Round 34.037 to 3 significant figures.
a. 34.04
b. 34
c. 34.037
d. 34.0​

Given:

Given that ABC is a right triangle.

The length of AB is 7 units.

The measure of ∠A is 65°

We need to determine the length of AC

Length of AC:

The length of AC can be determined using the trigonometric ratio.

Thus, we have;

Where the value of is 65° and the side adjacent to the angle is AC and the side hypotenuse to the angle is AB.

Substituting the values, we have;

Substituting AB = 7, we have;

Multiplying both sides by 7, we get;

Rounding off to the nearest hundredth, we get;

Thus, the length of AC is 2.96 units.

Answer:

3 for problem

Step-by-step explanation:

Answer:

n=6

"=T.INV(1-0.025,5)", and we got the critical values given by:  

n=12

"=T.INV(1-0.025,11)", and we got the critical values given by:  

Step-by-step explanation:

Previous concepts

The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.  

The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."

Solution to the problem

For n=6

In order to find the critical value we need to take in count that we are conducting a two tailed test, so we are looking on the t distribution with df=n-1=6-1=5 degrees of freedom, a value that accumulates of the area on each tail. We can use excel or a table to find it, for example the code in Excel is:  

"=T.INV(1-0.025,5)", and we got the critical values given by:  

For n=12  

In order to find the critical value we need to take in count that we are conducting a two tailed test, so we are looking on the t distribution with df=n-1=12-1=11 degrees of freedom, a value that accumulates of the area on each tail. We can use excel or a table to find it, for example the code in Excel is:  

"=T.INV(1-0.025,11)", and we got the critical values given by:  

The equivalent form of f(x) + g(x), if  f(x) = x² + 2x + 1 and g(x) = 3(x + 1)² is

4x² + 8x + 4, so option C is correct.

What is a function?

In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.

Given:

f(x) = x² + 2x + 1 and g(x) = 3(x + 1)²

Calculate the equivalent form as shown below,

f(x) + g(x) = x² + 2x + 1 + 3(x + 1)²

Simplify the above equation,

f(x) + g(x) = x² + 2x + 1 + 3(x² + 2x + 1)

f(x) + g(x) = x² + 2x + 1 + 3x² + 6x + 3

f(x) + g(x) = 4x² + 8x + 4

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In U.S. dollars, the equivalent money will be $100.74

What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?

• A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

• A mathematical equation is used to equate two expressions.

• Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

• For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

Given is your dinner in London cost 82 British pounds

Then in U.S. dollars, the equivalent money will be equivalent to -

x = 82 pounds = 82 x 1.2286 = $100.74

x = $100.74

Therefore, in U.S. dollars, the equivalent money will be $100.74

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