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frosja888 [35]
1 year ago
14

The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at

Mathematics
1 answer:
g100num [7]1 year ago
7 0
To solve this we are going to use the formula fro the force applied to a spring: F=ks
where
k is the spring constant 
s is the extension 

Since we know the F=ma, we can replace that in our formula and solve for a :
ma=ks
a= \frac{ks}{m}
where
a is the acceleration 
k is the spring constant
s is the extension 
m is the mass

We know for our problem that k=200, s=0.4, and m=25. So lets replace those values in our formula to find a:
a= \frac{ks}{m}
a= \frac{(200)(0.4)}{25}
a=3.5 \frac{m}{s^2}

We can conclude that the acceleration of the block when s=0.4m is 3.5 \frac{m}{s^2}.
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Naomi and her children went into a bakery where they sell donuts for $1.25 each and cookies for $0.75 each. Naomi has $15 to spe
LiRa [457]

Answer:

I dont know the ans can u pls tell me the ans if you get it

4 0
1 year ago
g An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the
blagie [28]

Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean amount of money spent on textbooks = $121.60

            \sigma = population standard deviation = $6.36

            n = sample of students = 36

            \mu = population mean

<em>Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>

<em />

So, 95% confidence interval for the population mean, \mu is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                      of significance are -1.645 & 1.645}  

P(-1.645 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.645) = 0.90

P( -1.645 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

P( \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.90

<u>90% confidence interval for</u> \mu = [ \bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } } ]

                                      = [ 121.60-1.645 \times {\frac{6.36}{\sqrt{36} } } , 121.60+1.645 \times {\frac{6.36}{\sqrt{36} } } ]

                                      = [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

5 0
2 years ago
The following table shows the salary of 7 people in an office last year.
kotegsom [21]

Answer:

a.  £24,714.29

b. £16,833.33

Step-by-step explanation:

The calculation of mean income is given below:-

Mean income = Total addition of salaries ÷ Number of workers

= £9,500 + £25,000 + £13,250 + £72,000 + £12,750 + £29,500 + £11,000

= £173,000 ÷ 7

= £24,714.29

Now,

the Mean income excluding Deva's salary:

= Formula of Mean income

= Total addition of salaries excluding Deva salary ÷ Number of workers

= (£9,500 + £25,000 + £13,250 + £12,750 + £29,500 + £11,000) ÷ 6

= £101,000 ÷ 6

= £16,833.33

7 0
2 years ago
Identify which line from the graph the following right triangles could lie on.
qaws [65]

Answer:

Step-by-step explanation:

Slope of line A = \frac{\text{Rise}}{\text{Run}}

                         = \frac{9}{3}

                         = 3

Slope of line B = \frac{9}{6}

                         = \frac{3}{2}

Slope of line C = \frac{6}{8}

                         = \frac{3}{4}

5). Slope of the hypotenuse of the right triangle = \frac{\text{Rise}}{\text{Run}}

                                                                                = \frac{90}{120}

                                                                                = \frac{3}{4}

Since slopes of line C and the hypotenuse are same, right triangle may lie on line C.

6). Slope of the hypotenuse = \frac{30}{10}

                                              = 3

Therefore, this triangle may lie on the line A.

7). Slope of hypotenuse = \frac{18}{24}

                                        = \frac{3}{4}

Given triangle may lie on the line C.

8). Slope of hypotenuse = \frac{21}{14}

                                        = \frac{3}{2}

Given triangle may lie on the line B.

9). Slope of hypotenuse = \frac{36}{24}

                                        = \frac{3}{2}

Given triangle may lie on the line B.

10). Slope of hypotenuse = \frac{48}{16}

                                          = 3

Given triangle may lie on the line A.

7 0
1 year ago
How does the graph of f(x)=3|x+2|+4 relate to its parent function
Mariana [72]
If parent functin is f(x)=|x|
it is moved to the left 2 units
vertically streched by a factor of 3
and moved up by 4 units in that order

because
to move a function to left c units, add c to every x
to vertically strech function by factor of c, multiply whole function by c
to move funciotn up c units, add c to whole function


so it is 2 to the left, verteically streched by a factor of 3 then moved up 4 units
5 0
2 years ago
Read 2 more answers
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