What is the domain of the
square root function graphed below?

What Is The Domain Of Thesquare Root Function Graphed Below?

Answers

Answer 1

Answer:

\(x \geq - 4\)

Step-by-step explanation:

The domain calls for the x-values. All the x-values of the function are greater than or equal to (because the point on (-4,0) is filled in) -4.


Related Questions

Scenario 1A Calculate the following amounts for a participating provider who bills Medicare and has no deductible left. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Coinsurance amount (20% paid by) $ Medicare payment (80 percent of the PFS) $ Provider write-off $ Scenario 1B Calculate the following amounts for a participating provider who bills Medicare and remaining annual deductible for the patient. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Patient pays $100 remaining on their deductible $ Remaining amount for Insurance and patient to pay $ (PFS - $100) Coinsurance amount (20% of remaining amount) $ Total paid by patient (deductible & 20% of remaining) $ Medicare payment (80 percent of the remaining amount) $ Provider write-off $

Answers

Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

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PLZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE

PLZZZZZZZZ HLPPPPPPPPP MEEEEEEEEEEEE

Answers

Answer:

D.8

Step-by-step explanation:

A cube's volume is basically the side length multiplied by itself 3 times, so if it was increased by a factor of 2, it would mean 2x2x2 which equals 8.

The answer is A........

Two trains leave the railroad station at noon. The first train travels along a straight track at 95 mph. The second train travels at 75 mph along another straight track that makes an angle of 130° with the first track. At what time are the trains 400 miles apart? Round your answer to the nearest minute.

Answers

Answer:

2:36pm

Step-by-step explanation:

Let's say it takes x hours after leaving the station when the trains are 400 miles apart

Let's refer to the two trains using the letters A and B for easier reference

A is the train that travels on a straight track due East
B is the train that travels on a track 130° relative to the path of train A

A travels at a speed of 95 mph
B travels at a speed of 75 mph

Let the distance between the two trains be 400 miles after they have traveled an unknown \(x\)  hours. We have to determine \(x\)


After \(x\) hours, train A would be \(95x\) miles from the railroad station and train B would be \(75x\) miles from the station

We can visualize this situation as given in the attached image.

You can see that A = 95x, B = 75x and the longest side is 400 miles

We will use the law of cosines to determine x

The Law of Cosines (also called the Cosine Rule) says:

\(c^2 = a^2 + b^2 - 2ab\cos (\theta)\)

where \(\theta\) is the angle opposite c i.e. the angle bounded by a and b which are the other two sides

Using the diagram as a reference we see

c = 400, a = 95x, b= 75x, \(\theta =\) 130°

Using this information and plugging values into the cosine rule formula we get

\(c^2 = a^2 + b^2 -2ab \cos(\theta)\\\\c^2 = (95x)^2 + (75x)^2 - 2(95x)(75x)\cos(130^\circ)\\\\c^2 = 9025x^2 + 5625x ^2 - 14250x^2\cdot \cos(130^\circ)\\\\\)

\(c^2 = x^2(9025 + 5625 -14250 \cdot \cos130^\circ)\\\\\\c^2 = x^2(14650 - (14250 \times -0.64278))\\\)

\(c^2 = (14650 - (-9159.72343))x^2\\\\c^2 = (14650 + 9159.72343)x^2 \\\\c^2 \approx 23809.7234x^2\\\\\)

But we know that c = 400 since that's what the question says
So we get

\(23809.7234x^2 = 400^2\\\\23809.7234x^2 = 160000\\\\x^2 = \dfrac{160000}{23809.7234} \approx 6.71994\\\\\\x = \sqrt{6.71994} = 2.59228\\\\\textrm{Rounding to nearest tenth}\\x = 2.6 \textrm{ hours}\\\\\)

So the two trains will be 400 miles apart 2.6 hours after they have left the station.

2.6 hours = 2 hours and 36 minutes

So the trains will be 400 miles 2 hours and 36 minutes after they have left the station

Since they have left at noon, they are 400 miles apart at 2:36pm



Two trains leave the railroad station at noon. The first train travels along a straight track at 95 mph.

