1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998

(a) Find the common difference d

(b) Find the value of n.​


pls help...

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

--------------

(b)

Given

[tex]a_{n}[/tex] = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

------------------


Related Questions

Complete the statements with equal to, greater than, or less than. 5 6 × 6 9 is ? 5 6 . 6 × 5 6 is ? 5 6 . 5 6 × 9 9 is ? 5 6 . 5 6 × 8 7 is ? 5 6 . 7 7 × 5 6 is ? 5 6 . 5 6 × 5 6 is ? 5 6 .

Answers

Answer:

someone already answered

Step-by-step explanation:

srry

Is 3/5 A.irrational, B.rational, C.natural and whole, or D.natural, whole integer and rational

Answers

Answer:

B

Step-by-step explanation:

3/5 is a fraction, meaning it isn't irrational, natural, whole or an integer, therefore the answer is rational (B).

Answer:

B.rational

Step-by-step explanation:

3/5 is written as a fraction so it is a rational number

It is not a whole number since it is a reduced fraction that is less than 1

ACB = DCE
A = 3x-10, C = 45°, D = 2x+10
Please help confused

Answers

Answer:

  x = 20

Step-by-step explanation:

The congruence statement tells you that angle A is congruent to angle D. (Both are listed first in the triangle names.) This means ...

  ∠A = ∠D

  3x -10 = 2x +10

  x = 20 . . . . . . . . . . add 10-2x to both sides

Please answer this correctly without making mistakes

Answers

Answer:

589

Step-by-step explanation:

l x w

19x11

5x31

5x45

589

Answer:

589 is the answer

A car travelled 80km in 48minutes. find the speed of the car in km/hr​

Answers

80km / 48 min = 1 2/3 km per minute.

1 2/3 km per minute x 60 minutes(1 hour) = 100 km per hour

Calculating a correlation can help describe a relation between two quantitative variables' ___ and ___ . However, it is not sufficient to use a correlation coefficient to describe two variables. The addition of ___ can provide other helpful details such as __ _."

Answers

Answer:

direction

shape

scatter plots

shape and outliers

Step-by-step explanation:

Correlation is defined as the degree of correspondence between two variables.

When the values increase together, correlation is positive and when one value decreases as the other increases, correlation is negative .

Calculating a correlation can help describe a relation between two quantitative variables' direction and shape. However, it is not sufficient to use a correlation coefficient to describe two variables.  The addition of scatter plots can provide other helpful details such as shape and outliers

Answer the inequality

Answers

Answer:

A.

Step-by-step explanation:

Add 4:

-5x ≤ 10

Divide by -5:

x ≥ -2

In a survey, participants were asked how much confidence they had in the economy.
The results were as follows:



Response Number

A great 3,187
deal

Some
9,120

Hardly 5,149
any



What is the probability that a sampled person has either some confidence or a great
deal of confidence in the economy? Write only a number as your answer. Round to
two decimal places (for example: 0.43). Do not write as a percentage.

Answers

Answer:

0.71

Step-by-step explanation:

Great Deal or Some = 12,307

Total Participants = 17,456

Probability = 12,307/17,456 = 0.71

Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 3 = 0. (Round your answer to four decimal places.) x2 =?

Answers

Answer:

[tex]x_{2} = 0.0000[/tex]

Step-by-step explanation:

The formula for the Newton's method is:

[tex]x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}[/tex]

Where [tex]f' (x_{i})[/tex] is the first derivative of the function evaluated in [tex]x_{i}[/tex].

[tex]x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}[/tex]

Lastly, the value of [tex]x_{2}[/tex] is determined by replacing [tex]x_{1}[/tex] with its numerical value:

[tex]x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}[/tex]

[tex]x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}[/tex]

[tex]x_{2} = 0.0000[/tex]

Triangles E F G and K L M are shown. Angles E F G and K L M are congruent. The length of side K L is 6, the length of side M L is 5, and the length of K M is 8. The length of E G is 24, the length of G F is 15, and the length of E F is 18. Can the triangles be proven similar using the SSS or SAS similarity theorems? Yes, △EFG ~ △KLM only by SSS. Yes, △EFG ~ △KLM only by SAS. Yes, △EFG ~ △KLM by SSS or SAS. No, they cannot be proven similar by SSS or SAS.?

Answers

Answer:

The Answer is C: Yes, △EFG~ △KLM by SSS or SAS

Step-by-step explanation:

SSS is for side-side-side

Both triangles have all three sides given, so the SSS similarity theorem is one way to prove these triangles are similar.

