Click to select the figure in the image that would portray the rotation of the given preimage and the rotation arrow,

Which is equivalent to sin 51°? A) cos 51° B) cos 39° C) tan 39° D) tan 51°

____ [38]

The answer is B
have a great day

8 0

2 years ago

A triangular piece of rubber is stretched equally from all sides, without distorting its shape, such that each side of the enlar

OverLord2011 [107]

Answer:

The area of the enlarged triangle is $4$ times the original area

Step-by-step explanation:

we know that

The scale factor is equal to divide the measurement of the length side of the enlarged triangle by the the measurement of the length of the corresponding side of the original triangle

In his problem

Let

x------> the length side of the original triangle

so

2x-----> is the length of the corresponding side of the enlarged triangle

$scale\ factor=\frac{2x}{x}=2$

$scale\ factor> 1$ -------> that means is increasing

The scale factor squared is equal to the ratio of the area of the enlarged triangle divided by the area of the original triangle

so

Let

m-------> the area of the enlarged triangle

n------> the area of the original triangle

r-------> scale factor

$r^{2} =\frac{m}{n}$

we have

$r=2$

substitute

$2^{2} =\frac{m}{n}$

$m=4n$

therefore

The area of the enlarged triangle is $4$ times the original area

8 0

2 years ago

For the 2017-2018 school year, at a 7% inflation rate, the average costs for one year of education at a two-year college are pro

zvonat [6]

For the 2017-2018 school year, the average costs for one year of education is:

Tuition/Fees: $4,391

Living Costs: $10,406

Books/Supplies: $1,724

Transportation: $2,313

Other Expenses: $3,025

With the given 7% inflation rate, the average cost will increase for the next session (2018-2019).

Hence, for year 2017-2018 the total expense will be sum of all the given costs.

= $4,391 + $10,406 + $1,724 + $2,313 + $3,025

= $21,859

8 0

2 years ago

Read 2 more answers

Estimate the sum of 299 and 388

myrzilka [38]

The estimate of 299 is 300. The estimate of 388 is 400. So, 300 + 400 = 700

8 0

2 years ago

Read 2 more answers

Assume the blood pressures of 10 people were measured before and after sleeping for the night. What is the corresponding critica

NeX [460]

Answer:

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.

Let put some notation

x=test value with right arm , y = test value with left arm

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x = 0$

Alternative hypothesis: $\mu_y -\mu_x \neq 0$

The first step is calculate the difference $d_i=y_i-x_i$

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{361}{5}$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}$

For the critical value we need to calculate the degrees of freedom given by:

$df = n-1= 10-1=9$

And since we have a one tailed test we need to look in the t distribution with 9 degrees of freedom a quantile who accumulates 0.05 of the area on a tail and we got:

$|t_{crit}| =1.833$

5 0

2 years ago