A force of 720 newtons stretches a spring 3 meters. A mass of 60 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Find the equation of motion.

Answer:

The solution is:

Step-by-step explanation:

Given the expression

[tex]0.5^{10}\div 0.5^7[/tex]

Solving

[tex]\frac{0.5^{10}}{0.5^7}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]

so

[tex]\frac{0.5^{10}}{0.5^7}=0.5^{10-7}[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:10-7=3[/tex]

[tex]=0.5^3[/tex]

[tex]=0.125[/tex]        ∵ [tex]0.5^3=0.125[/tex]

Therefore, the solution is:

[tex]\frac{0.5^{10}}{0.5^7}=0.125[/tex]

Sam's swimming pool cleaning has 73 customers.

The correct option is d.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Sam's Swimming Pool Cleaning has an annual net income of $46,900.

Sam charges $25 per week for each of his customers for 52 weeks.

His annual operating expenses, including labor and supplies, are $48,000.

His total income,

= 46900 + 48000

= 94900.

The number of customers = 94900/(25 x 52) = 73.

Therefore, the number of customers is 73.

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The approximate solution to the trigonometric inequality will be 0<=x<0.7896. Option A is correct.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

Given inequality;

tan(x/4)<1/5

x/4 = tan⁻¹(1/5)

0<=x<0.7896

The approximate solution to the trigonometric inequality will be 0<=x<0.7896.

Hence option A is correct.

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Answer:

A. 0 <= x < 0.7896

Step-by-step explanation:

EDG

Answer: the correct answer was- A binomial cumulative distribution function should be used because the question asks for determining the probability that at least five students have blonde hair.

i got this question right

Step-by-step explanation:

Answer:

The first and third quartile of the wingspans are 116.9 cm and 133.1 cm respectively.

Step-by-step explanation:

The first and third quartile of a normal distribution are:

[tex]Q_{1}=\mu-0.675\sigma\\\\Q_{3}=\mu+0.675\sigma[/tex]

The information provided is as follows:

[tex]\mu=125\\\sigma=12[/tex]

Compute the first and third quartile of the wingspans as follows:

[tex]Q_{1}=\mu-0.675\sigma=125-(0.675\times 12)=116.9\\\\Q_{3}=\mu+0.675\sigma=125+(0.675\times 12)=133.1[/tex]

Thus, the first and third quartile of the wingspans are 116.9 cm and 133.1 cm respectively.

Answer:

The proportional relationship is + 1.50 with each toppings. The cost for 6 toppings is $17.99.

Step-by-step explanation:

11.99 to 13.49 is + 1.50, 13.49 to 14.99 is + 1.50, and so on.

Answer:

there is nothing here so??

Answer:

where??? uhhhhhhhh lol

Answer:

1.9 litres is equvalent to 1900 mililitres

Answer:

Step-by-step explanation:

1). (40, 60)

m = 2

y - 60 = 2( x - 40 )

2). (5, - 1)

m = - 3

y - ( - 1) = - 3( x - 5 )

3). m = 2

y - 1 = 2( x + 2 )

y = 2x + 5

Answer:

25 transwind

Step-by-step explanation:

the wind speed in your country is probably 4cm and in the next six hours is going to change to carbon dioxide speed which is 25 transpiring

Answer:

the mean is 7.2 and the median is 8

Step-by-step explanation:

when you add up all the data you will get 36 which you divide by 5 since there are 5 different values.This will result to 7.2 as your final answer .Whereas for the median out of the 5 numbers the median would be the 3rd number which when you order them from smallest to largest it would be 8.

Answer:

6 and -3

Step-by-step explanation:

6 times -3 equals -18 because a positive times a negative equals a negative. 6 plus -3 equals 3, remember that a positive plus a negative can be rewritten as subtraction. So 6+(-3)=6-3, which equals 3.

