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erastova [34]
3 years ago
8

A bicyclist slow with a force of 3.5 × 10² N. if the bicyclist and bicycle have a total mass of 1.0 × 10² kg, what is the accele

ration
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
7 0

Answer:

3.5 m/s²

Step-by-step explanation:

We are given;

  • The force of a bicycle as 3.5 × 10² N
  • Mass of the bicycle as  1.0 × 10² kg

We are required to determine the acceleration of the bicycle;

From Newton's second law of motion;

F = ma

Rearranging this;

a = F÷ m

Therefore;

Acceleration = 3.5 × 10² N ÷ 1.0 × 10² kg

                     = 3.5 m/s²

Thus, the acceleration of the bicycle is 3.5 m/s²

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Ludmilka [50]
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The a and b represents the two edges, while c is the diagonal side and it is called the hypotenuse. Since you already know what the hypotenuse is and what one of the sides already are you just have to use the problem: c^2-a^2=b^2. Then if you plug the data you already have into the problem you will get 10^2-6^2=b^2. That then equals 100-36=b^2. Then you subtract and get b^2=64. Then you square root both sides and you get the answer b=8.
5 0
3 years ago
What is the solution to x-16=-12??
zhannawk [14.2K]
Plus 16 on both side and negative 12plus 16 is 4 so x equals 4
4 0
3 years ago
If JK answered / of the Math questions correctly, how many points did she get in a 50- item test?
Fittoniya [83]

Answer:

JK got 30 answers correct on a 50 item test.

Step-by-step explanation:

It is given that:

Total items on test = T = 50

Fraction of total items that were answered correctly = 3/5

We simply have to multiply the total number of questions by the fraction of correct answers.

So,

The correct answered number of items are:

= \frac{3}{5} * 50\\=30

Hence,

JK got 30 answers correct on a 50 item test.

4 0
3 years ago
C(1)=−20<br> c(n)=c(n−1)+10<br><br> Find the second term in the sequence. <br> ​
svet-max [94.6K]

Answer:

c(2) = -10

Step-by-step explanation:

The first equation says that the first term of the sequence is -20.

The second equation is saying that to find any term of the sequence, add 10 to the previous term.

c(2) = c(2-1) + 10

c(2) = c(1) + 10

c(2) = -20  + 10 = -10

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2 years ago
GRE Test: The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores o
Zepler [3.9K]

Answer:

a) \bar X=144.3

b) The 95% confidence interval would be given by (138.846;149.754)      

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3 represent the sample mean  

\mu population mean (variable of interest)

\sigma=8.8 represent the population standard deviation

n=10 represent the sample size  

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

\bar X=144.3

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that t_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

144.3-1.96\frac{8.8}{\sqrt{10}}=138.846    

144.3+1.96\frac{8.8}{\sqrt{10}}=149.754

So on this case the 95% confidence interval would be given by (138.846;149.754)    

Part c

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (5) we got:

n=(\frac{1.960(8.8)}{3})^2 =33.05 \approx 34

So the answer for this case would be n=34 rounded up to the nearest integer

Part d

n=(\frac{1.960(8.8)}{1})^2 =297.493 \approx 298

So the answer for this case would be n=298 rounded up to the nearest integer

Part e

n=(\frac{1.960(8.8)}{0.5})^2 =1189.97 \approx 1190

So the answer for this case would be n=1190 rounded up to the nearest integer

7 0
3 years ago
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