Dimensions of a house are 300 feet by
125 feet. If 1 inch represents 50 feet,
what are the dimensions of the house
on the drawing?

Answers

Answer 1

Answer:

divide 300 feet by 50 which is 6, divide 125 ft by 50 which is 2.5. Therefore your dimensions are 6 in by 2.5 in

if you're in putting in the computer it may want 2.5 in fraction form which is 2 1/2 in or in improper fraction form 5/2 in

Step-by-step explanation:


Related Questions

identify the function shown in the graph

Answers

Answer:

C

Step-by-step explanation:

The line crosses the y-axis at 3, and has a slope of -1/5. You can use the formula y=mx+b where m represents the slope and b is the point at which the line crosses the y-axis.

C. y=-1/5x+3 is the answer

Consider this function.
F(x) = x - 4 + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and
its inverse related?
Since the domain of the original function is limited to x 6, the range of the inverse function is y s6.
Since the domain of the original function is limited to x> 4. the range of the inverse function is ys 1.
Since the range of the original function is limited to y > 6, the domain of the inverse function is x 26
Since the range of the original function is limited to y 4, the domain of the inverse function is x 1.​

Answers

Answer:

Since the range of the original function is limited to y  6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The answer is the statement Since the range of the original function is limited to y > 6, the domain of the inverse function is x ≥ 6.

What is the domain of an inverse function?

The domain of the inverse of a relation is the same as the range of the original relation. In other words, the y-values of the relation are the x-values of the inverse.

What is a positive slope?

The positive slope definition tells us that a line with a positive slope is one where the right side of the line is higher than the left side of the line.

So, by the definition given above, we see that

if the range of the original function is limited to y > 6, the domain of the inverse function is x >= 6.

Learn more about the domain of inverse functions on:

https://brainly.com/question/12805901

#SPJ2

Oxidation state of O in H3O+

Answers

Answer:

Step-by-step explanation:

The oxidation state of O in H₃O⁺ is -2

From the question, the given ion is  H3O+.

This can be written properly as H₃O⁺

To determine the oxidation state of O (that is Oxygen) in H₃O⁺,

The oxidation state of H (Hydrogen) here is +1

∴ We can form the equation

(+1 × 3) + O = +1

(NOTE: The expression is equated to +1 because the overall charge on the given ion is +1)

Then, we have

+3 + O = +1

Now, subtract 3 from both sides

+3 -3 + O = +1 -3

∴ O = -2

Hence, the oxidation state of O in H₃O⁺ is -2

Learn more here: https://brainly.com/question/9691633

Find the infinite geometric sum, if possible: 50 + 150 + 450 + …

Answers

Answer:

Find the infinite geometric sum, if possible: 50 150 + 450 +... -75 25 1000000 Does not exist and

Step-by-step explanation:

Help me answer me some one please I will do 34 points 2 parts A and B

Answers

Given:

Funnel is in the shape of a cone.

Radius = 4 inches

Height = 10 inches

To find:

a) The volume of the funnel

b) How many quarts of oil are in the funnel.

Solution:

Volume of cone:

[tex]$V=\frac{1}{3}\pi r^2 h[/tex]

[tex]$V=\frac{1}{3}\times 3.14 \times 4^2 \times 10[/tex]

[tex]$V=167.47[/tex] in³

The volume of the funnel is 167.47 in³.

1 qt ≈ 58 in³

To convert cubic inch to quarts divide by 58.

[tex]$167.47in^3=\frac{167.47}{58}[/tex]

               = 2.9 quarts

Therefore 2.9 quarts of oil are in the funnel.

Put the following numbers in order from least to greatest:
4/7 12/26 1/2 18/35

Answers

Answer:

12/26, 1/2, 18/25, 4/7

Step-by-step explanation:

I NEED HELP PLS
A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
I WILL GIVE BRAINLIEST AND 95 POINTS I NEED HELP FAST. I NEED HELP PLS
A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
I WILL GIVE BRAINLIEST AND 95 POINTS I NEED HELP FAST.

Answers

Answer:

114.5 in³

Step-by-step explanation:

Volume of cone:

⅓ × 3.14 × 8² × 12

= 803.84 cm³

Volume of hemisphere:

⅔ × 3.14 × 8³

= 1071.786667 cm³

Total = 803.84 + 1071.786667

= 1875.626667 cm³

1 cm = 0.393701 inches

1 cm³ = 0.393701³ inches

Volume in in³:

1875.786667/0.393701³

= 114.4579471 in³

Two cards are drawn from a standard deck of 52 cards. A king is drawn first and not replaced. Find the probability of drawing a second card that is not a king.
P(not a king|king) =

Answers

Answer:

48/51

Step-by-step explanation:

The probability of not choosing a king after you've chosen the first king is 48/51 since there are 48 cards in the deck that are not kings and there are 51 cards left in the deck, including king cards.