Match each data set with the value that best describes its center.6 2 4 9Data set A: 2, 3, 1, 4, 2,0,0Data set B: 6.4, 5, 6, 5, 7, 8, 7Data set C: 1, 4, 0, 2, 4, 4, 6, 7Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

data set

center = ?

Step 02:

We must analyze the data sets to find the solution.

Data set A: 2, 3, 1, 4, 2, 0 , 0 ===> 4

Data set B: 6 , 4, 5, 6, 5, 7, 8, 7 ===> 6

Data set C: 1, 4, 0, 2, 4, 4, 6, 7 ===> 2

Data set D: 7, 8, 10, 11, 8, 9, 10, 9, 11 ===> 9

That is the full solution.

Choose the best answer. Let X represent the outcome when a fair six-sided die is rolled. For this random variable,
μX=3.5 and σX =1.71.
If this die is rolled 100 times, what is the approximate probability that the total score is at least 375? (a) 0.0000 (b) 0.0017 (c) 0.0721 (d) 0.4420 (e) 0.9279

Answers

The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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christina's pizza sells pizza by the slice for lunch. today, they sold 76 slices, including 20 slices of pepperoni pizza. what is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?

Answers

The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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Can someone please help? Factor until you can factor no more! Helpful Hint: Follow the Steps to Complete Factorization: 1) Arrange the terms in descending powers 2)
Separate the GCF 3) Factor trinomials 4) Factor any difference of squares


3x2 - 6x - 240

16y2 + 68y + 42

10x - 3 - 3x2

6y2 - 48 + 42y

jm + jn + km + kn

ab + 2a + 3b + 6

x2 + xy - 2x - 2y

mn - 4m - 5n + 20

Answers

Factor when dividing the function the remainder is zero. The factorized form of the function  is 3(x^2-2x-80).

What is a factor?

A factor of a function is a factor which when multiplied by another the result is the function itself.

here, we have,

We know that in order to factorize a function of the second-order, we need to take the common terms out from the expression,

f(x) = 3x^2 - 6x - 240

now,

Taking 3 as the common terms out of the entire function,

f(x) = 3x^2 - 6x - 240

     = 3(x^2-2x-80)

Hence, the factorized function, f(x) = 3x^2 - 6x - 240 is 3(x^2-2x-80)

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The graph below represents a map where each unit is 0.75 miles. Use the map to answer 6-8. Jim's car has 25 miles until it runs out of gas. Would jim be able to make it from his house to the grocery store and back without stopping for gas? Explain.

Answers

The distance between the grocery store and Jim's house shows that he can make it there and back without stopping for gas.

How to find the distance ?

To find the distance between Jim and the grocery store, use the distance formula which is:

=√ ( x2 - x1) ² + (y2 - y1 ) ²

The vertices are:

( 7, 3 ) and ( - 3, 10)

The distance is therefore :

= √ ( - 3  - 7 ) ² + ( 10 - 3  ) ²

= 12.206555615734

If every unit is 0.75 miles, the number of miles to the grocery store is:

= 12.206555615734 x 0. 75

= 9. 15 miles

Jim can therefore go to the grocery store and come back as the distance to and fro is less than 25 miles :

= 9. 15 x 2

= 18. 3 miles

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The graph below represents a map where each unit is 0.75 miles. Use the map to answer 6-8. Jim's car

I need it quick and thank you!

I need it quick and thank you!

Answers

The answer :
It’s the 4th one

PLS HELP WITH QUESTIONS 26 A B AND C WILL GET BRAINLIEST

PLS HELP WITH QUESTIONS 26 A B AND C WILL GET BRAINLIEST

Answers

Answer:

• \(x\) = 42°

• \(y\) = 74°  

• \(z\) = 114°

Step-by-step explanation:

To solve these problems, we have to use the triangle sum theorem, which states that "the sum of all the interior angles of a triangle is 180°".

A)

\(x\) + 90° + 48° = 180°

⇒ \(x\)  + 138° = 180°

⇒ \(x\) + 138° - 138° = 180° - 138°      [Subtracting 138° from both sides]

⇒ \(x\) = 42°

B)

The triangle in this question is an isosceles triangle, therefore the two angles at the base of the triangle are equal and have measures of \(y\).

\(y\) + \(y\) + 32° = 180°

⇒ 2\(y\) + 32° = 180°

⇒ 2\(y\) = 180° - 32°

⇒ 2\(y\) = 148°

⇒ \(\frac{2}{2} y\) = \(\frac{148^{\circ}}{2}\)             [Dividing both sides by 2]

⇒ \(y\) = 74°                    

C)

\(z\) + 28° + 38° = 180°

⇒ \(z\) + 66 = 180°

⇒ \(z\)  = 180° - 66°

⇒ \(z\) = 114°

Pls help…

A rectangular prism has volume 1,392 cubic feet, length 24 feet, and
height 29 feet. Find its width, in feet.

Answers

Answer:How to Find the Height of a Rectangular Prism when the Volume of a Rectangular Prism is given? The height of a rectangular prism can be calculated if the volume of the prism is given using the same formula, Volume (V) = base area × height of the prism.

Step-by-step explanation:

HELP ASAP
please answer the question below its a screenshot

HELP ASAP please answer the question below its a screenshot

Answers

The answer is the first one

Can someone help me please!!

Can someone help me please!!

Answers

Answer:

40°

Step-by-step explanation:

The red 75° curve means that both angles must sum up to 75°The question provides two angles 35° and n°Using math, you can do:n° + 35° = 75°Subtracting 35° from both sides of the equation:n° = 75° - 35° = 40°

Answer:

40°

Step-by-step explanation:

if the measurement of the two angles combined is 75 and one of the angles is 35, we can subtract 35 from 75 to get 40, which should be the answer for n, and you can check it by adding 40 and 35 to get 75, the total of both angles

Assembly of a television set in the factory is set to 45 minutes. Some workers take a shorter time (t) at this while some take longer. However, each varies no more than 8 minutes. Which inequality below represents this scenario?

Assembly of a television set in the factory is set to 45 minutes. Some workers take a shorter time (t)

Answers

Answer:

a

Step-by-step explanation:

The Barksalot Pet Clinic did a study of 75 dogs brought in for treatment. it found that 40 dogs had fleas, 27 had ticks, and 14 had both how many dogs had ticks but not fleas.

Answers

Answer:

there were 13 dogs with ticks but not fleas.

Step-by-step explanation:

Let's call the number of dogs with fleas "x" and the number of dogs with ticks "y".

From the information given, we know:

x = 40 (dogs with fleas)

x + y = 75 (total number of dogs)

y = 27 (dogs with ticks)

So, the number of dogs with ticks but not fleas is equal to y - the number of dogs with both:

y - 14 = 27 - 14 = 13

Therefore, there were 13 dogs with ticks but not fleas.

Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.) r(t)=⟨t,ln(t),tln(t)⟩,3≤t≤4 L=

Answers

The length of the curve defined by the vector function r(t) = ⟨t, ln(t), tln(t)⟩ over the interval 3 ≤ t ≤ 4 is approximately 2.0594 units.

To find the length of the curve defined by the vector function **r(t) = ⟨t, ln(t), tln(t)⟩** over the interval **3 ≤ t ≤ 4**, we can use the arc length formula for a vector function:

**L = ∫[a,b] √[dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt**

Let's calculate the integral using numerical approximation with four decimal places:

1. Calculate the derivatives of x(t), y(t), and z(t):

  - x'(t) = 1

  - y'(t) = 1/t

  - z'(t) = ln(t) + t/t

2. Calculate the squared derivatives:

  - (dx/dt)^2 = 1^2 = 1

  - (dy/dt)^2 = (1/t)^2 = 1/t^2

  - (dz/dt)^2 = (ln(t) + t/t)^2 = (ln(t))^2 + 2ln(t) + 1

3. Calculate the integrand:

  - √[1 + 1/t^2 + (ln(t))^2 + 2ln(t) + 1]