Answer:

-3/4

Step-by-step explanation:

3x+4y=12

-3x -3x

4y=-3x+12

÷4 ÷4

y=-3/4x+12

Answer:

-3/4 or -0.75

Example:

Answer:

126

Step-by-step explanation:

if it have 9 trips and each trip there is 14 people so we do 14×9=126

Answer:

(x+1)^2+(y+4)^2=16

Step-by-step explanation:

equation of the circle

(x-x0)^2+(y-y0)^2=r^2

where x0 and y0 is center of circle

and r is radius of the circle.

we know that the center point is the middle of the diameter

so x0=(x1+x2)/2

x0=(3+(-5))/2=-2/2=-1

y0=(-4+(-4))/2=-8/2=-4

so the midpoint or the center of circle is the points (-1,-4)

the formula to find the distance between two. points is √[(x2-x1)^2+(y2-y1)^2]

so r is the distance between the center point and one of the diameter endpoints.

let us take points (3,-4) and center point (-1,-4)

√(-1-3)^2+(-4-(-4))^2=

√(-4)^2+0^2=

√16=4

so the radius of the circle is 4

now the equation of the circle will be

(x-(-1))^2+(y-(-4))^2=4^2

(x+1)^2+(y+4)^2=16

Answer:

1.6627 (money wise, $1.66)

Step-by-step explanation:

Since its 130%, you know there was already a whole increase. So first you would do 1.279 + 1.279, which would give you 2.558. Then you need to calculate 30% of 1.279 for the rest of the increase. That gives you 0.3837 Add 2.558 and 0.3837 together, which would give you 2.9417. To get the INCREASE, you would have to subtract the new total from the original price, so 2.9417 - 1.279. This would give you 1.6627.

Answer:

56

Step-by-step explanation: so 5+6=11, 65 is th

reverse of 56, 56+9=65

Answer:

The equation of the line (in slope-intercept form) is y=4x-9

Answer:

More info

Step-by-step explanation:

I need more info than that please!`

1 feet = 12 inches  

3 feets= 36 inches

8 feets = 96 inches

hope this helps  

Assume the year that it would take to these trees have the same height is : x (years)

After x years, type A tree has heigth: 36 +23x (inches)

After x years, type B tree has heigth: 96 +17x (inches)

We have  36+23x = 96+17x

Solve the equation, we have x=10

Conclusion: It will take 10 years to these trees have the same height.

Answer:

8/9 + 1/6 = 1 1/18

Step-by-step explanation:

1. Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

8/9*2/2 + 1/6*3/3 = ?

2. Complete the multiplication and the equation becomes 16/18 + 3/18.

3. 16/18+3/18 = 19/18 = 1 1/18

Answer:

F

Step-by-step explanation:

6×3x=18x

6×2=12

18x+12-4

Answer:

see below

Step-by-step explanation:

   18x + 12 - 4  simplify

Answer: 1/9 of a mile

Step-by-step explanation:

3/27=x/1

27x=3

Divide by 27

3/27=1/9

Answer:

9

Step-by-step explanation: 9 +9 +9=27

Part (A)

The input variable is the shoe size because it is along the horizontal axis, or x axis. It's not clear what the units for the shoe size are, but it's possible the units are in inches.

The output variable is the y value, which in this case is the height. The units for the height is in inches.

====================================================

Part (B)

We have a positive trend. We determine this visually by noting the regression line, or trend line, is going upward as we move from left to right.

Algebraically, the equation for the trend line has a positive slope, which leads to a positive trend.

A positive trend is where x and y increase together. As shoe size goes up, height goes up as well.

While not all the points are on the line, there is a tendency for the points to go uphill as we move from left to right.

As for the strength of the correlation, that part is subjective. If we knew the correlation coefficient r, then we could be more certain; however, we don't know this value. So instead we have to eyeball the given graph and give an estimate. Based on the graph, I'd say there's a moderate positive correlation going on. It's somewhere in the middle of weak and strong positive correlation because the data points are somewhat scattered randomly, but they trend upward nonetheless.

====================================================

Part (C)

The rate of change is the slope. The slope is the coefficient of the independent variable x. In this problem, the slope is 1.728

So the rate of change is 1.728 inches per shoe size.

In other words, as the shoe size increases by 1 unit (1 inch perhaps?), the height will increase by roughly 1.728 inches.

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Extra info:

The equation

Height = 51.46 + 1.728(Shoe Size)

is the same as

y = 51.46 + 1.728x

where x is the shoe size and y is the height

We can rearrange that into

y = 1.728x + 51.46

So that it matches with the familiar y = mx+b slope intercept form. This is optional.

Answer:

420 over 225, 28/15

Step-by-step explanation: