In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 4,100 r.p.m. Transmission in first gear Drive-shaft speed (to nearest r.p.m.) =
a) 1367
b) 12,300
c) 6560

Answer:

Step-by-step explanation:

Applying BODMAS here;

We first solve what is in the brackets:

9x - 81 -3 = -8x - 16

We then put the like terms together:

9x + 8x = -16 + 81 + 3

We then do the addition:

17x = -16 + 84

We then do the subtraction:

17x = 68

Simplifying this gives:

x = [tex]\frac{68}{17}[/tex] = 4

C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

The advantage of experimental probability over theoretical probability is that option C. It is not always possible to calculate theoretical probability in complex situations, but experimental probability can be calculated any time experiments can be run.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Experimental probability is the probability where the probability of something is found by real experiments.

This is not computed by assuming or calculation.

Theoretical probability is the probability where the probability of something is found theoretically.

The probability is found using formulas and calculation.

So, it is not always possible to calculate theoretical probability in complex situations.

But experimental probability can be found in any case using experiments.

Hence the correct option is C.

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Answer:

[tex]\sqrt{85}  or 9.22[/tex]

Step-by-step explanation:

You need to remember the following equation:

[tex]a^{2} + b^{2} = c^{2}[/tex]

Where a and b is the lengths of the two sides and c is the hypotenuse.

So simply plug these values into this:

[tex]6^{2} + 7^{2} = h^{2}[/tex]

36 + 49 = h^2

36 + 49 = 85

So the hypotenuse is the square root of 85:

[tex]\sqrt{85}  = 9.22[/tex]

Answer:

A F(x)=30x

Step-by-step explanation:

just plug number in to the equations to see which one matches

Answer: [tex]f(x)=30\cdot2^{2x}[/tex]

Step-by-step explanation:

Given: A wildlife preservation group records the number of squirrels in a city park.

The first count recorded = 30 squirrels.

A second count of 60 squirrels is recorded six months later, and 120 squirrels are counted at the end of one year.

The growth rate of squirrel=[tex]\frac{120}{30}=4=2^2[/tex]

The exponential growth equation is given by :-

[tex]y=Ab^n[/tex], where A is the initial amount , b is the growth rate and n is the time period.

If the growth rate remains constant, then the function represents the number of squirrels after x years is given by :-

[tex]f(x)=30\cdot(2^2)^x=30\cdot2^{2x}[/tex]

Answer: length = 7 c, and width = 6 cm

Step-by-step explanation:

Answer:

$0.25 per pound.

Step-by-step explanation:

Let us find unit rate for both quantities.

[tex]\text{Price per pound}=\frac{8.75\text{ dollars}}{2.5\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.5\frac{\text{ dollars}}{\text{ pound}}[/tex]  

Therefore, cost of per pound for first given rate is $3.5.

Now let us find unit rate for second quantity.

[tex]\text{Price per pound}=\frac{9.75\text{ dollars}}{3\text{ pound}}[/tex]

[tex]\text{Price per pound}=3.25\frac{\text{ dollars}}{\text{ pound}}[/tex]

We can see that price for second quantity is less than 1st. To find the savings per pound we will subtract 3.25 from 3.5.

[tex]\text{Savings per pound}=3.50-3.25[/tex]

[tex]\text{Savings per pound}=0.25[/tex]

Therefore, we will save $0.25 per pound by buying the least expensive.

Answer:

0.25

Step-by-step explanation:

Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].

So if the perimeter of the larger polygon is

[tex]s_1+s_2+s_3=85[/tex]

then the perimeter of the smaller polygon would be

[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]

so its perimeter would be 34 meters.

Final answer:

The perimeter of the smaller similar polygon is 34 meters, calculated by setting up and solving the proportion 2/5 = P/85.

Explanation:

When dealing with similar polygons, the ratio of their corresponding side lengths is the same as the ratio of their perimeters. Given that the ratio of the sides is 2 to 5, and the perimeter of the larger polygon is 85 meters, we can set up a proportion to find the perimeter of the smaller polygon.

Let the perimeter of the smaller polygon be P. The proportion will be 2/5 = P/85. To find P, we cross-multiply and get: 2 * 85 = 5 * P. Simplifying, we find that P equals 34 meters. Hence, the perimeter of the smaller polygon is 34 meters.

Answer:The answer is mostly C) 10

Step-by-step explanation:

It's C because when you go to day 9, you count after 58 by adding 4 more, which equals 62 and then, since day 10) is 68 people that means that the answer is C.