SAS is for side-angle-side

Both triangles have one angle measurement given, and two side lengths given, therefore we can also use the SAS similarity theorem to prove the two triangles are similar.  

Since both SSS and SAS work to prove the triangles are similar, the correct answer is C: Yes, △EFG~ △KLM by SSS or SAS

(I also just answered this question on the assignment and got it correct)

Answer:

Answer is C

Step-by-step explanation:

Took it on Edg

What’s the correct answer for this question?

Answers

Answer:

the radius

Step-by-step explanation:

the correct answer is the radius

An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 6 plays, 8 poetry books, and 4 nonfiction books. Step 1 of 2 : If she wants to include no more than 3 poetry books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

Answers

Answer:

the number of possible reading schedules is 1.064301638 × 10¹²

Step-by-step explanation:

Given that :

The English teacher needs to pick 10 books to put on her reading list for the next school year.

If the English teacher picks at most  3 poetry books i.e no  more than 3 poetry books from 8 books. and other books are picked from (6+4+4 ) = 14 books

Thus; the number of ways to pick the books are :

[tex]\left[\begin{array}{c}8\\0\\ \end{array}\right] \ \left[\begin{array}{c}14\\10\\ \end{array}\right]+ \left[\begin{array}{c}8\\1\\ \end{array}\right] \left[\begin{array}{c}14\\9\\ \end{array}\right] + \left[\begin{array}{c}8\\2\\ \end{array}\right] \left[\begin{array}{c}14\\8\\ \end{array}\right] + \left[\begin{array}{c}8\\3\\ \end{array}\right] \left[\begin{array}{c}14\\7 \\ \end{array}\right][/tex]

[tex]= [ \dfrac{8!}{0!(8-0)!}* \dfrac{14!}{10!(14-10!)} ] + [ \dfrac{8!}{1!(8-1)!}* \dfrac{14!}{9!(14-9)!}]+ [ \dfrac{8!}{2!(8-2)!}* \dfrac{14!}{8!(14-8)!}] + [ \dfrac{8!}{3!(8-3)!}* \dfrac{14!}{7!(14-7)!}][/tex]

[tex]= [ 1*1001]+[8*2002]+[28*3003]+[56*3432][/tex]

[tex]\mathbf{= 293293}[/tex]

However, to determine how many reading schedules that are possible we use the relation:

Number of ways to pick a book × [tex]^{10}P_{10}[/tex]

[tex]= 293293* \dfrac{10!}{(10-10)!}[/tex]

= 293293 ×  10!

= 1.064301638 × 10¹²

Thus , the number of possible reading schedules is 1.064301638 × 10¹²

Select and place the symbol that will make the statement true |-a| |a|

Answers

Answer:

|-a|=|a|

Step-by-step explanation:

The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.

Therefor this is how we can solve this.

|-a| __ |a|

  a __ a

a=a

HELP PLEASE SIMPLIFY !!!

Answers

Answer:

[tex]=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]

Step-by-step explanation:

[tex]x^{\frac{1}{3}}\left(x^{\frac{1}{2}}+2x^2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=x^{\frac{1}{3}},\:b=x^{\frac{1}{2}},\:c=2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+x^{\frac{1}{3}}\cdot \:2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\\mathrm{Simplify}\:x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}:\quad x^{\frac{5}{6}}+2x^{\frac{7}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=x^{\frac{5}{6}}[/tex]

[tex]x^{\frac{1}{3}}x^{\frac{1}{2}}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=\:x^{\frac{1}{3}+\frac{1}{2}}\\=x^{\frac{1}{3}+\frac{1}{2}}\\\mathrm{Join}\:\frac{1}{3}+\frac{1}{2}:\quad \frac{5}{6}\\\frac{1}{3}+\frac{1}{2}\\\mathrm{Least\:Common\:Multiplier\:of\:}3,\:2:\quad 6\\Adjust\:Fractions\:based\:on\:the\:LCM\\=\frac{2}{6}+\frac{3}{6}[/tex]

[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2+3}{6}\\\mathrm{Add\:the\:numbers:}\:2+3=5\\=\frac{5}{6}\\=x^{\frac{5}{6}}\\2x^2x^{\frac{1}{3}}=2x^{\frac{7}{3}}\\=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]

The value of m compared to the standard is
1/1000
1000
1/100
10

Answers

Idk either but it looks like the reciprocal so I would guess 1/m

solve 5(x+4)<75 sdsdsd

Answers

Answer:

x < 11

Step-by-step explanation:

[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]

[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]

[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]

The required solution of inequality is,

⇒ x < 11

We have to simplify the expression,

⇒ 5 (x + 4) < 75

We can simplify it by definition of inequality as,

⇒ 5 (x + 4) < 75

⇒ 5x + 20 < 75

Subtract 20 both side,

⇒ 5x + 20 - 20 < 75 - 20

⇒ 5x < 55

⇒ 5x - 55 < 0

⇒ 5 (x - 11) < 0

⇒ x - 11 < 0

⇒ x < 11

Therefore, The required solution of inequality is,

⇒ x < 11

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ6

B point is (-5,-4) moves through the translation (x+1 , y-3) what will be the coordinates of B

Answers

Answer:

(-4,-7)

Step-by-step explanation:

Adding 1 to the x and subtracting 3 from the y we get

-5+1= -4

And

-4-3= -7

Every product manufactured by a company goes through 6 different tests before being shipped out. It is known that the probability that a product passes any single test is 0.9 and the tests are independent. Only those products that pass the first three tests and also pass at least one of the three remaining tests are shipped out. Find the probability that a manufactured product is shipped out.

Answers

Answer:

The Probability that the product is shipped out is 0.7283

Step-by-step explanation:

Here, we are given that, a product passes through 6 tests before it is shipped out and a product is shipped out only if it passes all the first 3 tests and at least 1 of the remaining 3 tests.

We have P(pass)= 0.9, is the Probability of passing any test.

Which implies, P(fail)= 1- 0.9= 0.1

We have to find the Probability that the product is shipped out.

P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests) •••••••••••(i)

We can take the product as the tests are Independent.

Now, let us obtain

P(it passes first 3 tests ) = P(pass)*P(pass)*P(pass)

=P(pass)]^3 = (0.9)^3 = 0.729

Hence, P( it passes first 3 tests)= 0.729 •••••••(ii)

Now,

P(passes at least 1 of the remaining 3 tests)

= 1-P(fails all the 3 remaining tests)

= 1-(0.1)^3 = 1 - 0.001 = 0.999

Hence,

P(passes atleast 1 of the remaining 3 tests)=0.999 ••••••••(iii)

Now, substituting the 2nd and 3rd equations in the first equation, we have;

P(product is shipped out) = P(it passes first 3 tests )*P(passes at least 1 of the remaining 3 tests)

= (0.729)*(0.999)

= 0.728271

= 0.7283

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.

Answers

Answer:

The correct answer would be A

(I am not guessing I had the same quiz before)

How many tons is 22,000 pounds?

Answers

Answer:

1 ton = 2,000 pounds

Step-by-step explanation:

With that said, 22,000 pounds is 11 tons because 2,000 x 11 = 22,000.

So 22,000 pounds is 11 tons.

Hope it helps and pls mark me brainliest if it did! :)

Design and complete a frequency table for Belinda.
Belinda ask 20 people, how many hours of TV did you watch last week?

Here is the results
3,17,4,4,6,11,14,14,1,20,9,8,9,6,12,7,8,13,13,9.
Belinda wants to show these result in a frequency table.
She will use 4 equal groups.
The first group will start with 1 hour and the last group will end with 20 hours.

Answers

Answer:

Step-by-step explanation:

Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours

The class groups would be

1 to 5

5 to 10

10 to 15

15 to 20

The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are

(1 + 5)/2 = 3

(5 + 10)/2 = 7.5

(10 + 15)/2 = 12.5

(15 + 20)/2 = 17.5

The frequency table would be

Class group Frequency

1 - 5 4

5 - 10 8

10 - 15 6

15 - 20 2

The total frequency is 4 + 8 + 6 + 2 = 20

Find lim x→3 sqrt 2x+3-sqrt 3x/ x^2-3x. you must show your work or explain your work in words plsss I need help

Answers

I'm assuming the limit is supposed to be

[tex]\displaystyle\lim_{x\to3}\frac{\sqrt{2x+3}-\sqrt{3x}}{x^2-3x}[/tex]

Multiply the numerator by its conjugate, and do the same with the denominator:

[tex]\left(\sqrt{2x+3}-\sqrt{3x}\right)\left(\sqrt{2x+3}+\sqrt{3x}\right)=\left(\sqrt{2x+3}\right)^2-\left(\sqrt{3x}\right)^2=-(x-3)[/tex]

so that in the limit, we have

[tex]\displaystyle\lim_{x\to3}\frac{-(x-3)}{(x^2-3x)\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

Factorize the first term in the denominator as

[tex]x^2-3x=x(x-3)[/tex]

The [tex]x-3[/tex] terms cancel, leaving you with

[tex]\displaystyle\lim_{x\to3}\frac{-1}{x\left(\sqrt{2x+3}+\sqrt{3x}\right)}[/tex]

and the limand is continuous at [tex]x=3[/tex], so we can substitute it to find the limit has a value of -1/18.

What is the answerrrrrrrrrrrr :(((((((((((

Answers

Answer: The answer is choice 3

Step-by-step explanation:

i think the answer is c

Step-by-step explanation:

i don't think u would want a whole explanation

Could someone please help me with the steps for this problem? Factor by grouping: w²+3w+w+3

Answers

Answer:

Please see steps below

Step-by-step explanation:

In order to factor by grouping, we divide the four terms given into two groups, and extract on each group any common factor  we can.

In our example, we can select the terms: [tex]w^2[/tex]  and [tex]w[/tex] as one of our groups, and [tex]3w[/tex] and 3 in the other group. Then we re-organize the expression as:

[tex](w^2+w)+(3x+3)[/tex]

Now we extract from the first binomial group, the factor [tex]w[/tex] as a common factor of both terms, and from the second group we extract the factor "3" as common factor of those two terms:

[tex](w^2+w)+(3x+3)\\w(w+1)+3(w+1)[/tex]

We notice now that after the extraction, we are left with two exactly equal binomial factors [tex](w+1)[/tex] that appeared in the first group and in the second group. We proceed then to extract it as common factor for the two groups:

[tex]w(w+1)+3(w+1)\\(w+1)(w+3)[/tex]

this last product of two binomials ([tex](w+1)\,(w+3)[/tex] is the result of factoring the original expression.

Mr. Hobbs took out a loan of $12,000 for 4 years at a simple annual
interest rate of 7%. How much interest did he pay?

Answers

Answer:

Step-by-step explanation:

I= P*r*t

I = 12000* 7% *4

Total interest paid was $3360.

Answer: $3,360

Step-by-step explanation:

Determine whether the geometric series 192 + 48 + 12 + ... converges or diverges, and identify the sum if it exists.


A.) Converges: 768

B.) Diverges

C.) Converges; 64

D.) Converges; 256

Answers

Answer:

D.) Converges; 256

Step-by-step explanation:

x0= 192

x1 = 48 = 192/4

x2 = 12 = 192/(4 x 4)

Therefore, this series can be written as:

[tex]x_n = \frac{192}{4^n}[/tex]

Applying limits at infinity:

[tex]\lim_{n \to \infty} x_n= \lim_{n \to \infty} (\frac{192}{4^n}) = \frac{192}{\infty}=0[/tex]

Since the terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

[tex]S=\frac{x_0}{1-r} \\S=\frac{192}{1-\frac{1}{4} }\\S=256[/tex]

Thus, the answer is D.) Converges; 256

A tree grows three feet per year. What happens to the growth of the
When the number of years increases, the number of feet decrea
When the number of years decreases, the number of feet stays
When the number of years increases, the number of feet increas
When the number of years decreases, the number of feet increa

Answers

Answer:

The answer is C :,)

Step-by-step explanation:

Answer:

The answer to your question is c

Step-by-step explanation:

Because the years have to increase for it to grow.

What’s the correct answer for this question?

Answers

Answer:

Height = 12 inches

Step-by-step explanation:

Volume = Area × Height

1080 = 90 × H

H = 1080/90

H = 12 inches

What is the measure of XYZ?
please help me out

Answers

Answer:

The answer is C.

Step-by-step explanation:

You have to divide it by 2 :

∠XYZ = 148° ÷ 2

= 74°

Consider a manufacturing process with a quality inspection station. In the past, 10% of parts are defective. As soon as one defective part is found, the process is stopped. If 6 parts have been inspected without finding a defective part, what is the probability that at least 9 total parts will be inspected before the process is stopped

Answers

Answer:

0.9

Step-by-step explanation:

10% is equal to 0.1

The probability of having defective parts in a pile of parts is 0.1

Before the process is stopped, 1 part has to be defective.

In a pile of 9 parts, the probability that a part is defective 0.1 of 9, which is = 0.9 hence, approximately one (1) part will be defective in a pile of 9 parts and the process will be stopped.

Since there was no defective part among the first 6 parts, P(d) was 0

That is, probability of a defective part was zero.

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As the Renaissance began in Italy, a philosophy called humanism developed. Humanism is *a) The belief that there is worth and potential in all individuals.b) The belief that people survive based on nature.c) The role of God in society.4. The Renaissance began in __________ in the _____________: *a) France/ 1400sb) Italy/1300sc) England/1200s5. Classical artists (500 B.C.E. to 500 C.E) created sculptures, pottery, murals and mosaics. There purpose was to show the importance of *a) Ordinary peopleb) Civic leadersc) Gods and goddessesd) All of the Above6. The Medieval Art period (500 to 1300C.E.) created stained glass windows, sculptures, paintings, and tapestries. The purpose of much medieval art was to *a) Show the importance of humanity in daily lifeb) Teach religion to people who could not read or writec) Connect ancient Greek and Roman figures to medieval times7. The Renaissance Art period (1300s to early 1600s) created sculptures, murals, paintings, and drawings. 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Rich families helped to encourage a boom in arts and learning by... *a) Paying for the creation of statues, paintings, buildings, and avenuesb) Building new centers of learning, such as universities and hospitals.c) Both A and B.12. As the Renaissance began, many towns demanded self-rule and developed into independent city-states. This form of government, in which the people elected officials, was called: *a) Democraciesb) Republicsc) Capitalist13. The spirit of the Renaissance can best be described as... *a) a rebirth of classical (ancient Greek and Roman) art and idealsb) a time of great advancements in art, architecture, science and philosophyc) a time when people began to believe that humanity could solve the worlds problemsd) all of the above14. Which of the following cities is known as the cradle or birthplace of the Renaissance? *b) Venicec) Parisd) Florence15. The Medici family is famous for being the godfathers of the Renaissance. What does this mean? *a) They were ruthless but also great patrons of the arts.b) They were assassins.c) They were some of the greatest artists of the Renaissance.16. ___________________ is the belief that individuals can learn and achieve great things. *a) Humanismb) Secularismc) Individualism17. ___________________ is a movement towards government and philosophy to control society rather than only religion. *a) Humanismb) Secularismc) Rationalism18. ___________________ is the belief that you can come to know the world just by thinking about it. *a) Humanismb) Secularismc) Rationalism19. The Catholic Church believed that life after death was more important than life on Earth. This conflicts with humanists because *a) Humanists believe God is the most important figure in society.b) Many humanists tried to balance an emphasis on afterlife with an interest in daily lifec) There was no conflict.20. The growth of Humanism created a new philosophy. This philosophy tried *a) to separate the workings of government from the Churchb) to unify government and Churchc) to make individuals travel throughout Europe21. What kind of art does the following piece represent? *Captionless Imagea) Classicalb) Medievalc) Renaissance22. Which kind of art does the following piece represent? *Captionless Imagea) Classicalb) Medievalc) Renaissance I need help with number 8 please help me Tanner-UNF Corporation acquired as a long-term investment $240 million of 6% bonds, dated July 1, on July 1, 2016. Company management has the positive intent and ability to hold the bonds until maturity. The market interest rate (yield) was 8% for bonds of similar risk and maturity. Tanner-UNF paid $200 million for the bonds. The company will receive interest semiannually on June 30 and December 31. As a result of changing market conditions, the fair value of the bonds at December 31, 2016 was $210 million. Required: 1. Prepare the journal entry to record Tanner-UNFs investment in the bonds on July 1, 2016. 2. Prepare the journal entry by Tanner-UNF to record interest on December 31, 2016, at the effective (market) rate. 3. At what amount will Tanner-UNF report its investment in the December 31, 2016, balance sheet? Why? 4. Suppose Moodys bond rating agency downgraded the risk rating of the bonds motivating Tanner-UNF to sell the investment on January 2, 2017, for $190 million. Prepare the journal entry to record the sale. Which is an example of federal supremacy? Congress does not have the power to create federal banks. The Supreme Court can decide whether a law or act is constitutional. Congress has powers that are not specifically outlined in the Constitution. A state is not allowed to tax federal money because federal law is superior. A doctor has told Frida she must engage in physical activities to improve her heart health and minimize the chance of injury. Which of the following is best for her to try? Which nations gain superpower status after World War II 1. Shannon is conducting an experiment where she flips a coin and then rolls a six sided die. How many total possible outcomes are there in this experiment1. 82. 123. 142. How many possible outcomes are there when Shannon flips a head and rolls an even number?1. 32. 43. 63. What is the theoretical probability that Shannon flips a tail and rolls a two?1. 2/122. 1/123. 3/12