What is the factored form of this expression?
9x2 – 64y2

9514 1404 393

Answer:

Step-by-step explanation:

These are all Law of Cosine problems. A generic expression for the length of side 'c' opposite angle C, which is defined by sides 'a' and 'b' is ...

  c² = a² +b² -2ab·cos(C)

The square root of this gives the side length:

  c = √(a² +b² -2ab·cos(C))

Rearranging the equation, we can obtain an expression for the angle C.

  C = arccos((a² +b² -c²)/(2ab))

These two formulas are used to solve the offered problems.

__

1) AC = √(13² +14² -2·13·14·cos(109°)) ≈ √483.506

  AC ≈ 22.0

__

2) BC = √(7² +10² -2·7·10·cos(123°)) ≈ √225.249

  BC ≈ 15.0

__

3) ∠B = arccos((24² +28² -14²)/(2·24·28)) = arccos(1164/1344)

  ∠B ≈ 30.0°

__

4) ∠B = arccos((6² +9² -14²)/(2·6·9)) = arccos(-79/108)

  ∠B ≈ 137.0°

Answer:

triangular pyramid

Step-by-step explanation:

Answer:

triangular pyramid

cone

Step-by-step explanation:

Answer:

12.57

Step-by-step explanation:

same as last time you know

Answer:

0.06938775

Step-by-step explanation:

This is the correct answer.

Answer:

44

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

0.2x = 12

Same as: 1/5x = 12

Multiply both sides by 5

x = 60

0.3 * 60 = 18

Answer:34

85% of 40 = 34

Step-by-step explanation:85 percent of 40? = 34.

Answer:

34

Step-by-step explanation:

Answer:

$34.30

Step-by-step explanation:

Use the equation:

F=P(r)

F=final price

P=principal (starting) amount

r=rate, normally a percent and has to be converted to a decimal

**Since this problem asks us to go down, there is no 1+r. That's when it gives us the final price and asks us to find the original.

Plug in the values: F = 49(.7)

F=$34.30 (don't forget the $ sign)

Answer:

Step-by-step explanation:

Greatest common factor of 6x and 9y is 3.

6x + 9y = 3(2x + 3y)

:::::

Greatest common factor of 3c and 11c is c.

3c + 11c = (3+11)c

Answer: A

Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10

Step-by-step explanation: Khan Answer

For vegetarian orders 70% order again, so with a sample size of 50 we will have an estimated 35 people order again: [tex].7*50=35,50-35=15[/tex] This results in 35 successes and 15 failures. For gluten-free orders 65% order again, so with a sample size of 50 we will have an estimated 32.5 people order again:[tex].65*50=32.5,50-32.5=17.5[/tex] This results in 32.5 successes and 15 failures. Because these are all greater than 10, we can assume normality.

Answer:

Approximately normal, because we expect 35 successes and 15 failures from vegetarian orders, and 32.5 and 17.5 from gluten-free orders, and all of these counts are at least 10

Step-by-step explanation:

Answer:

1. a. 75.39 in² b. 65.97 in²

2. Decreased

Step-by-step explanation:

1.

a. Find the surface area of the cheese before it is cut, round to the nearest hundredth.

Since the cheese is a cylinder with radius, r = 3 inches and height, h = 1 inch, its tital surface area, A = 2πr(r + h)

Substituting the values of the variables into the equation, we have

A = 2πr(r + h)

A = 2π(3 in)(3 in + 1 in)

A = (6π in)(4 in)

A = 24π in²

A = 75.39 in²

b. Find the surface area of the remaining cheese after the wedge is removed, round to the nearest hundredth.

Since the area of the wedge, A' is one-eight the area of the cheese, A

A'= A/8

= 75.39 in²/8

= 9.42 in²

The area of the remaining cheese is thus, area of cheese - area of wedge  = A - A' = 75.39 in² - 9.42 in² = 65.97 in²

Question 2 - Did the surface area increase, decrease, or remain the same

Since the area of the remaining cheese, A' = 65.97 in² < A = 75.39 in², area of original cheese, the surface area decreased.

