Find the missing side lengths. Leave your answers as radicals in simplest form.

Sep by step explanation pls​

Find The Missing Side Lengths. Leave Your Answers As Radicals In Simplest Form. Sep By Step Explanation

Answers

Answer 1

Answer:

[tex]a =22[/tex]

[tex]b = 11[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find a and b

Using cosine formula, we have:

[tex]\cos \theta = \frac{Adjacent}{Hypotenuse}[/tex]

So, we have:

[tex]\cos (30) = \frac{11\sqrt 3}{a}[/tex]

Make a the subject

[tex]a = \frac{11\sqrt 3}{\cos (30)}[/tex]

[tex]\cos(30) = \frac{\sqrt 3}{2}[/tex]

So, we have:

[tex]a = \frac{11\sqrt 3}{\frac{\sqrt 3}{2}}[/tex]

Rewrite as:

[tex]a = 11\sqrt 3 \div \frac{\sqrt 3}{2}[/tex]

This gives:

[tex]a = 11\sqrt 3 * \frac{2}{\sqrt 3}[/tex]

[tex]a = 11 * 2[/tex]

[tex]a =22[/tex]

To solve for b, we use Pythagoras theorem

[tex]a^2 = b^2 + (11\sqrt 3)^2[/tex]

[tex]22^2 = b^2 + (11\sqrt 3)^2[/tex]

[tex]484 = b^2 + 363[/tex]

Collect like terms

[tex]b^2 = 484 - 363[/tex]

[tex]b^2 = 121[/tex]

Take positive square roots

[tex]b = \sqrt {121[/tex]

[tex]b = 11[/tex]


Related Questions

Practice:

Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary, round your results to the nearest hundredth.
-105°

a. (-0.97, -0.26)
b. (1, -0.97)
c. (-0.26, -0.97)
d. (-026,0)

Please select from the best answer from choices provided

Answers

Answer:

C. (-0.26, -0.97)

Step-by-step explanation:

I calculated it logically

A rectangular prism has a length of 4 feet a height of 14 feet and a width of 2 feet what is its volume in cubic feet?

Answers

Answer:

112 cubic feet

Step-by-step explanation:

The answer is 112 cubic feet:

Why: Area of Rectangular Prism= L x W x H(LenghtxWidthxHeight)

                                                        4 x 2 x 14 = 112

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number

Answers

This question is incomplete, the complete question is;

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and preview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was 4 minutes. Use that as a planning value for the standard deviation in answering the following questions. Round your answer to next whole number,

a) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.

b) If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.

Answer:

a) the required Sample Size is 40

b) the required Sample Size is 62

Step-by-step explanation:

Given the data in the question;

standard deviation σ = 4 minutes

a)

margin of error E = 75 seconds = ( 75 / 60 )minutes = 1.25 minutes

And 95% confidence.

Now, Critical Value of z for 0.95 confidence interval;

∝ = 1 - 0.95 = 0.05

[tex]Z_{\alpha /2[/tex] = 1.96

so, sample size n will be;

n = [ [tex]Z_{\alpha /2[/tex] × σ/E ]²

we substitute;

n = [ 1.96 × (4/1.25) ]²

n =  [ 1.96 × 3.2 ]²

n = [ 6.272 ]²

n = 39.338

Since we referring to a number of sample, its approximately becomes 40

Therefore, the required Sample Size is 40

b)

margin of error E = 1 minutes

And 95% confidence.

Now, Critical Value of z for 0.95 confidence interval;

∝ = 1 - 0.95 = 0.05

[tex]Z_{\alpha /2[/tex] = 1.96

so, sample size n will be;

n = [ [tex]Z_{\alpha /2[/tex] × σ/E ]²

we substitute;

n = [ 1.96 × (4/1) ]²

n =  [ 1.96 × 4 ]²

n = [ 7.84 ]²

n = 61.466

Since we referring to a number of sample, its approximately becomes 62

Therefore, the required Sample Size is 62

Plsss help me with #4

Answers

Answer:x=20, y=22

Step-by-step explanation:

40/2=20

66/3=22

plz plz plz plz help me plz it is due in 1 hour and no links plz​

Answers

Answer:

B

Step-by-step explanation:

The formula for the area of a triangle is given as:

A = ½*base*height

A = ½*b*h

A = (bh)2

If we know the area (A) and the base, to find the height, the following would be done:

Divide both sides by b

A/b = h/2

Multiply both sides by 2

[tex] \frac{A}{b} * 2 = h [/tex]

As we can see here, to find the base, we would divide the area by the vase, then multiply what we get by 2.

