Answer:

Substitute *x* = 3 - 2 cos(*θ*) and d*x* = 2 sin(*θ*) d*θ* (where "sin" = "sen"). So we have

∫ sin(*θ*) / (3 - 2 cos(*θ*)) d*θ* = 1/2 ∫ 1/*x* d*x*

= 1/2 ln|*x*| + *C*

= **1/2 ln(3 - 2 cos(***θ***)) + ***C*

(We can remove the absolute value because -1 ≤ cos(*θ*) ≤ 1, so 1 ≤ 3 - 2 cos(*θ*) ≤ 5, and |*x*| = *x* when *x* ≥ 0.)

Help me factorise 25tx squared + 20t - 24 please?

The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides? Part B Explain how you know. Provide at least one reason for your answer.

Lydia has money in two savings accounts. One rate is 7% and the other is 13%. If she has $300 more in the 13% account and the total interest is $252, how much is invested in each savings account?

Find the equation of the axis of symmetry in the coordinates of the vertex of the graph of the function y=4x^2-8x-3

Pls help this is very easy

The perimeter of this isosceles triangle is 22 cm. If one side is 6 cm, what are the possible lengths of the other two sides? Part B Explain how you know. Provide at least one reason for your answer.

Lydia has money in two savings accounts. One rate is 7% and the other is 13%. If she has $300 more in the 13% account and the total interest is $252, how much is invested in each savings account?

Find the equation of the axis of symmetry in the coordinates of the vertex of the graph of the function y=4x^2-8x-3

Pls help this is very easy

**Answer:**

Graph A

**Step-by-step explanation:**

Say that the car rental rate stands for c dollars ( $ ). We know that Jamal's trip lasts for 4 days, paying $ 24 in expenses for gas, and $ 128 for taxi services. Based on these requirements for his trip the question asks for a graph that models this situation, but lets start with the inequality.

______

The big key here is the part " which graph **shows the range of car rental rates that would be cheaper than the taxi service. **" Our inequality must thus have the variable " c " on the same side as the payment for gas ($ 24 ), and must be less than the taxi service ( $ 128 ), or in other words a less than sign. Another point is the car rental rate. We know it stands for c, but it is dependent on the number of days. Hence we can conclude the following inequality,

24 + 4c < 128 - Subtract 24 from either side,

4c < 104 - Divide by 4 on either side, isolating c,

c < 26

**The range of car rental rates that would be cheaper than the taxi service should be { c | 0 ≤ c < 26 }, knowing variable c stands for the car rental rates.**

______

The graph that models this range should be the first one, option A. This graph is not accurate however, as it extends infinitely in the negative direction, and you can't have negative money, or rather be in debt - in this situation.

**Answer:**

A is the answer

**Step-by-step explanation:**

**Answer:**

**(a) The critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.**

**(b) The critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.**

**(c) The critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.**

**Step-by-step explanation:**

We have to find the critical t values for each of the following levels of significance and sample sizes given below.

As we know that in the t table there are two columns. The horizontal column is represented by the symbol **P** which represents the level of significance and the vertical column is represented by the symbol '' which represents the degrees of freedom.

**(a) **A right-tailed test of a population mean at the α=0.01 level of significance with 15 degrees of freedom.

So, here the level of significance = 0.01

And the degrees of freedom = n - 1 = 15

**Now, in the t table, the critical value of t at P = 0.01 and 15 degrees of freedom is 2.602.**

**(b) **A left-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 20.

So, here the level of significance = 0.05

And the degrees of freedom = n - 1

= 20 - 1 = 19

**Now, in the t table, the critical value of t at P = 0.05 and 19 degrees of freedom is -1.729.**

**(c) **A two-tailed test of a population mean at the α=0.05 level of significance with a sample size of n = 13.

So, here the level of significance = = 0.025 {for the two-tailed test}

And the degrees of freedom = n - 1

= 13 - 1 = 12

**Now, in the t table, the critical value of t at P = 0.025 and 12 degrees of freedom is -2.179 and 2.179.**

3xy / 20

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**Answer:**

the answer is 9.879

**Answer:**

with exponents, you take a number and multiply it by itself.

**Step-by-step explanation:**

the root of a number is the number that can be multiplied a certain amount of times to get us that number.

therefore roots get you to the root of a number.

Hope it helps!

(even if its two weeks late.....)

The two events are independent of each other.

This means that:

This means that: