Solve the equation below.

Answer:

A = 36.8°

B = 23.2°

a = 7.6

Step-by-step explanation:

Given:

C = 120°

b = 5

c = 11

Required:

Find A, B, and a.

Solution:

✔️To find B, apply the Law of Sines

[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]

Plug in the values

[tex] \frac{sin(B)}{5} = \frac{sin(120)}{11} [/tex]

Cross multiply

Sin(B)*11 = sin(120)*5

Divide both sides by 11

[tex] sin(B) = \frac{sin(120)*5}{11} [/tex]

[tex] sin(B) = \frac{sin(120)*5}{11} [/tex]

Sin(B) = 0.3936

B = [tex] sin^{-1}(0.3936) [/tex]

B = 23.1786882° ≈ 23.2° (nearest tenth)

✔️Find A:

A = 180° - (B + C) (sum of triangle)

A = 180° - (23.2° + 120°)

A = 36.8°

✔️To find a, apply the Law of sines:

[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]

Plug in the values

[tex] \frac{sin(36.8)}{a} = \frac{sin(23.2)}{5} [/tex]

Cross multiply

a*sin(23.2) = 5*sin(36.8)

Divide both sides by sin(23.2)

[tex] a = \frac{5*sin(36.8)}{sin(23.2) [/tex]

a = 7.60294329 ≈ 7.6 (nearest tenth)

Step-by-step explanation:

-2<-1<1, so f(-1)=-1-2=-3

Answer:

im not 100 percent sure but i think its

140 inches squared

Step-by-step explanation:

Answer:

Part a:

Since the calculated z= 8.1649 falls in the critical region  z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.

Part b:

P (Type II Error)=  0.6628

Step-by-step explanation:

The null and alternate hypothesis are

H0: μ1 ≥ μ2   against the claim Ha: μ1 < μ2

This is left tailed test

The critical region for this test at 0.10 ∝ is z < ± 1.28

The test statistic

z= x1-x2/ s/√n

z= 66-61/ 3/√24

z= 5/0.61238

z= 8.16486

Since the calculated z= 8.1649 falls in the critical region  z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.

Part b:

P (Type II Error)  = P ( accept H0/ H0 is false)

z ( ∝)= X-u/s/√n

1.28= X-61/0.61238

X= 61.7838

So I will incorrectly fail to reject the null as long as a draw a sample mean that greater than 61.7838

 The probability of a Type II error is given by

P (z> 61.7838-66/24)

P (z>- 0.42161)

From the tables

P (z>- 0.42161)=  0.6628

Answer:

120, 60

Step-by-step explanation:

half a century = 60 + 10 x 2 = ted.

she is 60.

Answer:

x = -3

Step-by-step explanation:

2x + 9 = 3

2x = 3 - 9

2x = -6

x = -3

Answer:

- 3

Step-by-step explanation:

given

2x + 9 = 3

2x = 3 - 9

2x = - 6

x = - 6/2

x = - 3

hope it helps :)

Answer:

A sample of 383 would be required.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In an earlier study, the population proportion was estimated to be 0.3.

This means that [tex]\pi = 0.3[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

How large a sample would be required in order to estimate the fraction of people who black out at 6 or more Gs at the 80% confidence level with an error of at most 0.03?

A sample of n is needed.

n is found when M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.28\sqrt{\frac{0.3*0.7}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.28\sqrt{0.3*0.7}[/tex]

[tex]\sqrt{n} = \frac{1.28\sqrt{0.3*0.7}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.28\sqrt{0.3*0.7}}{0.03})^2[/tex]

[tex]n = 382.3[/tex]

Rounding up:

A sample of 383 would be required.

Answer:

The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] is approximately 0.0002

Step-by-step explanation:

The given Reynolds number of the model = The Reynolds number of the prototype

The drag coefficient of the model, [tex]c_{m}[/tex] = The drag coefficient of the prototype, [tex]c_{p}[/tex]

The medium of the test for the model, [tex]\rho_m[/tex] = The medium of the test for the prototype, [tex]\rho_p[/tex]

The drag force is given as follows;

[tex]F_D = C_D \times A \times \dfrac{\rho \cdot V^2}{2}[/tex]

We have;

[tex]L_p = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2 \times L_m[/tex]

Therefore;

[tex]\dfrac{L_p}{L_m} = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2[/tex]

[tex]\dfrac{L_p}{L_m} =\dfrac{17}{1}[/tex]

[tex]\therefore \dfrac{L_p}{L_m} = \dfrac{17}{1} =\dfrac{\rho _p}{\rho _p} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_p} \right)^2 = \left(\dfrac{V_p}{V_m} \right)^2[/tex]

[tex]\dfrac{17}{1} = \left(\dfrac{V_p}{V_m} \right)^2[/tex]

[tex]\dfrac{F_p}{F_m} = \dfrac{c_p \times A_p \times \dfrac{\rho_p \cdot V_p^2}{2}}{c_m \times A_m \times \dfrac{\rho_m \cdot V_m^2}{2}} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}[/tex]

[tex]\dfrac{A_m}{A_p} = \left( \dfrac{1}{17} \right)^2[/tex]

[tex]\dfrac{F_p}{F_m} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}= \left (\dfrac{17}{1} \right)^2 \times \left( \left\dfrac{17}{1} \right) = 17^3[/tex]

[tex]\dfrac{F_m}{F_p} = \left( \left\dfrac{1}{17} \right)^3[/tex]= (1/17)^3 ≈ 0.0002

The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] ≈ 0.0002.