Help immediately. Must do all for max reward it’s sideways

Answers

Answer:

8.

10x-1=14x-37[corresponding side of congruent triangle are equal]

37-1=14x-10x

36=4x

x=36/4

x=9

9.

6x+13=16x-7[corresponding angle of congruent triangle are equal]

13+7=16x-6x

10x=20

x=20/10

x=2

10.

8x-27=4x+33

8x-4x=33+27

4x=60

x=60/4

x=15

PQ=8×15-27=93

11.3x+5=12x-13

13+5=12x-3x

9x=18

x=18/9=2

now

<BDC=12×2-13=11

12.

5x-8=9x-28

28-8=9x-5x

4x=20

x=20/4

x=5

now

<YWX=5x-8+9x-28=5×5-8+9×5-28=34

13..5x-4=2x+5

5x-2x=5+4

3x=9

x=9/3=3

now

ML=5×3-4=11

ML=11

Evaluate the expression for x = 4.
10 + 2x - 3
O A. 15
B. 45
C. 36
D. 12

Answers

Answer:

The answer to this equation is A.

the answer is a because if you follow the pemdas rule you do 2*4 = 8 + 10 = 18 and 18-3 is 15

Help ASAP I’ll mark brainliest

Answers

Answer:

B

Step-by-step explanation:

It is B because it is going up which is positive and the dots are closer to each other.

A and D is negative but strong

C is weak no correlation

Use side ratios to determine if the triangles in each pair are similar. If so, complete the similarity statement. NO LINKS!!!​

Answers

9514 1404 393

Answer:

  3)  ΔQRS ~ ΔQFG

  5)  ΔRST ~ ΔGFE

Step-by-step explanation:

3) Shortest to longest, the side ratios are ...

  RQ : QS = 6 : 12 = 1 : 2 (reduced)

  FQ : QG = 2 : 4 = 1 : 2 (reduced)

  ΔQRS ~ ΔQFG

__

5) FE : EG : GF = 18 : 24 : 26 = 9 : 12 : 13 (reduced)

  ST : TR : RS = 27 : 36 : 39 = 9 : 12 : 13 (reduced)

  ΔRST ~ ΔGFE

A scale drawing of a park is 1 inch equal to 15 feet. What is the actual area of the park?

Answers

Answer:

Step-by-step explanation:

To get the current area of the park you must multiply by 15 the number of inches indicated on the map.

What is the height of the tree in the figure to the nearest tenth of a foot?
h
40°
75 ft

Answers

I think that would be B 0.11

please help i will mark brainlist

Answers

Answer:196.8

Step-by-step explanation:brainlyest plz plz I need it for my rank

196.8 because you have to multiply 8•12 and 2.05

50 students were asked what they did last night. 16 said they read a book, 41 said they watched TV, 7 said they did neither, how many students did both​

Answers

Answer:

14 students

Step-by-step explanation:

Given

Let:

[tex]b \to[/tex] read a book

[tex]t \to[/tex] watched TV

So, we have:

[tex]n = 50[/tex] -- total

[tex]b = 16[/tex]

[tex]t = 41[/tex]

[tex]none = 7[/tex]

Required

Students that did both (x)

This is calculated using:

[tex]Total = Books\ only + TV\ only + Both + None[/tex]

So, we have:

[tex]n = (b - x) + (t - x) + x + none[/tex]

This gives:

[tex]50 = (16 - x) + (41 - x) + x + 7[/tex]

Open brackets

[tex]50 = 16 - x + 41 - x + x + 7[/tex]

[tex]50 = 16 - x + 41 +7[/tex]

Collect like terms

[tex]x = 16 - 50 + 41 +7[/tex]

[tex]x = 14[/tex]

Hence, 14 students did both

which geometric series converges?
a. 1/6+1/6+1/6+1/6
b. 1/6+2/6+4/6+8/6
c. 6+12+24+48
d. 6+2+6/9+6/27

Answers

Answer:

D

Step-by-step explanation:

Ed2021

The series 6+2+6/9+6/27 is a required converging geometric series. Option D is correct.


Which geometric series converges is determined from the options below

a. 1/6+1/6+1/6+1/6    b. 1/6+2/6+4/6+8/6   c. 6+12+24+48  d. 6+2+6/9+6/27.

What is geometric progression?

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Options A B and C have been omitted because the series given in the corresponding option has the increasing order. Option D has a decreasing order with the common ratio between the preceeding values of the series being 1/3. Thus option D is the correct option.

Thus, the series 6+2+6/9+6/27 is a required converging geometric series. Option D is correct.

Learn more about geometric progression here: https://brainly.com/question/4853032

#SPJ2

Determine the number of real solutions:
1. y = -x? +2 x + 6
2. y = 2x² - 6x + 5
3. y = x² + 8x + 16

Answers

Here is my answer.. correct me if im wrong.

A report published by the Federal Reserve Bank of New York in 2012 reported the results of a nationwide study of college student debt. Researchers found that the average student loan balance per borrower is $23,300. They also reported that about one-quarter of borrowers owe more than $28,000. Assuming that the distribution of student loan balances is approximately normal.

Requird:
Estimate the proportion of borrowers who owe more than 54,000.

Answers

Answer:

The proportion of borrowers who owe more than 54,000 is 0%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Researchers found that the average student loan balance per borrower is $23,300.

This means that [tex]\mu = 23300[/tex]

They also reported that about one-quarter of borrowers owe more than $28,000.

This means that the 1 subtracted by the p-value of Z is 0.25 when X = 28000, that is, when X = 28000, Z has a p-value of 0.75, so when X = 28000, Z = 0.675. We use this to find [tex]\sigma[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{28000 - 23300}{\sigma}[/tex]

[tex]0.675\sigma = 4700[/tex]

[tex]\sigma = \frac{4700}{0.675}[/tex]

[tex]\sigma = 6963[/tex]

Estimate the proportion of borrowers who owe more than 54,000.

This is 1 subtracted by the p-value of Z when X = 54000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{54000 - 23300}{6963}[/tex]

[tex]Z = 4.41[/tex]

[tex]Z = 4.41[/tex] has a p-value of 1

1 - 1 = 0

The proportion of borrowers who owe more than 54,000 is 0%.

3.1 The following table shows the employees of a small manufacturing company
cross-classified based on age and work category.
Work category
Age Production Sales
Office Total
Group
<25
50
50
102
25-40
24
50
>40
40
4
10
54
Total
160
30
110
N
3.1.1 Copy and complete the cross-tabulation table above.
[3]
3.1.2 An employee is selected at random from this population. Calculate the
probability that the employee is:
(a) Under 40 years of age.
[1]

Answers

Answer:

please edit this i dont know what all this means yet

Step-by-step explanation:

PLEASE HELP
log (5x – 10) = log (6 – 5x)

Answers

Answer: look at the picture

Step-by-step explanation: Hope this help :D, Can I have a Brainliest I really needed it please

1. Name the angle below in four ways. Then classify it as acute, right, obruse, or straight.
Please anwser :/​

Answers

Answer:

Ok so I know the angle is acute

Step-by-step explanation:

because the angle looks smaller than a 90 degree angle...

what is the volume of a rectangular prism with a length of 4 a width of 6 and a height of 2?​

Answers

Answer: Volume = 48

Step-by-step explanation:

V = L * W * H

V = 4 * 6 * 2

V = 48

If f(x) = -x^3+ 2x^2 - 3, find f(2).
PLEASE PLEASE

Answers

Answer:

Step-by-step explanation:

f(x) = -x^3+ 2x^2 - 3

Putting value of x = 2

F(2) = - (2)^3 + 2(2)^2 - 3

= - 8 + 8 - 3

= - 3

Option B is the correct answer

Find the component form of the resultant vector.
u=-12i + 35j
Find: -8u
A) 10V 47 - 1 + 10j
B) -40i + 35j
C) 961 – 280j
D) 151 – 5V3.j

Answers

Answer:

C) 96i – 280j

Step-by-step explanation:

Multiplying vector by constant:

When a vector is multiplied by a constant, each component of the vector is multiplied by this constant.

In this question:

u = -12i + 35j

-8u = -8(-12i + 35j) = (8*12i - 8*35j) = 96i - 280j.

The answer is C) 96i – 280j

Please answer for branliest

Answers

There is a 50% probability.

First add up all of the sections to get a total.

10 Green + 15 Purple + 2 Blue + 3 Red = 30.

There are 15 purple out of 30.

15/30 = 1/2 probability, which is 50%.
50%, 1/2 or .50
the total amount is 30 and purple is accountable for 15
make the fraction 15/30

50 PTS for answer!! I need help! "Work this one out," said Monica to her colleague. "I drive from my home to the office every morning. At the back of my house is a short, fairly narrow driveway approximately 300 yards long. I drive my car down this driveway in a westerly direction, yet when I stop the car at the end of the driveway it is facing east."
"Does the driveway go round in a circle?" asked the colleague.

"No," replied Monica, "it is absolutely straight."

What is the explanation?

Answers

es norte sur este y oeste  es un camino completamente recto esta en circulo por ue esta la brujula que apunta al norte y al sur

The length of a rectangle 4ab. The width is . 3ab Find the perimeter of the rectangle in terms of ab

Answers

Answer:

14ab

Step-by-step explanation:

p = 2l + 2w

p = 2(4ab) + 2(3ab)

p = 8ab + 6ab

p = 14ab

if sin= 3/4 what are the values of cos 0 and tan 0

Answers

Answer:

Your choice is correct

Step-by-step explanation:

The first choice

Volume answer rn djdjd

Answers

Answer:

133.7π cm^3 or approximately 418.77430072 cm^3.

Step-by-step explanation:

For the cylinder half, use the formula: π*r^2*h, or pi times radius squared times height.

Since the diameter is 8, which means the radius is 4, and the height is 6, the volume of the cylinder would be 96π or 301.59289474...

For the cone on top, use the formula 1/3 (π*r^2*h), or one third pi times radius squared times height. Don't forget to calcuate the part in parentheses before dividing it by three.

Because the overall height was 13, you can subtract the 6 from the cylinder to get the cone's height. It has a height of 7 and a radius of 4 just like the cylinder. The volume of the cone is 112π/3 or 37.3π.

Now add both volumes together to get 133.7π cm^3 or approximately 418.77430072 cm^3.

Find the angle which is vertical

Answers

Answer:

<2

Step-by-step explanation:

A vertical angles are "pairs of opposite angles made by two intersecting lines." We can see that the same two lines that form <5 form an angle opposite to it, <2.

A recent survey of 252 customers, selected at random from a database with 12,861 customers, found that 208 are satisfied with the service they are receiving. Find the upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database.

Answers

Answer:

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

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].

Sample of 252 customers, 208 are satisfied:

This means that [tex]n = 252, \pi = \frac{208}{252} = 0.8254[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8254 + 2.575\sqrt{\frac{0.8254*0.1746}{252}} = 0.8870[/tex]

As a percentage:

100%*0.8870 = 88.70%

The upper bound of a 99% confidence interval for the percentage satisfied for all customers in the database is 88.70%.

HELP MEEE! I NEED IT RIGHT NOW!

Answers

Answer:1/16 for each of us

Step-by-step explanation:

Since only 1/4 is left and you and the teachers are splitting it up,you’d get 1/16 each because the half of 1/4 (1/8) was split into 2 (1/16)

Other Questions
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