle are negative. This happens in the third quadrant, hence Graph 2 shows an angle in which cos(θ) = -8/17 and sin (θ) is negative.

The secant of an angle is given by one divided by the cosine of the angle, that is:

sec(θ) = 1/cos(θ)

Considering the numeric value of the secant in this problem, we have that:

-13/12 = 1/cos(θ)

-13cos(θ) = 12

cos(θ) = -12/13

The cosine is negative in the second and the third quadrant, hence graph 1 shows these equivalent angles.

Applying the inverse cosine, the angles are given as follows:

θ = arccos(-12/13)

θ = 157.38º and θ = 202.62º. (two equivalent angles).

An angle of 315º is on the fourth quadrant of the unit circle, hence Graph 3 shows this angle.

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Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.

The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:

c² = a² + b² - 2 × a × b × Cos C.

Considering right triangle ABD,

BD = a

DC = b

BC = c

Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:

BD = √(7.5² + 5²)

BD = √(7.5² + 5²)

BD = 9.0 cm

Use the law of cosines to find the length of BC:

BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.

Substitute

BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38

BC² = 250 - 184.4

BC² = 65.6

BC = √65.6

BC = 8.1 cm

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The solution set of real numbers that are 3 units from -2 is :

|x +2| = 3

Here

Function : |x +2| = 3

since ,

|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3

x = 3 - 2 ∨ x = -3 - 2

x = 1 ∨ x = -5

| - 2 - 1 | = | -3| = 3

| -2 -(-5) | = | -2 + 5 | = 3.

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Answer:

y = -x + 1

Step-by-step explanation:

y =mx + b

It is crossing the y axis at 1 that is the b

The slope (m) is -1.  From one point on the line to another you go down 1 and left 1.  That represents a negative slope of 1

Answer:

I think the answer is 0.

Step-by-step explanation:

-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4

To convert from radical form to exponential in fractional form, we can follow:

Firstly, notice that 9 is the same as 3 squared:

Now, we can apply the change:

Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:

So, the expression in the simples form and fractional exponent is:

The quadratic formula for a polynomial is given by:

Therefore, option (C) is correct.

A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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Answer: g/15 = 3 ; g = 45 gifts.

Step-by-step explanation: You would basically have to multiply 15 by 3, and it equal 45. This answer choice shows an equation that will make the answer 45, so it is right.

g/15 will equal 3.

Then, you would break them apart and do the denominator (15) multiplied by the numerator (3).

This will get you the answer 45.

So, you will get the answer choice A.

Answer:

Step-by-step explanation:

The time interval of interest is 6 hours

There is an average of 18 trains per 24 hours or 18/(24/6)=49/12 trains per 6 hours.

The probability can be found using the Poisson distribution with parameter

λ=49/12

In linear equation,  that price of shorts before discount was $25

What in mathematics is a linear equation?

Assume that the price of shorts after the discount is x

Total payment = price of shorts + taxes

We know that:

total payment = $21

taxes = 5% = 0.05 of the price

This means that:

21 = x + 0.05x

21 = 1.05x

x = $20

Therefore, the price of the shorts is $20 after the discount

Now, we will get the price of the shorts before the discount:

Assume that the price of shorts before discount is y

We know that:

The discount was 20%

This means that Jennifer paid:

100% - 20% = 80% of the price of the shorts

Therefore:

80% of the price = $20

0.8y = 20

y = $25

This means that price of shorts before discount was $25.

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Answer:  The correct answer is x=18 and y=59

Step-by-step explanation:

Opposite angles are congruent:

(6x+13) = (7x-5)

Solve for x:

6x+13−7x=7x−5−7x

−x+13−13=−5−13

−x=−18

x=18

Plug x value in for y:

Y=180-(7x-5)

Y=180-(126-5)

Y=180-121

Y=59

If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

The equation is

y = -x

The slope intercept form

y = mx+b

Where m is the slope of the line

Comparing the slope intercept form and the given equation

Slope of the line m = -1

The line is passing through the points (-8,2)

The point slope form of the line

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-2 = -1(x-(-8))

y-2 = -1(x+8)

y-2 = -x-8

y = -x-8+2

y = -x-6

Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

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Answer:

8.1

Step-by-step explanation:

just calculate 45 of 18%

Answer:

12 more days

Step-by-step explanation:

Every time cheeseburger will be served: 4th day, 8th day, 12th day, 16th day

Every time pizza wil be served: 6th day, 12th day, 18th day

Since 12 is a common number, every 12 days both cheeseburgers and pizzas will be served

The radius of the full-size pool is 2 times greater than the radius of kiddie pool

The formula for determining the area of a circle is expressed mathematically as;

Area = πr²

Where;

From the information given, we have that;

Radius = √A/3

Where;

A is the radius of the circle

For the circular kiddie, we have;

Radius = √28/3

Find the ratio

Radius = √9. 3

Find the square root

Radius = 3 feet

For the circular pool

Radius = √ 113/3

Find the ratio

Radius = √37. 66

Find the square root

Radius = 6 feet

We then have;

Radius of the pool/radius of the kiddie pool

6/3

Find the quotient

2

Hence, the value is 2

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The amount of charge on the capacitor after 0.06 seconds = 0.042 millicoulombs

An electric circuit is defined as the device that aids in transmission of electricity generated by a battery or a generator.

A capacitor is defined as the device that has the ability to store energy in an electric circuit.

The amount of charge in a capacitor decreases in one second by = 30%

The original charge on the capacitor = 1 millicoulombs

30 % of 1millicoulombs = 30/100 * 1 = 0.3

1millicoulombs - 0.3 millicoulombs = 0.7 millicoulombs .

If 0.7 millicoulombs = 1 second

X millicoulombs = 0.06 second

Make X millicoulombs the subject of formula;

X millicoulombs = 0.06 × 0.7 = 0.042 millicoulombs.

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Answer: 198

Step-by-step explanation:

9 * 36 = 324

9 * 14 = 126

324 - 126 = 198

Hope this helps!

Answer:

a) 199

f(-6)= 5(-6)^2 - 3 (-6) + 1 =199

b) 37

f(3)= 5(3)^2 - 3 (3) + 1 =37

It is not possible to write a linear inequality such that the solution contains only positive values of x and y.

This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.

The beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

Given that, a lighthouse is located on a small island 4 km away from the nearest point P.

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

[tex]\frac{d\theta}{dt}[/tex] = 6 rev/min

= 6π rad/min

tan θ = x/6

[tex]\frac{d}{dt}tan\theta=\frac{d}{dt}(\frac{x}{6} )[/tex]

[tex]sec^2\frac{d\theta}{dt} = \frac{1}{6}(\frac{dx}{dt} )[/tex]

[tex]\frac{dx}{dt}=6sec^2\theta\frac{d\theta}{dt}[/tex]

At x=1 km; tan θ= x/6 = 1/6

[tex]sec^2 \theta= 1+tan^2 \theta= 1 + (\frac{1}{6})^2[/tex]

[tex]sec^2 \theta = \frac{10}{9}[/tex]

[tex]\frac{dx}{dt} = 6 sec^2\theta \frac{d\theta}{dt}[/tex]

dx/dt = 6 × 10/9 × 6π

dx/dt = 125.66 km/min

Therefore, the beam of light along the shoreline when it is 1 km from P is moving at 125.66 km/min.

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121670000 different license plates are possible.

A license plate consists of 7 characters.

The first 4 characters are numerals from 0 to 9.

each character can be in 10 ways

so possible ways = 10 * 10 * 10 * 10  = 10000

The last 3 characters are letters excluding I, O, and X.

                    Each character can be in 26 - 3 = 23 Ways

                         Possible ways = 23 *23 * 23  = 12167

Number of possible different license plates  = 10000 * 12167

                                                                          = 121670000

Motor vehicle registration is the registration of a motor vehicle with a public authority, whether compulsory or otherwise. The purpose of registering a motor vehicle  is to establish a link between the vehicle and the owner or user of the vehicle. This link may be used for taxation or criminal investigations.

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If the two equations are x - y = 11 and -x + y = -11 then the system has  infinitely many solutions.

Let the two equations be

x - y = 11 ..................(1)

-x + y = -11  ..................(2)

Express the first equation in the term of x and substitute it into the second equation:

From (1) and (2), we get

-(y + 11) + y = -11

simplifying the above equation, we get

-y - 11 + y = -11

-y + y = 11 - 11

0 = 0

So, the system has infinitely many solutions.

Therefore, the correct answer is option c. infinitely many solutions.

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Answer:

154 feet squared

Step-by-step explanation:

1. Divide 14 by 2

2. Use the equation pie times radius squared

3. Answer is 153 foot squared

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(4\times10^3) + (3.2\times 10^1)}[/tex]

[tex]\mathsf{= 4\times10^3 + 3.2\times 10^1}[/tex]

[tex]\mathsf{= 4\times10\times10\times10 + 3.2\times10}[/tex]

[tex]\mathsf{= 4\times100\times10 + 3.2\times10}[/tex]

[tex]\mathsf{= 4\times1,000 + 3.2\times10}[/tex]

[tex]\mathsf{= 4,000 + 32}[/tex]

[tex]\mathsf{= 4,032}[/tex]

[tex]\mathsf{\approx 4.032\times10^3}[/tex]

[tex]\huge\text{Thus, your answer SHOULD be: \boxed{\mathsf{4.032\times10^3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

I got you, the answer is c+32.

Step-by-step explanation:

Hope this helps. Please mark branliest if right.