Answer:

D-B-A-C

Step-by-step explanation:

Answer: B

Step-by-step explanation:

108 divide by 54 = 2

That equation means she paid 2 dollars per ticket, not 1 dollar for 2 tickets

(There is no 1 in the equation also)

Answer:

The answer is A

Step-by-step explanation:

x to the power of 1 is the lowest x and when you multiply -5 and -5 you get 5 so the answer is A.

Answer:

[tex]PC = 0.333[/tex]

Step-by-step explanation:

Given

[tex]AB = 5[/tex]

[tex]AP = 4[/tex]

[tex]DP =12\\[/tex]

See attachment

Required

Find PC

When two chords intersect, the product of the segments are always equal.

In chord DC, the segments are DP and PC

In chord AB, the segments are AP and PB

So:

[tex]DP * PC = AP * PB[/tex]

This gives:

[tex]12 * PC = 4 * PB[/tex] --- (1)

In chord AB, we have:

[tex]AB = AP + PB[/tex]

Make PB the subject

[tex]PB = AB - AP[/tex]

This becomes

[tex]PB = 5 - 4[/tex]

[tex]PB = 1[/tex]

[tex]12 * PC = 4 * PB[/tex] --- (1) becomes

[tex]12 * PC = 4 * 1[/tex]

[tex]12 * PC = 4[/tex]

Make PC the subject

[tex]PC = \frac{4}{12}[/tex]

[tex]PC = 0.333[/tex]

Answer:

C or D

Step-by-step explanation:

Answer:

I'm not sure would love to help but dont know the answer

Answer:

14 months until there equal

Answer:

14 months

Step-by-step explanation:

Answer:

56m

Step-by-step explanation:

5+7+5+11+7+16+5

= 56

Answer:

3(x^2 x Y)(4z x X)(2y x Z)

Step-by-step explanation:

Answer:

[tex]3(x^{3} * 2y^2*4z^2)[/tex]

Step-by-step explanation:

x^2(x) = x^3

2y(y) = 2y^2

4z(z) = 4z^3

Multiple it all by 3

Answer:

A

Step-by-step explanation:

since mean is the most annoying to calculate I went through and did everything else, the range is the same as both charts go 0-6. The median is is the middle number which means store 1 has a higher number of 3' s but our option says store 2 is greater and B is the mode, the number that shows up the most.

Answer:

Answer is F. y = 6x

Step-by-step explanation:

Answer:

The mean is of 33.6

The margin of error is of 5.2.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

In this question:

Lower bound: 28.4

Upper bound: 38.8

Mean

(28.4+38.8)/2 = 33.6.

The mean is of 33.6

Margin of error:

(38.8 - 28.4)/2 = 5.2

The margin of error is of 5.2.

Answer:

314.96in

Step-by-step explanation:

Answer: Because the question uses the word “distinct” meaning obvious, and clear, I would select AB, AC, CB. (If it’s asking for all the possible line segments, I would select AB, AC, CB, BA, CA, BC).

Answer:

3.294

Step-by-step explanation:

Answer:

the answer gonna be 3

Answer: I the answer is 3 100%

Step-by-step explanation: I took the test

Answer:

Step-by-step explanation:

Probably D,  he's measuring voltage across the wire.. and then across the light bulb,   there would be very little across the wire and a lot across the light bulb

Answer:

Courtney is travelling at 9mph

Christy is travelling at 18mph

Step-by-step explanation:

Courtney's speed = x

Christy's speed = y

Christy travels 9 mph faster than Courtney: x+9=y

Distance = speed * time

Courtney's distance after 7 hours = 7x

Christy's distance after 7 hours = 7y

After 7 hours, they're 189 miles apart:

7x+7y=189

x+y=27

x+y=27

x+x+9=27

2x=18

x=9

y=x+9

y=9+9

y=18

Answer:

There was a increase of 1.7% over these three​ years

Step-by-step explanation:

Multipliers:

For a decrease of a%, we multiply by: [tex]\frac{100-a}{100}[/tex]

For a increase of a%, we multiply by: [tex]\frac{100+a}{100}[/tex]

What was the percentage​ increase/decrease of groundhogs over these three​ years?

Decrease of 12%(multiplication by 0.88).

Increase of 6%(multiplication by 1.06).

Increase of 9%(multiplication by 1.09).

After these three years:

0.88*1.06*1.09 = 1.017

1.017 - 1 = 0.017

0.017*100% = 1.7%

There was a increase of 1.7% over these three​ years

Answer:

The correct answer is C. I tried B and got it wrong

Step-by-step explanation:

Answer:

Step-by-step explanation:

When looking at a graph, the greatest speed will be the steepest part. Even though one line is further than another, does not mean it is faster.