Answer: c 10

Step-by-step explanation:

Since each day 4 more people sign up, on day 7, 50 will have signed up; on day 8, 54 people; day 9, 58 people; and day 10, 62 people

Answer:

767

Step-by-step explanation:

Answer:

Point R = 8

Step-by-step explanation:

-2.5 r = -20

The solution to this equation is represented by a number line

In the given equation we have only the variable 'r'

We will get the value of 'r' while solving the above equation

That 'r' value is the solution point R on number line

[tex]-2.5r = -20[/tex]

divide by -2.5 on both sides

[tex]r=\frac{-20}{-2.5}[/tex]

r= 8 is our solution

Answer:

[tex] \displaystyle y _{ \text{parallel}} = \frac{5}{6} x- 2[/tex]

Step-by-step explanation:

we are given a equation of line

[tex] \displaystyle y = \frac{5}{6} x - 10[/tex]

we want to figure out the line Parallel to the given line and passes through (12,8)

to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line

figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,

[tex] \displaystyle m _{ \text{parallel}} = \frac{5}{6} [/tex]

now we need to figure out the y-intercept and the equation to do so we can consider the following formula:

[tex] \displaystyle y - y_{1} = m(x - x_{1})[/tex]

we the point where the parallel line passes i.e [tex](x_1,y_1)=(12,8)[/tex] and we already got that the slope is ⅚ thus substitute:

[tex] \displaystyle y - 8= \frac{5}{6} (x- 12)[/tex]

we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so

distribute:

[tex] \displaystyle y - 8= \frac{5}{6} x- \frac{5}{6} \times 12[/tex]

reduce fraction:

[tex] \displaystyle y - 8= \frac{5}{6} x- 5 \times 2[/tex]

simplify multiplication:

[tex] \displaystyle y - 8= \frac{5}{6} x- 10[/tex]

add 8 to both sides:

[tex] \displaystyle y = \frac{5}{6} x- 2[/tex]

and we are done!

I hope this helps, sorry for my messy handwriting. If you have any questions feel free to ask me!

Answer:

130 m

Step-by-step explanation:

Let surface of ocean be at 0 feet (sea level)

The distance from albatross to surface is 100 and the distance from surface to shark is 30 m. The total distance between them is [tex]100+30=130[/tex]

Distance between shark and albatross is 130 m

Answer:

130 m

Step-by-step explanation:

Answer:

left 3 units

down 1 unit

Step-by-step explanation:

The required transformation is obtained by shifting of 3 units left and 1 unit down. The correct options are (c) and (d).

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

The given functions are as below,

f(x) = [tex]2^{x - 6} + 3[/tex]

And, g(x) = [tex]2^{x - 3} + 2[/tex]

It can be rewritten as,

g(x) = [tex]2^{x - 3} + 2[/tex] = [tex]2^{x - 6 + 3} + 3 - 1[/tex]

It clearly shows as per the rule of transformation, f(x) is shifted 3 units left and 1 unit down to get g(x).

Hence, the parent function f(x) is shifted 3 units left and 1 unit down.

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Answer: [tex]10(512 – c) + 5c = 3,570[/tex]

Step-by-step explanation:

Given : The number of student tickets sold is represented by c.

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each.

The sellers collected $3,570 from 512 tickets sold.

Since , the total tickets sold = 512

Therefore , the number of adults ticket = [tex]512-c[/tex]

Now, cost of total child tickets : [tex]5c[/tex]

Cost of total adult tickets = [tex]10(512 – c)[/tex]

Now, according to the cost of the tickets , we have the following equation :-

[tex]10(512 – c) + 5c = 3,570[/tex]

Answer:

35.7

Step-by-step explanation:

First, you would calculate how many gallons of gasoline the car gets. To do this, divide your total mileage of 500 miles by the mpg (30). Now you know how many gallons of gasoline will be used by the car. After calculating, you get 16.67. Multiply this by how much it costs per gallon of gasoline, and you get an answer of $35.7.

Answer: 7 + 2/3(12) = 15

90/15 = $6 for adult tickets

Answer:

280 minutes

Step-by-step explanation:

First, you must find the miles per minute:

112/14 = 8

Then you must multiply the miles per minute by the amount of miles:

35 * 8 = 280

Answer: The triangle mentioned here is an acute angled triangle.

Step-by-step explanation: x+x+10+2x-6=180°(angle sum prop. of triangles)

               =                             4x+4=180°

               =                             4x=174°

               =                             x=44°

therefore, x=44°

                 ,x+10=44+10=54°

                 ,2x-6=2(44)-6=82°

Answer:

Given the function:

f(x) = the quantity of x squared plus 3x minus 4 , all over x plus 4

i,e

[tex]f(x) = \frac{x^2+3x-4}{x+4}[/tex]

or

[tex]f(x) = \frac{x^2+4x-x-4}{x+4}[/tex]

or

[tex]f(x) = \frac{x(x+4)-1(x+4)}{x+4}[/tex]

or

[tex]f(x) = \frac{(x+4)(x-1)}{x+4}[/tex]

⇒y= f(x) = x -1                 ......[1]

Find the x-intercepts and y-intercepts for the equation [1] ;

y-intercepts defined as the graph crosses the y-axis;

substitute x =0 to solve for y;

y = 0-1 = -1

y = -1

x-intercepts defined as the graph crosses the x-axis;

substitute y =0 to solve for x;

0 = x-1

or

x = 1

Plot these points (0 , -1) and (1, 0) on the graph for the given function as shown below.

Answer:

The regular price was $93.03

Step-by-step explanation:

In order to find the regular price, divide the amount spent by the percentage of which she paid for it. Since it was 25% off, she paid 75% of the overall price.