Answer: Their are 4 kings in a deck of cards, so the answer would be P( Cards that aren't Kings/Total cards) so the probability is .92 or 92%.

17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d
represents horizontal distance.
a. What is the maximum height the dolphin reaches?
b. How far did the dolphin jump?

Answers

Final answer:

The maximum height that the dolphin reaches is 5 units, which occurs at a horizontal distance of 5 units. The dolphin's total horizontal jump distance is 10 units.

Explanation:

The maximum height the dolphin reaches (the vertex of the parabola) is found by the formula -b/(2a) for the maximum or minimum of a parabola ax^2 + bx + c. In your equation, a = -0.2 and b = 2. Therefore, the horizontal distance, d, at the maximum height is d = -b/(2a) = -2/(-0.4) = 5 units. Substituting d = 5 into the original equation gives h = -0.2*5^2 + 2*5 = 5 units. Thus, the maximum height the dolphin reaches is 5 units.

The dolphin's horizontal distance (the 'd' value when h = 0) specifies the full length of the jump. Solving the equation -0.2*d^2 + 2*d = 0 gives d = 0 (the start of the jump) and d = 10 (the end of the jump). Thus, the dolphin jumped 10 units horizontally.

Learn more about Parabolic Motion here:

https://brainly.com/question/34164083

#SPJ3

The maximum height reached by the dolphin is 5 meters, and it jumps a horizontal distance of 10 meters. This is determined by analyzing the quadratic equation for maximum height and the point where the dolphin returns to the water surface.

To determine the maximum height (h) the dolphin reaches, we need to analyze the given quadratic equation h = -0.2d² + 2d. Because the coefficient of d² is negative, the parabola opens downward, indicating that the vertex of the parabola will give us the maximum height. The vertex of a parabola in the form of h = ad² + bd + c is given by the formula d = -b/(2a). In this case, a = -0.2 and b = 2, so the horizontal distance (d) at the vertex is d = -2/(2 × (-0.2)) = 5 meters. Plugging this back into the equation, we get h = -0.2(5)² + 2(5) = -0.2(25) + 10 = -5 + 10 = 5 meters.

So, the maximum height reached by the dolphin is 5 meters.

The dolphin jumps until it returns to the water surface, which means the height h becomes 0. We solve the quadratic equation 0 = -0.2d² + 2d by factoring out d: 0 = d(-0.2d + 2). This gives us two solutions: d = 0 (the starting point) and -0.2d + 2 = 0 which leads to d = 10.

Therefore, the dolphin jumped a horizontal distance of 10 meters

Which of the following is a complex number?
0 -7
O 2+√3
O 4 + 91

Answers

The second one because it has a square root symbol and the other ones are all numbers whole numbers

I’m the equation (h+9+g) what are the constants?

Answers

Answer:

if you subscride to my yotube i will tell you it is ytmonkey do now if you want help

Step-by-step explanation:

Goodmorning, Anyone know the answer to this?

Answers

Answer:

1. 5

2. 66/25

3. -7.2

4. 25/24

A) 30°
B) 36°
C) 42°
D) 55°
**Include explanation**
To be marked brainliest!

Answers

Answer:

B, 36 degrees

Step-by-step explanation:

Because AB and CB are congruent, so are arcs AB and CB. Therefore, 3x+12=6x-12

24=3x

x=8

3x+12=3(8)+12=24+12=36 degrees, or answer choice B. Hope this helps!

Alice buys a book for £19.80
A year later she sells the book for £12.87
Calculate the percentage decrease in the value of the book.

Answers

Answer:35%

Step-by-step explanation:

The percentage decrease in the value of the book is 35%.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Cost of the book = £19.80

Selling price of the book = £12.87

The percentage decrease in the value of the book.

= (19.80 - 12.87)/19.80 x 100

= 6.93/19.80 x 100

= 35%

Thus,

The percentage decrease is 35%.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

The function f(x) = 3x^3 - 2x is odd because

A.f(3) = f(-3)
B.f(3) = -f(3)
C.f(-3) = -f(3)
D.-f(3) = f(3)^2
E. None of these

Answers

Answer:

C

By substuting x=- 3 the answer will be negative

Jack tossed a coin 3 times. Which tree diagram shows all the possible outcomes of the coin landing heads up or tails up?

Answers

Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.

