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VashaNatasha [74]
3 years ago
14

The law of cosines is used to find the measure of Z.

Mathematics
2 answers:
TEA [102]3 years ago
7 0

Answer:

C. 51º

Step-by-step explanation:

Shtirlitz [24]3 years ago
6 0

Answer:

C. Z=51^{\circ}

Step-by-step explanation:

We have been given a triangle. We are asked to find the measure of angle Z using Law of cosines.

Law of cosines: c^2=a^2+b^2-2ab\cdot \text{cos}(C), where, a, b and c are sides opposite to angles A, B and C respectively.

Upon substituting our given values in law of cosines, we will get:

16^2=19^2+18^2-2(19)(18)\cdot \text{cos}(Z)

256=361+324-684\cdot \text{cos}(Z)

256=685-684\cdot \text{cos}(Z)

256-685=685-685-684\cdot \text{cos}(Z)

-429=-684\cdot \text{cos}(Z)

\frac{-429}{-684}=\frac{-684\cdot \text{cos}(Z)}{-684}

0.627192982456=\text{cos}(Z)

\text{cos}(Z)=0.627192982456

Now, we will use inverse cosine or arc-cos to solve for angle Z as:

Z=\text{cos}^{-1}(0.627192982456)

Z=51.1566718^{\circ}

Z\approx 51^{\circ}

Therefore, the measure of angle Z is approximately 51 degrees.

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Mai bought gas for her car. Gas cost $2.95 per gallon Mai bought 8.2 gallons What was the total cost for Mai's gas?
yulyashka [42]

Answer: $24.19

Step-by-step explanation:

From the question, we are informed that Mai bought gas for her car which cost $2.95 per gallon and that she bought 8.2 gallons.

The total cost for Mai's gas will be:

= $2.95 × 8.2

= $24.19

7 0
3 years ago
PLEASE HELP ME I BEG I WILL GIVE BRAINLIEST
ohaa [14]

Answer:

Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484

Standard deviation = √(0.1484/6

s = 0.16

Standard error = s/√n = 0.16/√6 = 0.065

Part B

Confidence interval is written as sample mean ± margin of error

Margin of error = z × s/√n

Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5

Therefore, z = 3.365

Margin of error = 3.365 × 0.16/√6 = 0.22

Confidence interval is 2.48 ± 0.22

Part C

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 2.3

For the alternative hypothesis,

H1: µ > 2.3

This is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.48

µ = population mean = 2.3

s = samples standard deviation = 0.16

t = (2.48 - 2.3)/(0.16/√6) = 2.76

We would determine the p value using the t test calculator. It becomes

p = 0.02

Assuming significance level, alpha = 0.05.

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.

Step-by-step explanation:

7 0
3 years ago
Please help me with this
masha68 [24]

Answer:

12

Step-by-step explanation:

10x-11+3x-2+3x+1=180

16x-12=180

16x=192

x=12

7 0
2 years ago
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3/4 times 2 1/2 times 4/5
amm1812
The answer to your problem is 6
5 0
3 years ago
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I rlly need to know this asap
balu736 [363]
Box A has 12 balls and Box B has 8 balls.
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