The three hands of an accurate 12-hour clock make a total of _?_ complete revolutions around the clock’s face every 24 hours. (A) 72 (B) 733 (C) 1466 (D) 10 104

Answer:

Step-by-step explanation:

Find the characteristic polynomial of the​ matrix, using either a cofactor expansion or the special formula for 3times3 determinants.​ [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row​ operations, because the variable lambda is​ involved.]

[tex]\texttt {let} A = \left[\begin{array}{ccc}4&-4&0\\-4&7&0\\4&6&5\end{array}\right][/tex]

The characteristics polynomial of A is [tex]|A- \lambda I|[/tex]

[tex]\to|A-\lambda I|=\left[\begin{array}{ccc}(4-\lambda)&-4&0\\-4&(7-\lambda)&0\\4&6&(5-\lambda)\end{array}\right][/tex]

[tex]=(4-\lambda)[7-\lambda)(5-\lambda)-0]+4[-4(5-\lambda)-0]+0[-4\time 6-4(7-\lambda)]\\\\=(4-\lambda)[35-7\lambda-5\lambda+\lambda^2]+4[-20+4\lambda]+0\\\\=(4-\lambda)[35-12\lambda+\lambda^2]-80+16\lambda\\\\=140-48\lambda+4\lambda^2-35\lambda+12\lambda^2-\lambda^3-80+16\lambda\\\\=-\lambda^3+16\lambda^2-67\lambda+60[/tex]

Answer:

(-1, 3)

Step-by-step explanation:

5x + 3y = 4

2x + y = 1 ⇒ y=1-2x

Answer:

The equation can be y = -7x+11

Answer:

  105 seconds

Step-by-step explanation:

We can use the relation ...

  distance = speed · time

to write equations for the distance each girl travels as a function of time t since Jillian started.

  Jillian's distance = (6 ft/s)(t)

  Samantha's distance = (7 ft/s)(t -15) . . . . Samantha starts 15 seconds after the clock starts running

These distances are the same when ...

  6t = 7(t -15)

  6t = 7t -105 . . . . eliminate parentheses

  105 = t . . . . . . . . add 105-6t

Jillian had been walking 105 seconds when the two girls met.

Answer:

4-5 12 -13

Step-by-step explanation:

Answer:

Hello There Again. The correct answer is D.

Explanation: Why is D. Because 5x2=10 which everyone know that 5x2=10x3x1=30 So the best choice will be D.

Hope It Helps!

Answer:

a) 92% probability that a randomly selected mortgage will not​ default

b) 47.22% probability that nine randomly selected mortgages will not default

c) 52.78% probability that the derivative from part​ (b) becomes​ worthless

Step-by-step explanation:

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

Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default.

This means that [tex]p = 0.08[/tex]

(a) What is the probability that a randomly selected mortgage will not​ default?

Either it defaults, or it does not default. The sum of the probabilities of these outcomes is 1. So

0.08 + p = 1

p = 0.92

92% probability that a randomly selected mortgage will not​ default

(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the​ others?

This is P(X = 0) when n = 9. So

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

[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]

47.22% probability that nine randomly selected mortgages will not default.

​(c) What is the probability that the derivative from part​ (b) becomes​ worthless? That​ is, at least one of the mortgages defaults

Either none defect, or at least one does. The sum of the probabilities of these events is 100%. So

p + 47.22 = 100

p = 52.78

52.78% probability that the derivative from part​ (b) becomes​ worthless

Answer:

a) A sample size of 195 is needed.

b) Smaller

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.999}{2} = 0.0005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.0005 = 0.9995[/tex], so [tex]z = 3.27[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

a. How large a sample must be drawn so that a 99.9% confidence interval for will have a margin of error equal to 4.1.

We need a sample size of n.

n is found when [tex]M = 4.1[/tex]

We have that [tex]\sigma = 17.5[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4.1 = 3.27*\frac{17.5}{\sqrt{n}}[/tex]

[tex]4.1\sqrt{n} = 3.27*17.5[/tex]

[tex]\sqrt{n} = \frac{3.27*17.5}{4.1}[/tex]

[tex](\sqrt{n})^{2} = (\frac{3.27*17.5}{4.1})^{2}[/tex]

[tex]n = 194.8[/tex]

Rounding up

A sample size of 195 is needed.

b. If the required confidence level were 95%, would the necessary sample size be larger or smaller?

Same as above for n, the difference is that z would be 1.96 instead of 3.27. So a smaller sample size.

Answer:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

101.5 98.7 95.4 92.3 109.8 104.7

We can calculate the mean with the following formula:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]

Answer: (x+8)²

Step-by-step explanation:

When you complete the square, the factor is squared. You want to first factor the equation.

x²+16x+64=0

(x+8)(x+8)=0

Now that we have factored the equation, we can put in into squares.

(x+8)²

Answer

8 and 0 (Khan)

Answer:

i dont know how many decimals you need but its 5.56

tell me if u want an explanation

Answer:

5.74456264654

Step-by-step explanation:

Answer:

B:

Step-by-step explanation:

P(A or B) = P(A)+P(B)-P(A and B)

0.5 = 0.4 + P(B) -0.2

P(B) = 0.5-0.4+0.2

P(B) = 0.3

Find the probability of each one:

Taffy would be 1/6

Chips would be 1/3

Soda would be 1/3

For the probability of all three multiply them together:

1/6 x 1/3 x 1/3 = 1/54

Answer:

16

Step-by-step explanation:

The midpoint theorem says that if a line bisects the two sides of the triangle , it is parallel to the third side and half of it

Thus the x = 1/2 × 32 = 16

Step-by-step explanation:

5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus

if 5/6=20

6/6=?

that is 6/6x20 divide by 5/6

=24fruits

Answer:

length = 50 + 50 = 100 yards

width = 50 yards

Step-by-step explanation:

The area of parking lot for the the ice cream stand is given as  5000 yard². The length of the yard is 50 yard longer than its width.

Let

width = a

length = 50 + a

The parking lot is definitely a rectangle .

Area of a rectangle = length × width

area =  (50 + a)a

5000 = (50 + a)a

5000 = 50a + a²

a² + 50a - 5000 = 0

The numbers that can be multiply together to give you -5000 is -50 and 100 and this same number can be added to give 50. Therefore,

a² - 50a + 100a - 5000 = 0

a(a - 50) + 100(a - 50) = 0

(a + 100)(a - 50) = 0

a = -100 or 50

We can't use negative value so we use 50.

length = 50 + 50 = 100 yards

width = 50 yards

Answer:

279 and 950

Step-by-step explanation:

Outliers are numbers that are significantly greater or lesser than the other numbers in the data set.

The other numbers are very close together on a numerical scale, with the exception of 279 and 950.

Therefore, these two numbers are the outliers.

The outliers are 279 and 950

Learn more about the outlier here: https://brainly.com/question/9933184?referrer=searchResults

Answer:

They should not be exactly the same but they should be close.

Step-by-step explanation:

The first thing that we must take into account is the following:

Experimental probability is the result of an experiment, and theoretical probability is based on the mathematical model developed in probability theory. With the above, we can affirm that the precision of the results of the experiments depends directly on the sample size of the experiment and the precision is greater when the sample size is greater.

This means that the odds are most likely not the same, they must be very close since it has been repeated a considerable number of times and the more times it is done the closer they will be to being the same.

Answer:

(a) True

(b) False

(c) True

(d) False

(e) False

(f) True

(g) False

(h) True

(i) True

(k) True

Step-by-step explanation:

(a) Two lines parallel to a third line are parallel

True

(b) Two lines perpendicular to a third line are parallel

Only for  lines on the same plane

Therefore, false

(c) Two planes parallel to a third plane are parallel

True

(d) Two planes perpendicular to a third plane are parallel

The two planes can be at an angle to each other and so intersect

Therefore, false

(e) Two lines parallel to a plane are parallel

Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect

Therefore, false

(f) Two lines perpendicular to a plane are parallel

True

(g) Two planes parallel to a line are parallel

Where the planes are not parallel to each other, they will intersect

Therefore, false

(h) Two planes perpendicular to a line are parallel

True

(i) Two planes either intersect or are parallel

True

(k) A plane and a line either intersect or are parallel

True.

Answer:

6w = 30

Step-by-step explanation:

We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.

The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.

This is 2 X (length + width)

From the questions, we can get the dimensions of the rectangle using clues from the various statements made.

From the statement"a rectangular painting length more than twice the width" we can see that the

L = 2w ------------------------- equation 1

substituting this value into the formula for the perimeter of the rectangle we have

30 = 2(2w + w)

30 = 6w

w= 5

from equation 1

L =2 X (5) = 10

Hence, we can set up the equation

6w = 30

However, the closest option to what we have is option D

6w + 6 = 30 - 4

complete question:

Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve

Answer:

D.6w + 6 = 30 = 4

Step-by-step explanation:

perimeter = 30 inches

width = w

length = 2w + 3

perimeter of a rectangle = 2l + 2w

where

w = width

l = length

Therefore,

perimeter of a rectangle = 2(2w + 3) + 2w

perimeter of the rectangle = 4w + 6 + 2w

perimeter = 6w + 6

recall

perimeter = 30 inches

6w + 6 = 30

6w = 24

divide both sides by 6

w = 24/6

w = 4

Answer:

  (a, b, c) = (8, 3, 2)

Step-by-step explanation:

Remove cubes from under the radical. Combine terms.

  [tex]\sqrt[3]{16} +2\sqrt[3]{54} =\sqrt[3]{2^3\cdot 2}+2\sqrt[3]{3^3\cdot 2}\\\\=2\sqrt[3]{2}+2\cdot 3\sqrt[3]{2}=(2+6)\sqrt[3]{2}\\\\=8\sqrt[3]{2}\equiv a\sqrt[b]{c}\ \longrightarrow\ \boxed{(a,b,c)=(8,3,2)}[/tex]

saying it is cloudy is the defining that it's so gloomy outside or is probably paraphrasing to how someone feels

hope this helps

Answer:

a. Option D

b. H₀ : p₁ = p₂, H₁: p1 ≠ p₂

Step-by-step explanation:

a. A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the proportions of two populations. This test is usually appropriate under the conditions that:

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

b. Null hypothesis: H₀ : p₁ = p₂

   Alternative hypothesis: H₁ : p₁ ≠ p₂

Answer:

37.67%

Step-by-step explanation:

Suppose initially a price of $ 100

Increasing per month at a rate of 2.7%. Which is equal to 0.027

Now applying the formula:

Vf = Vi * (1 + m) ^ n

where Vf is the final quantity, Vi is the initial value, m is the rate and n is the number of months.

We know that 1 year, is 12 months, since the rate is monthly means, n = 12, we replace:

Vf = 100 * (1 + 0.027) ^ 12

Vf = 137.67

It means price increase in 1 year = 137.67 - 100 = 37.67

Which means that n a year increases to 37.67%

Answer:

Arc length : In his pizza, Arc length is the outer boundary of pizza and it can be calculated if we know the side length of the pizza and the central angle

Area of sector: since the whole pizza piece is a sector hence to calculate it's area we can use the formula of area of sector

(In degrees) = m/360 (πr²)

(In radians) = 1/2r²∅(theta)

Answer:

16

Step-by-step explanation:

there are 2 tbs of whipped cream per sundae so you have to divide 32 by 2 and get 16

Answer:  8

Step-by-step explanation:

For every 1 sundae, the shop uses 4 spoonfuls of sprinkles. The ratio of sundaes to spoonfuls of sprinkles is 1:4.

The shop used 32 spoonfuls of sprinkles.

Since the number of spoonfuls of sprinkles was multiplied by 8, we also need to multiply the number of sundaes by 8.

The shop made 8 sundaes.

Answer:

50%

Step-by-step explanation:

27 to 30 is exactly the "box" of the box plot and that, by definition, contains 50% of the results.

Answer:

50%

Step-by-step explanation:

Hope this will help