4. Integrate the integrand over the given interval:

  - L = ∫[3, 4] √[1 + 1/t^2 + (ln(t))^2 + 2ln(t) + 1] dt

Using a calculator or numerical integration software, the approximate value of the integral is **L ≈ 2.0594** when rounded to four decimal places. Therefore, the length of the curve is approximately 2.0594 units.

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What is the LCM and GCF of 12 and 18?

Answers

Answer:

Step-by-step explanation:

The least common multiple (LCM) of two numbers is the smallest number that is divisible by both of the numbers. The greatest common factor (GCF) of two numbers is the largest number that divides both of the numbers evenly.

For the numbers 12 and 18, we can find the LCM and GCF as follows:

Prime factorize the numbers:

12 = 2^2 * 3

18 = 2 * 3^2

Find the LCM by taking the highest exponent for each prime factor:

LCM(12, 18) = 2^2 * 3^2 = 36

Find the GCF by taking the lowest exponent for each prime factor:

GCF(12, 18) = 2 * 3 = 6

So, the LCM of 12 and 18 is 36 and the GCF is 6.

Please I beg you help me I will mark you brainliest

Please I beg you help me I will mark you brainliest

Answers

Answer:

Best answer would be D

Step-by-step explanation:

For A, the statement is only true with x as 1

For B, other values for x can make the equation wrong

And for C, it's just wrong.

A student does daycare for 3 different families in the summer. The chart lists how much she charges each family per week.



Which equation can be used to model how much she charges each family every week?

m=80d
m=37d
m=40d
m=35d+10

Answers

Answer:

Step-by-step explanation:

Crownfashions.com wants to estimate the average time that visitors to its website spend browsing the site. In a random sample of 49 visits this week, average browsing time is 13.6 minutes. Assume you know the population standard deviation is 5.2 minutes. Construct an 80% confidence interval estimate of average browsing time for the population of crownfashion.com visitors this week. Report the margin of error indicated by the interval.

Answers

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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What is the cosine ratio of

What is the cosine ratio of

Answers

Answer:

Therefore, the exact value of cos 30 degrees is written as 0.8660 approx. √3/2 is the value of Cos 30° which is a trigonometric ratio or trigonometric function of a particular angle

I need help with this question that’s for my geometry class.

I need help with this question thats for my geometry class.

Answers

By Euclid's axioms we proved that AC=BD

Things which are equal to the same thing are also equal to one another.

If equals be added to equals, the wholes are equal.

If equals be subtracted from equals, the remainders are equal.

Things which coincide with one another are equal to one another.

The whole is greater than the part.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

    BD=BC+CD ........(2)

   subtract 1-2

we get, AC-BD=AB+BC-BC-CD

  AC-BD=AB-CD

we know AB=CD so we get

  AC-BD=0

 AC=BD

Hence, Proved

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Answer:

We established that AC=BD using Euclid's axioms.

Step-by-step explanation:

Things that are equivalent to one another are also equivalent to the same object.

The wholes are equal if equals are added to equals.

The remainders are equal when equals are subtracted from equals.

Things are equivalent to one another if they occur simultaneously.

A component cannot possibly equal the whole.

given that , B is in between A and C

and C is between B and D

and also given that AB=CD

let AC=AB+BC .......(1)

   BD=BC+CD ........(2)

  subtract 1-2

we get, AC-BD=AB+BC-BC-CD

 AC-BD=AB-CD

we know AB=CD so we get

 AC-BD=0

 AC=BD

Hence, Proved

Help please I need help

Help please I need help

Answers

Uisng circle theorems, the angles are

m∠UXV = 72°m∠ST = 21°m∠WV = 108°m∠TW = 93°m∠TUW = 159°

What are circle theorems?