Step-by-step explanation:

The coin is tossed 3 times. We need to find the tree diagram that shows all the possible outcomes of the coin landing heads up or tails up

Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.

Answer:

the first one is 8 then the seconed one is 3

Step-by-step explanation:

i just took the quiz

96^2+b^2=100^2

what is b?

Answers

Answer:

b = ± 28

Step-by-step explanation:

Given

96² + b² = 100² ( subtract 96² from both sides )

b² = 100² - 96² = 10000 - 9216 = 784 ( take the square root of both sides )

b = ± [tex]\sqrt{784}[/tex] = ± 28

The answer is b =28 hope it’s helps

please help!, thank you so much!​

Answers

Answer: 8? What are the answer choices??

Explanation: C= 2(3.14)r

50= 2(3.14)r

First do 50 divided by 2 which equals 25. Then divide 25 by 3.14 to equal 7.96.... Or 8

If George bought 2 cookies for the price of $1, and he had $5, how much does he have now?

Answers

Answer:

4 dollars

Step-by-step explanation:

5 minus 1 equals 4

The sum of two numbers is 14. The first number is 2/5 of the second number. What are the numbers?​

Answers

Answer:

4 and 10

Step-by-step explanation:

To solve this problem, we need to find all the numbers between 1 and 13 that have a sum of 14. The list is shown below:

1 + 13,   2 + 12,   3 + 11,   4 + 10,   5 + 9,   6 + 8,   7 + 7

Now we must figure out which set of numbers include one number that is 2/5 of the value of the other. We can do that by turning the sets of numbers into fractions as shown below:

[tex]\frac{1}{13}\neq \frac{2}{5}[/tex]

[tex]\frac{2}{12}\neq \frac{2}{5}[/tex]

[tex]\frac{3}{11}\neq \frac{2}{5}[/tex]

[tex]\frac{4}{10}= \frac{2}{5}[/tex]    (answer)

[tex]\frac{5}{9}\neq \frac{2}{5}[/tex]

[tex]\frac{6}{8}\neq \frac{2}{5}[/tex]

[tex]\frac{7}{7}\neq \frac{2}{5}[/tex]

The first number is 4, and the second number is 10, and their sum is indeed 14, as given in the problem.

Let's call the first number "x" and the second number "y." According to the information given:

The sum of the two numbers is 14, so we can write the equation:

x + y = 14

The first number (x) is 2/5 of the second number (y), which can be expressed as:

x = (2/5)y

Now, we can solve this system of equations using substitution. First, we'll substitute the expression for x from the second equation into the first equation:

(2/5)y + y = 14

To make the equation easier to solve, we can get rid of the fraction by multiplying both sides of the equation by 5 (the denominator of 2/5):

5(2/5)y + 5y = 5 * 14

This simplifies to:

2y + 5y = 70

Now, combine like terms:

7y = 70

To solve for y, divide both sides by 7:

y = 70 / 7

y = 10

Now that we've found the value of y, we can find the value of x using the second equation:

x = (2/5)y

x = (2/5) * 10

x = 4

So, the two numbers are:

x = 4

y = 10

for such more question on first number

https://brainly.com/question/19079438

#SPJ2

Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled by the equation a(t) =

Answers

Answer:

a. Alice

b. Briana

c. 0.51 minutes

Step-by-step explanation:

a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for

2t - 1 > 0

2t > 1

t > 1/2 minutes

b. They finish when their covered distance is equal to 5 kilometers. For Alice:

t/4 = 5

t = 5*4 = 20 minutes

For Briana:

√(2t - 1) = 5

2t - 1 = 5²

2t = 25 + 1

t = 26/2

t = 13 minutes

c. They are side by side when they have covered the same distance, that is:

t/4 = √(2t - 1)

(t/4)² = 2t - 1

t²/16 = 2t - 1

t² = 16*(2t - 1)

t² = 32t - 16

t² - 32t + 16 = 0

Using quadratic formula:

[tex]t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]

[tex]t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)} [/tex]

[tex]t = \frac{32 \pm 30.98}{2} [/tex]

[tex]t_1 = \frac{32 + 30.98}{2} [/tex]

[tex]t_1 = 31.49 [/tex]

[tex]t_2 = \frac{32 - 30.98}{2} [/tex]

[tex]t_2 = 0.51 [/tex]

Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.