Step-by-step explanation:

Area of triangle = 1/2×base×height

= 1/2×32×18

= 288in²

Answer:

2

Step-by-step explanation:

Rearrange the data set in numerical order: 1, 2, 2, 3, 5 and take the number in the middle.

Answer:

0.9995 = 99.95% probability that a rivet is defective

Step-by-step explanation:

For each rivet, there is only two possible outcomes. Either they are defective, or they are not. Rivets are defective independently of one another, each with the same probability, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

An aircraft seam requires 29 rivets.

This means that [tex]n = 29[/tex]

23% of all seams need reworking

This means that [tex]p = 0.23[/tex]

What is the probability that a rivet is defective?

This is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{29,0}.(0.23)^{0}.(0.77)^{29} = 0.0005[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0005 = 0.9995[/tex]

0.9995 = 99.95% probability that a rivet is defective

Answer:

1 1/3

Step-by-step explanation:

Answer:

12/9= 1 and 1/3

Step-by-step explanation:

Answer:

Normal distribution.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

Samples larger than 30, which means that the sampling distribution for the sample proportion follows a normal distribution.

Answer:

I am pretty sure 237

Step-by-step explanation:

Answer:

the answer is 2575 I believe

Step-by-step explanation:

(2500x3x1/100)

(2500+75)

Answer:

$15

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A= πr squared

D=r*2

r=24

π=3.14

A= π(24 * 24) = 576

A= π576

A=10808.64

A=10808.6

Answer:b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

because it has two parallel side and and other are just lines but being quadrilateral its sum is 360

Answer:

.42

Step-by-step explanation:

Step-by-step explanation:

Divide 8.40 by 20, use a calculator. Make sure to put $ in your answer.

Answer:

Step-by-step explanation:

t is the number of years since 2003.

f(t) = $18,500×0.88^t

t = 2 in 2005

f(2) = $18,500×0.88²≅ $14,300

Answer:

$14300.00

Step-by-step explanation:

100 - 12 = 88%

88% = 0.88

$18500 x 0.88² = $14326.40

To the nearest hundread:

$14326.40 = $14300.00

0.88² means to the power of 2 since it is 2 consecutive years I did to the power of 2. If it was 3 consecutive years then you do 0.88³.

Hope this helps!

Answer:

The number of required shelves is 5

You have to find the HCF of 45, 105, and 75.

Answer:

12

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

100/20 (the number of questions) = 5 (how much each question is worth)

16(the number of questions she got correct) times 5 is 80

She got 80 percent correct

That means that she missed 20 percent

Answer:

180 people

Step-by-step explanation:

Total of people surveyed = 1,000

% of people that selected travelling as their favorite hobby = 18 %

Number of people that selected travelling = % that selected travelling of 1,000

= 18% of 1,000

= 18/100 × 1,000

= 180 people

Therefore, 180 people selected travelling as their favorite hobby.

Answer:

$29.75

Step-by-step explanation:

$8.50 for 1 hour

So for 3 hours, it will be 8.50 + 8.50 + 8.50 equaling to 25.50

So far the total is $25.50 for 3 hours ONLY!

Now, for half of an hour it will be half of a price, making 8.50 into 4.25

Finally, add $25.50 + $4.25 giving you the totality of $29.75 as the final pay after working for 3 1/2 hours

Answer:

[tex]v=\dfrac{\pi}{2}\ ft/s[/tex]

Step-by-step explanation:

Given that,

A wheel with radius 1 foot makes 1 revolution in 4 seconds

We need to find the linera velocity of a point on the edge of the wheel. We know that, the linear velcity is given by :

[tex]v=r\omega[/tex]

Where

[tex]\omega[/tex] is angular velcocity,[tex]\omega=2\pi\ rad[/tex]

[tex]\omega=\dfrac{1}{4}\times 2\pi\\\\=0.5\pi\ rad/s[/tex]

So

[tex]v=1\times 0.5\pi\\\\v=\dfrac{\pi}{2}\ ft/s[/tex]

So, the linear velocity of the wheel is equal to [tex]\dfrac{\pi}{2}\ ft/s[/tex].

Answer:

pi/2

B

Step-by-step explanation:

Got it right on EG