Circle theorems are theorems that govern the properties of a circle.

To find the given angles in the circle, we proceed as follows

1. m∠UXV

We know that m∠WXS = m∠UXV (vertically opposite angles}

Since

m∠WXS  = 72° and m∠WXS = m∠UXV

So, m∠UXV = 72°

2. m∠ST

We know that m∠WXS + m∠ST + m∠TXU = 180°  (angle along a diameter)

Making m∠ST subject of the formula, we have that

m∠ST = 180°  - m∠WXS - m∠TXU

Since the angles

m∠WXS  = 72° and m∠TXU = 87°

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

m∠ST = 180°  - m∠WXS - m∠TXU

m∠ST = 180°  - 72°  - 87°  

m∠ST = 180°  - 159°

m∠ST = 21°

So, m∠ST = 21°

3. m∠WV

We know that m∠WXS + m∠WV = 180°  (angle along a diameter)

Making m∠WV subject of the formula, we have that

m∠WV = 180°  - m∠WXS

Since m∠WXS  = 72°

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

m∠WV = 180°  - m∠WXS

m∠WV = 180°  - 72°

m∠WV = 108°

So, m∠WV = 108°

4. m∠TW

We know that m∠WXS + m∠ST = m∠TW    

Since

m∠WXS  = 72° and m∠ST = 21°

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

m∠TW = ∠WXS + m∠ST

= 72° + 21°

= 93°

So, m∠TW = 93°

5. m∠TUW

We know that m∠TXU + m∠UXV = m∠TUV  

Since m∠TXU  = 87° and m∠UXV = 72°

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

m∠TUV = ∠TXU + m∠UXV

= 87° + 72°

= 159°

So, m∠TUW = 159°

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Experimental probability level g iready

Answers

Experimental probability refers to the probability of an event occurring based on empirical or observed data from experiments or real-life situations.

What is the probability about?

It is determined by conducting multiple trials or observations and recording the outcomes to estimate the likelihood of a specific event happening.

To calculate the experimental probability of an event, you need to divide the number of times the event occurred by the total number of trials or observations. The formula for experimental probability is:

Experimental probability = Number of favorable outcomes / Total number of trials or observations

For example, suppose you want to determine the experimental probability of flipping a coin and getting heads. If you flip the coin 50 times and get heads 20 times, the experimental probability of getting heads would be:

Experimental probability of getting heads = 20 / 50

= 0.4 or 40%

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Explain Experimental probability

4. Celia is making biscuits. Her recipe calls for 1/3 cup of flour, but
she only has a 1/2 cup measure. About how full should she fill the
measuring cup?

Answers

Answer:

I think it is 5/6

Step-by-step explanation:

She should do 5/6 of the way because 1/3x1/2=5/6

Answer:

16.5% full

Step-by-step explanation:

1/2 in decimal is 0.5

1/3 in decimal is 0.33

0.5x0.33=0.165

0.165 as a percentage is 16.5%

One uranium atom has a diameter of 3.5×10−8
centimeters. What is the sum of 1,000,000 uranium atoms’ diameters, in centimeters, written in standard notation?

A.) 3.5
B.) 0.35
C.) 0.035
D.) 0.0035

Answers

The first trick is to know that adding something 1,000,000 times is the same as 1,000,000 times that number.

So, you're really asked to do 1000000 x 3.5x10^-8.

Well, 1000000 = 10^6, so we can rewrite that as:

     10^6 x 3.5x10^-8

And that equals 3.5 x 10^-2.

Written in stanrd notation, that'd be 0.035.

Answer: C

Problem 1, page 54: Prove that any subset of a well-ordered set
is well-ordered (in the inherited ordering).

Answers

To prove that any subset of a well-ordered set is well-ordered, we showed that every non-empty subset of the given subset has a least element.

To prove that any subset of a well-ordered set is well-ordered in the inherited ordering, we can follow these steps:

1. Let's start by defining what it means for a set to be well-ordered. A set is well-ordered if every non-empty subset has a least element.