$69.77/75% = $93.03

Answer:

Thus; Jupiter travels at 480 miles/m and in 6 minutes, it will travel 2880 miles.

Step-by-step explanation:

First to convert it you need to multiply 8 miles per second by 60 seconds because there are 60 seconds in a minute:

 8 miles    x    60 s 

1 second        1 min

The unit of seconds will cancel out so you will get 480 miles/ min

To get how far it travels in 6 min you need to multiply the speed by 6 minutes

480 miles   x  6 min = 2880

  1 min

The unit of minutes will cancel out to get 2880 miles

Answer:  True, False, True

Step-by-step explanation:

To determine steepness, compare the coefficients of each function:

f(x) = 4x²      coefficient is: 4

g(x) = [tex]\dfrac{15}{4}x^2[/tex]   coefficient is: 4.75

h(x) = [tex]\dfrac{4}{15}x^2[/tex]   coefficient is: 0.27

f(x)  ??? h(x)

 4    >  0.27

f(x) is steeper than h(x)

               h(x) ??? g(x)

               0.27 <   4.75

               h(x) is LESS steep than g(x)

                                              g(x) ??? f(x)

                                              4.75 >   4

                                              g(x) is steeper than f(x)

Answer: 11.6 units.

Step-by-step explanation:

1. Plot the points as you can see in the graph attached.

2. As you can see, the lenght TA is 3 units.

3. Apply the formula for calculate the distance between two points, to calculate the length TP and TA. The formula is:

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

4. Therefore, you have:

[tex]TP=\sqrt{(1-3)^{2}+(4-0)^{2}}=4.47units[/tex]

[tex]AP=\sqrt{(4-3)^{2}+(4-0)^{2}}=4.12units[/tex]

5. The perimeter is the sum of the the lenght of each side, therefore:

[tex]Perimeter=3units+4.47units+4.12units\\Perimeter=11.59units[/tex]

6. To the nearest tenth unit:

[tex]Perimeter=11.6units[/tex]

Answer:

l = 20.5 cm

h = 17.5 cm

w =  9.5 cm

Step-by-step explanation:

Conditions

l+w =30     Solving for w     30 - l = w

h = l-3

V = l*w*h

Substituting in

V = l * (30-l) * (l-3)

   = (30l-l^2) (l-3)

   = 30 l^2 - l^3 - 90l + 3l^2

Combining like terms

Step-by-step solution

-l^3 + 33 l^2 - 90 l

To find the maximum we need to take the first derivative and then set it equal to zero

-3l^2 + 66l -90 = 0

Factor out a -3

-3 (l^2 -22l +30) =0

Using my calculator and the quadratic formula

l = 11 - sqrt(91)

l = 11 + sqrt(91)

l = 1.5 or 20.5  approximately

If l = 1. then

h= l-3   would be negative  so

l = 20.5

h = l-3

h = 17.5 approximately

w = 30-l = 9.5 approximately

Answer:

16 rotations.  

Step-by-step explanation:

We have been given that Shawn is coasting down a 500 cm long ramp on his inline skates. The wheels on his inline skates are 32 cm in circumference.

To find the number of rotations we will divide length of ramp by 32 as distance covered by wheels in one rotation will be equal to 32 cm.

[tex]\text{Number of rotations}=\frac{\text{Total distance}}{\text{Circumference of wheel}}[/tex]

[tex]\text{Number of rotations}=\frac{500}{32}[/tex]

[tex]\text{Number of rotations}=15.625\approx 16[/tex]

Therefore, each wheel must make 16 rotations while Shawn is coasting down the ramp.

Answer:

1/9

Step-by-step explanation:

1/3 ÷ 3 is the set-up for the problem we are trying to solve.

Remember when we divide fractions we multiply by the reciprocal. So we have:

1/3 × 1/3 since the reciprocal of 3/1 is 1/3

Multiplying 1/3 x 1/3 we find the product is 1/9

Therefore, each person would receive 1/9 of the watermelon

The relationship between the weight of a person on Earth and the

person's weight on the Moon is a  proportional relationship.

Reasons:

The weight of the person on Earth = 120 pounds

Weight of the person on the Moon = 20 pounds

Required:

The weight of a person that weighs 93 pounds on Earth on the Moon

Solution:

Let x represent the factor (acceleration due to gravity) on Earth, let y

represent the factor on the Moon, and let m, represent the mass of the

person, we have;

x·m = 120

y·m = 20

Therefore;

[tex]\displaystyle \mathbf{\frac{x \cdot m}{y \cdot m}} = \mathrm{\frac{x}{y} } = \frac{120}{20} = 6[/tex]

For the person that weighs 93 pounds on Earth, we have;

[tex]\displaystyle \mathrm{\frac{x}{y} } = \mathbf{\frac{93}{Weight \ on \ the \ Moon}} = 6[/tex]

Which gives;

[tex]\displaystyle Weight \ of\ the \ person\ on \ the\ Moon = \frac{93}{6} = 15.5[/tex]

The weight of the person on the Moon = 15.5 pounds

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