MATHEMATICS COLLEGE

Estimate the quotient by rounding the expression to relate to a one-digit fact. Explain your thinking in the space below. a. 432 ÷ 73 _ b. 1,275 ÷ 588 _

Answers

Answer 1

Answer:

Estimations are used to get the approximated value of an expression.

The estimate of 432 ÷ 73 is 5.714
The estimate of 1,275 ÷ 588 is 1.667

$\mathbf{(a)\ 432 / 73}$

Round up to 1 digit

$\mathbf{432 / 73 \approx 400 / 70}$

Divide

$\mathbf{432 / 73 \approx 5.714}$

Hence, the estimate of 432 ÷ 73 is 5.714

$\mathbf{(b)\ 1275 / 588}$

Round up to 1 digit

$\mathbf{ 1275 / 588 \approx 1000 / 600}$

Divide

$\mathbf{ 1275 / 588 \approx 1.667}$

Hence, the estimate of 1,275 ÷ 588 is 1.667

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a car travels 27 miles on each gallon of gas. How many miles can the car travel on 8 1/3 gallons of gas
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Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)Vertex: (−3, 4); point: (0, 13)
Which is the correct?
I will mark you brainliest what is 1+1

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.If the veterinarian gives a 30-pound dog 5 milligram of the medicine, which equation relates the weight, w, and the
dosage, o?

Answers

Question: The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight,w, and the dosage, d?

Answer: d= 1/50w

Explanation: I took the test in Edgenuity.

Hope this helps!

APEX. I’ll make you the brainliest . I need this ASAP :(Part 2: Use the formula you selected in part 1 to find the area of a circle with diameter 8 feet. Show your work and round your answer to the nearest hundredth. (2 points)
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Part 3: Use the formula you selected in Part 1 to find the area of a circle with diameter 10 feet. Show your work and round your answer to the nearest hundredth. (2 points)
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Part 4: Find the difference of your answers from part 2 and 3 to find the difference in the areas. Show your work and round your answer to the nearest hundredth. (1 point)

Answers

Answer:

Part 1= Pi * R Squared

Part 2: 50.27

Part 3: 78.54

Part 4: 28.27

Step-by-step explanation:

Part 1: Memorize the formula

Part 2: 8 feet diameter = Pi * 4 squared. 8 feet is the diameter so the radius is 4. 4 squared is 16. 16 * pi = approximately 50.27, but is 50.24 if 3.14 is used as pi.

Part 3: Pi * 5 squared since 10 is diameter. 25 * pi which is close to 78.54, but is 78.5 is 3.14 is used for pi.

Part 4: I subtracted Part 3 from Part 2.

What is the circumference of the circle?1) 2 by 6 rectangle is inscribed in circle

2) 5 by 5 square is inscribed in circle

3) 5 by 6 rectangle is inscribed in circle

4)2 by 15 rectangle is inscribed in circle

5) 1 by 12 rectangle is inscribed in circle

Answers

I think it is 2 hope this helped you

Answer:

1. 6 pi

2. 7 pi

3. 8 pi

4. 15 pi

5. 12 pi

Step-by-step explanation: Just took the USATestprep test and got them all correct, sorry I dont have a proper answer on how I got them.

Driving along, terry notices that the last four digits on his car's odometer are palindromic. a mile later, the last five digits are palindromic. after driving another mile, the middle four digits are palindromic. one more mile, and all six are palindromic. what was the odometer reading when terry first looked at it? form a linear system of equations that expresses the requirements of this puzzle.

Answers

Designate the initial digits, left to right, as {a, b, c, d, d, c}.

After adding one mile, the digits are {a, b, c, d, c, b}, so the relevant equation is
10c +b = 10d +c +1

After adding another mile, the digits are {a, b, c, c, b, e}, so the relevant equation is
100c +10b +e = 100d +10c +b +1

After another mile, the digits are {a, b, c, c, b, a}, so the relevant equation is
a = e +1

In summary, we have 3 equations in 5 unknowns.
b + 9c -10d = 1
9b +90c -100d +e = 1
a - e = 1
along with the constraints {a, b, c, d, e} ∈ {0, ..., 9}

_____
These have the solution {a, b, c, d, e} = {1, 9, 8, 8, 0}, so the odometer readings were
198888
198889
198890
198891

Let P be the relation defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party. Not being registered or being registered as an independent also counts as a registration. Check all properties that P has.anti-symmetric

reflexive

transitive

symmetric

Answers

Answer:

This relation is symmetric, reflexive and transitive, but not anti-symmetric. Therefore it is an equivalence relation.

Step-by-step explanation:

Let's first prove that it is reflexive:

$\forall x : xRx \quad ?$

The explanation is as follows: let x be some american citizen, $xRx$ means that this person x is registered for the same political party as himself. This is obviously truth, because we are talking about the same person.

Next comes symmetry:

$xRy \iff yRx$

What does this statement mean? It means that if a is in the same party as b, then b is in the same party as a, and viceversa. This must be true, for the statement $xRy$ tells us that x is in the same party as y, which can also be stated as "x and y are both in the same party". This last statement also implies that y is in the same party as x, which is written as: $yRx$ . That proves that:

$xRy \implies yRx$

And the converse follows from the same reasoning.

Now for Transitivity:

$aRb \, \wedge bRc \implies aRc$

What this statement means in this context is that if a,b and c are american citizens, and we have that it is simultaneously true that both a and b are in the same party, and that also b and c are in the same party, then a and c must be also in the same party. This is true because parties are exclusive organisations, you cannot be both a democrat and a republican at the same time, or an independent and a republican. Therefore if a and b belong to the same party, and b and c also belong to the same party, it must be true that a belongs to the same party as b, and the same holds for c, therefore a and c belong to the same party (b's party). which we write as: $aRc$ . Thus it is true that R is a transitive relation.

Finally, Antisymmetry is NOT a property of this relation.

Let's see why, antisymmetry means:

$xRy \wedge x \neq y \implies \neg yRx$

That would mean that if x and y are two distinct american citizens $x\neq y$ , then if x is in the same party as y ( $xRy$ ), then it is not true that y is in the same party as x! ( $\neg yRx$ )

Clearly this isn't true, for example if x and y are two distinct democratic party members, we can say that $xRy$ that is, x and y are registered for the same party, and given that this relation is symmetric, as we have shown, we can also say $yRx$ , but this comes in conflict with the definition of antisymmetry. Thus we conclude that the relation R is not antisymmetric.

On a final note, it's interesting to point out that reflexivity, symmetry and transitivity are the requirements for a relation to be an equivalence relation, which is a very useful concept in maths.

Final answer:

The relation P defined on the set of all American citizens by xPy is reflexive and symmetric, but not transitive.

Explanation:

The relation P defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party has the properties of reflexivity, symmetry, but not transitivity.

Reflexivity means that every element is related to itself. In this case, every American citizen is registered for the same political party as themselves, including those who are registered as independent or not registered at all.

Symmetry means that if x is related to y, then y is related to x. In this case, if two American citizens are registered for the same political party, they are related to each other.

However, the relation P does not have the property of transitivity. Transitivity means that if x is related to y and y is related to z, then x is related to z. In the case of the relation P, if two American citizens are registered for the same political party and another two American citizens are registered for the same political party, it is not necessarily true that the first two citizens are also registered for the same political party as the second two citizens.