2. Now, consider a well-ordered set S and a subset A of S. We want to show that A is well-ordered in the inherited ordering from S.

3. To prove that A is well-ordered, we need to show that every non-empty subset of A has a least element.

4. Let B be a non-empty subset of A. Since B is a subset of A, it is also a subset of S.

5. Since S is well-ordered, we know that every non-empty subset of S has a least element. Let's call this least element x.

6. Now, if x belongs to B, then x is the least element of B. We have shown that B has a least element.

7. On the other hand, if x does not belong to B, we can consider the set B' = B ∪ {x}. B' is still a subset of S and A since B is a subset of A.

8. Since B' is a non-empty subset of S, it has a least element, which we will call y.

9. Now, if y belongs to B, then y is the least element of B. Otherwise, if y = x, then x is the least element of B' and therefore also the least element of B.

10. We have shown that in either case, B has a least element.

11. Since B was an arbitrary non-empty subset of A, this holds for any non-empty subset of A.

12. Therefore, we have proven that any subset of a well-ordered set is well-ordered in the inherited ordering.

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P3. (15 points) Given the logic expression: F(X,Y,Z)=
(X+
X
ˉ

Y
ˉ
)

(X+Y+
Z
ˉ
)+
(X+
Y
ˉ
+X
Y
ˉ
)

(
X
ˉ

Y
ˉ
Z) a. Use the theorems of Boolean algebra to simplify the formula given above into a minimum-cost expression b. Draw the circuit diagram for the simplified expression using only NOR gates. P4. (15 points) Given the logic expression: F(A,B,C,D)=
A
ˉ
(
A
ˉ
+C)
(A
B
ˉ
+
A
ˉ

B
ˉ
+
C
ˉ
)(B+
B
ˉ
C)

a. Use the theorems of Boolean algebra to simplify the formula given above into a minimum-cost SOP expression b. Draw the circuit diagram using only NAND gates

Answers

Circuit diagram using only NOR gates: X = NOR = F(X,Y,Z), Y =NOR= F(X,Y,Z), Z = NOR = F(X,Y,Z)

a) To simplify the expression F(X,Y,Z) using Boolean algebra:

F(X,Y,Z) = (X + XY)(X + Y + Z) + (X + Y + XY)(XYZ)

Using the distributive law, we can rewrite the expression:

F(X,Y,Z) = X(X + Y + Z) + XY(X + Y + Z) + XYZ

Applying the absorption law, we have:

F(X,Y,Z) = X + XY + XYZ

The simplified expression is F(X,Y,Z) = X + XY + XYZ.

b) Circuit diagram using only NOR gates:

     _________

-----|         |

   X |    NOR  |-------

-----|___   ___|      |

      |  | |         |

      |  | |   ______|

      |  | |  |       |

      |  | |  |  NOR  |-----

      |  | |  |___   ___|

      |  | |      | |

    Y |__|_|______| |

                     |

                 ___|___

                |       |

              Z |  NOR  |

                |___   _|

                    |

                 F(X,Y,Z)

P4. (15 points)

a) Simplifying the expression F(A,B,C,D) using Boolean algebra:

F(A,B,C,D) = A(A + C)(AB

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S is the centroid of the triangle. Find IT if ST= 9

S is the centroid of the triangle. Find IT if ST= 9

Answers

Answer:

IT = 13.5

Step-by-step explanation:

Recall: According to the Centroid theorem the Centroid of is ⅔ of the distance of the vertex of the triangle to the midpoint of the opposite side.

This means that:

ST = ⅔(IT)

ST = 9 (given)

Substitute

9 = ⅔(IT)

Multiply both sides by 3

3*9 = 2(IT)

27 = 2(IT)

Divide both sides by 2

27/2 = IT

IT = 13.5

True or False.
If a set of vectors {v1, v2, ...., vp} in R^n is linearly dependent, then p>n.

Answers

The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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