Answer:

a) Alice starts first, b) Briana gets the finish line first, c) [tex]t \approx 0.509\,min[/tex]

Step-by-step explanation:

a) Alice starts first, since binomial inside the squared root is equal to zero when [tex]t = \frac{1}{2}\,min[/tex], whereas Alice begins at [tex]t = 0\,min[/tex].

b) The instant when each competitor reach finish line is:

Alice

[tex]5\,km = \frac{t}{4}[/tex]

[tex]t = 20\,min[/tex]

Briana

[tex]5\,km = \sqrt{2\cdot t - 1}[/tex]

[tex]25\,km^{2} = 2\cdot t - 1[/tex]

[tex]t = 13\,min[/tex]

Briana gets the finish line first.

c) Alice and Briana are side by side when [tex]a(t) = b(t)[/tex]. Then:

[tex]\frac{t}{4} = \sqrt{2\cdot t - 1}[/tex]

[tex]\frac{t^{2}}{16} = 2\cdot t - 1[/tex]

[tex]t^{2} - 32\cdot t + 16 = 0[/tex]

The roots of the second order polynomial are:

[tex]t_{1} \approx 31.492\,min[/tex] and [tex]t_{2} \approx 0.509\,min[/tex]

Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.

9-6a-24a^2 factor completely

Answers

There answer would be 24a^2-6a+9 because you would put the greatest exponer first then start to decrease from your terms.

-3 (2a - 1) (4a + 3)

I need help with this asap please !!

Answers

Answer:

Answer is x=7

Step-by-step explanation:

[tex]given \: that \: triangle \: stu \: is \: \\ similarto \: triangle \: plm \\ by \: similarity \: theorem \\ \frac{st}{pl} = \frac{tu}{lm} = \frac{su}{pm} \\ \frac{x + 1}{72} = \frac{2x - 3}{99} \\ cancelling \: by \: 9 \: which \: is \: common \\ \frac{x + 1}{8} = \frac{2x - 3}{11} \\ 11(x + 1) = 8(2x - 3) \\ 11x + 11 = 16x - 24 \\ 11 + 24 = 16x - 11x \\ 35 = 5x \\ therefore \: x = 7[/tex]

HAVE A NICE DAY!

THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.

Make a table of 4 additional speeds equivalent to 50 miles per hour.

Answers

Answer:

80.4672kmh

22.352m/s

43.4488 knots

73.3333 fps

Step-by-step explanation:

can someone plsss helppp meee

Answers

Answer:

i think its 2.7 or 1.7 iriririeieire

The answer is Y=6x-5. And I think it is fully simplified

Given P(A) = 0.6, P(B) = 0.45 and P(AorB) = 0.66 , find the value of P(A and B) , rounding to the nearest thousandth, if necessary .

Answers

Answer:

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

                 = 0.6 + 0.45 - 0.66

                 = 0.39

The value of P(A AND B), given the probabilities of P(A), P(B), and P(A OR B),  is found to be 0.39.  

To find the probability of both events A and B occurring, we use the formula for the probability of the union of two events, which is P(A OR B) = P(A) + P(B) \'96 P(A AND B). We rearrange this formula to find P(A AND B) by subtracting P(A) and P(B) from P(A OR B):

P(A AND B) = P(A) + P(B) \'96 P(A OR B)

Substituting the given values:

P(A AND B) = 0.6 + 0.45 \'96 0.66 = 0.39

So, the probability of A and B occurring together, P(A AND B), is 0.39, which rounds to the nearest thousandth as required.

There are 5 designs of necklaces available at a jewelry store. Each design is available in 3 types of stones. How many different combinations of 1 design and 1 stone of necklace can you have?

Answers

Answer:

3 stone necklaces

Step-by-step explanation:

so theres 5 designs and 3 stones you can only have 1 stone with one if your looking to put one on each necklace there will be three with one stone and two without

Quien me ayuda a hacer esta operación :(, es súper urgente

Answers

Answer:

y≥ 5+5/3x

Step-by-step explanation:

5x-3y≤-15

-5x .     -5x

-3y≤-15 -5x

/-3 .     /-3 .(flip inequality when dividing or multiplying by a negative number)

y≥ 5+5/3x

Ryan is putting a clothesline in his rectangular backyard. He wants to put it between two trees on the edge of his
property. He has measured his property, and made the sketch shown below, where all the lengths listed are in
meters.
10
Tree
What is the smallest length of rope that Ryan could buy which would stretch from one tree to the other?

Answers

Answer: 25 meters.

Step-by-step explanation:

The missing figure is attached.

Draw a Right triangle as the one shown in the second picture, where "a" is the smallest length of rope  (in meters) that Ryan could buy, which would stretch from one tree to the other tree.

You need to use the Pythagoream Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse and "b" are "c" are the legs of the Right triangle.

In this case you can identify that:

[tex]b=25-10=15\\\\c=20[/tex]

Knowing those values, you can susbtitute into  [tex]a^2=b^2+c^2[/tex] and then solve  for "a" in order to find its value.

You get:

[tex]a^2=15^2+20^2\\\\a=\sqrt{15^2+20^2}\\\\a=25[/tex]

Evaluate the expression when b=-5.
b^2-8b-6

Answers

Step-by-step explanation:

[tex] {b}^{2} + 8b - 6 \\ {5}^{2} - 8 \times 5 - 6 \\ 25 - 40 - 6 \\ = - 21[/tex]

Answer:

59

Step-by-step explanation:

This is a substitution question

So we will have to solve by substituting the given value into the equation

So let's solve

b^2-8b-6

And b is given to be-5

So let's substitute

(-5)^2-8(-5)-6

25+40-6

65-6

59

Therefore the final answer is 59

Other Questions
Which is the best summary of Harris's point of viewabout the war?.The Vietnam War represented a call to freedomaround the world..The Vietnam War was waged in opposition todemocratic principles..The Vietnam War resulted in greater loss of lifethan World War I.The Vietnam War was fought to stop the reign ofpetty dictators URGENT!!! Which is equal to sin of angle e?a) cos of angle Db) cos of angle Fc) sin of angle Dd) sin of angle F Select three details from The Bully that are most important when making a summary?A.J.T. is mean to other students at the school, including Michael.B.Michael helps J.T. instead of reacting in a mean way.C.Michaels cheeks turn red when he picks up his fallen books.D.The crowd of students in the hall waited to see.E.Ramon helps Michael and gives him advice.HELP!!! A.P.S Please answer ASAPA guitar shop is offering two deals on their guitars. Each guitar is $50 less than its initial sale price. In addition, customers receive a further discount of $3 off each $5 of the sale price. Write a function that represents the final price of a guitar f(x) with an initial price of x. If a guitars initial price was $200, what would it be with the discount? The information system used by Caesar's Entertainment, which combines data from internal TPS with information from financial systems and external sources to deliver reports such as profit-loss statements and impact analyses, is an example of DSS. ESS. CDSS. MIS. SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores. The pressure in a car tire is 198 kPa at 27C. After a long drive, the pressureis 225 kPa. What is the temperature of the air in the tire? Assume that thevolume is constant. Make sure your answer is rounded to nearest wholenumber and your final answer has the units of K.* Read the sentence below and answer the following question: You shouldnt provoke him; he is in a bad mood already. Use context to determine the meaning of provoke. Be nice to Call Annoy Take pictures Need answer has soon has possible A bag contains 32 red blocks, 47 green blocks, 21 yellow blocks, and 25 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability.P(green or purple) O3(g)+NO(g)O2(g)+NO2(g) Write the equalibrium expression What makes the evidence effective?o It makes a statement based on experience.O It helps the reader visualize the concept.o It gives a statistic that appeals to logic.DONE What most closely does the "mirroring shield" reflect?A. PerseusB. MedusaC. The staring boyD. The garland-bearing girlCA-CCSS:ARAR Consider how McKnight Valley River Park Lodge could use capital budgeting to decide whether the $ 11 comma 500 comma 000 River Park Lodge expansion would be a good investment. Assume McKnight Valley's managers developed the following estimates concerning the expansion: LOADING...(Click the icon to view the estimates.) Assume that McKnight Valley uses the straight-line depreciation method and expects the lodge expansion to have a residual value of $ 950 comma 000 at the end of its ten-year life. The average annual net cash inflow from the expansion is expected to be $ 2 comma 779 comma 548. Compute the payback for the expansion project. Round to one decimal place. Question 3 of 102 PointsWhich of the following best describes the purpose of market research?OA. To help producers make more money.B. To measure the overall health of the economy.C. To make production more efficient.D. To provide consumers with quality information. 964 two correct wrong place147 one correct wrong place189 one correct right place286 one correct wrong place523 all wrong A supply schedule is used to show the __________. A. cost of producing a good B. supply in a given market C. total value of all goods produced D. transportation costs in a given ma For the following reaction, 76.0 grams of barium chloride are allowed to react with 67.0 grams of potassium sulfate. barium chloride (aq) potassium sulfate (aq) barium sulfate (s) potassium chloride (aq) Help ASAP, will give brainliest!!!Which type of nuclear reaction produces a neutron, energy, and one large nuclei?A.nuclear fissionB.nuclear fusionC.thermodynamic reaction D.combustion In a test of the effectiveness of garlic for lowering cholesterol, 8181 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.40.4 and a standard deviation of 16.216.2. Use a 0.010.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 00. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses?