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kolbaska11 [484]
3 years ago
6

Round to the nearest Cent.

Mathematics
2 answers:
Westkost [7]3 years ago
5 0
1. $.0999 = $.1

2. $2.0192 = $2.02

3. $21.5953 = $21.60

4. $35.6667 = $35.67

5. $1.3999 = $1.40

6. $25.3333 = $25.33
kompoz [17]3 years ago
3 0
1- $0.01 2- $2.02 3- $21.60 4- $35.67 5- $1.40 6- $25.33
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Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me​
o-na [289]

Answer:

\frac{3}{2}

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

                   = - cos60cosx - sin60sinx

                   = - \frac{1}{2} cosx - \frac{\sqrt{3} }{2} sinx

squaring to obtain cos² (120 + x)

= \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

                   = -cos60cosx + sin60sinx

                   = - \frac{1}{2}cosx + \frac{\sqrt{3} }{2}sinx

squaring to obtain cos²(120 - x)

= \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + \frac{1}{4}cos²x + \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x + \frac{1}{4}cos²x - \frac{\sqrt{3} }{2}sinxcosx + \frac{3}{4}sin²x

= cos²x + \frac{1}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}cos²x + \frac{3}{2}sin²x

= \frac{3}{2}(cos²x + sin²x) = \frac{3}{2}

                 

5 0
2 years ago
The amount of lateral expansion (mils) was determined for a sample of n = 8 pulsed-power gas metal arc welds used in LNG ship co
Alona [7]

Answer:

95% Confidence interval for the variance:

3.6511\leq \sigma^2\leq 34.5972

95% Confidence interval for the standard deviation:

1.9108\leq \sigma \leq 5.8819

Step-by-step explanation:

We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².

The sample, of size n=8, has a standard deviation of s=2.89 miles.

Then, the variance of the sample is

s^2=2.89^2=8.3521

The confidence interval for the variance is:

\dfrac{ (n - 1) s^2}{ \chi_{\alpha/2}^2} \leq \sigma^2 \leq \dfrac{ (n - 1) s^2}{\chi_{1-\alpha/2}^2}

The critical values for the Chi-square distribution for a 95% confidence (α=0.05) interval are:

\chi_{0.025}=1.6899\\\\\chi_{0.975}=16.0128

Then, the confidence interval can be calculated as:

\dfrac{ (8 - 1) 8.3521}{ 16.0128} \leq \sigma^2 \leq \dfrac{ (8 - 1) 8.3521}{1.6899}\\\\\\3.6511\leq \sigma^2\leq 34.5972

If we calculate the square root for each bound we will have the confidence interval for the standard deviation:

\sqrt{3.6511}\leq \sigma\leq \sqrt{34.5972}\\\\\\1.9108\leq \sigma \leq 5.8819

6 0
3 years ago
For f(x) = 6x + 20, what is the value of x for which f(x)= -4 ?
Ymorist [56]

Answer:

x = -4

Step-by-step explanation:

Plug in -4 into the function and solve for x:

f(x) = 6x + 20

-4 = 6x + 20

-24 = 6x

-4 = x

So, the answer is x = -4

3 0
2 years ago
These are two angles that add up to 180° that share a common vertex. What do you call these angles?
Yuri [45]

Answer:

• linear angles

• supplementary angles (all linear angles are supplementary)

Step-by-step explanation:

If the angles share a side and are measured in opposite directions from that side, the non-common edges of these angles form a straight line, so these angles are sometimes called "linear" angles.

Since their sum is 180°, they are always "supplementary" angles. (Supplementary angles need not share a vertex or a side.)

8 0
3 years ago
Simply the expression 6-2X+5+4x
Lerok [7]

Answer:

2x + 11

I hope this helps!

4 0
3 years ago
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