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3 years ago

The transitive property of equality states that:

Mathematics

2 answers:

Olenka [21]3 years ago

8 0

Answer:

The correct answer option is: If a = b and b = c, then a = c.

Step-by-step explanation:

The Transitive Property of Equality states that if one value, lets say $a$ is equal to another value, call it $b$ , which is equal to another value, call it $c$ , then the very first value $a$ would be equal to the third value $c$ .

So from the given answer options, the correct option is: If a = b and b = c, then a = c.

Naily [24]3 years ago

5 0

Answer: If $a=b$ and $b=c$ , then $a=c$

Step-by-step explanation:

Let be "a", "b", and "c" all real numbers, the Transitive property of equalities states that :

If $a=b$ and $b=c$ , then $a=c$

You can observe that if two numbers are equal to the same number, then all this numbers are equal to each other.

For example, applying the Transitive property of equalities to:

$x+3=5$ and $2x+1=5$

You can equate them:

$x+3=2x+1$

And solve for "x":

$3-1=2x-x\\\\x=2$

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How the solve 14% of 27

iogann1982 [59]

Answer:

3.78

Step-by-step explanation:

How you do this problem is by simply multiplying 14% by 27. You have to remember that 14% is equivalent to 0.14, so you have to do 0.14 * 27 and you will get 3.78.

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3 years ago

Read 2 more answers

A sequence is a set of

uysha [10]

Answer:

set of related events, movements, or things that follow each other in a particular order.

Step-by-step explanation:

a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence.

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3 years ago

Let the (x; y) coordinates represent locations on the ground. The height h of

grigory [225]

The critical points of h(x,y) occur wherever its partial derivatives $h_x$ and $h_y$ vanish simultaneously. We have

$h_x = 8-4y-8x = 0 \implies y=2-2x \\\\ h_y = 10-4x-12y^2 = 0 \implies 2x+6y^2=5$

Substitute y in the second equation and solve for x, then for y :

$2x+6(2-2x)^2=5 \\\\ 24x^2-46x+19=0 \\\\ \implies x=\dfrac{23\pm\sqrt{73}}{24}\text{ and }y=\dfrac{1\mp\sqrt{73}}{12}$

This is to say there are two critical points,

$(x,y)=\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)\text{ and }(x,y)=\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)$

To classify these critical points, we carry out the second partial derivative test. h(x,y) has Hessian

$H(x,y) = \begin{bmatrix}h_{xx}&h_{xy}\\h_{yx}&h_{yy}\end{bmatrix} = \begin{bmatrix}-8&-4\\-4&-24y\end{bmatrix}$

whose determinant is $192y-16$ . Now,

• if the Hessian determinant is negative at a given critical point, then you have a saddle point

• if both the determinant and $h_{xx}$ are positive at the point, then it's a local minimum

• if the determinant is positive and $h_{xx}$ is negative, then it's a local maximum

• otherwise the test fails

We have

$\det\left(H\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)\right) = -16\sqrt{73} < 0$

while

$\det\left(H\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)\right) = 16\sqrt{73}>0 \\\\ \text{ and } \\\\ h_{xx}\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)=-8 < 0$

So, we end up with

$h\left(\dfrac{23+\sqrt{73}}{24},\dfrac{1-\sqrt{73}}{12}\right)=-\dfrac{4247+37\sqrt{73}}{72} \text{ (saddle point)}\\\\\text{ and }\\\\h\left(\dfrac{23-\sqrt{73}}{24},\dfrac{1+\sqrt{73}}{12}\right)=-\dfrac{4247-37\sqrt{73}}{72} \text{ (local max)}$

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3 years ago

a truck is dispatched for delivery at 8:30 am to a customer 50 miles away. assume that the average speed of the truck is 25 mile

igomit [66]

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6 0

3 years ago

There are 320 students in a school. 16 come to school by car. 96 walk to school. Estimate the probability that a particular stud

lorasvet [3.4K]

Answer:

a. The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

Step-by-step explanation:

Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

$P(A)=\frac{number of favorable cases}{number of possible cases}$

In this case, the number of possible cases is always the same, which is equal to the total number of students. So the number of possible cases is 320 students. The number of favorable cases varies as follows:

a. Number of favorable cases= number of students that arrive by car= 16

So: $P(A)=\frac{16}{320}$

P(A)= $\frac{1}{20}$ = 0.05, which equals 5%

The probability that a particular student arrives by car is $\frac{1}{20}$ = 0.05, which equals 5%.

b. Number of favorable cases= number of students that walk to school= 96

So: $P(A)=\frac{96}{320}$

P(A)= $\frac{3}{10}$ = 0.3, which equals 30%

The probability that a particular student walks to school is $\frac{3}{10}$ = 0.3, which equals 30%.

c. Number of favorable cases= number of students that do not walk to school = 320 students - number of students that walk to school= 320 students - 96 students= 224 students

So: $P(A)=\frac{224}{320}$

P(A)= $\frac{7}{10}$ = 0.7, which equals 70%

The probability that a particular student does not walk to school is $\frac{7}{10}$ = 0.7, which equals 70%.

d. Number of favorable cases= number of students that do not walk or come by car= 320 students - number of students that walk to school - number of students that arrive by car= 320 students - 96 students - 16 students= 208 students

So: $P(A)=\frac{208}{320}$

P(A)= $\frac{13}{20}$ = 0.65, which equals 65%

The probability that a particular student does not walk or come by car is $\frac{13}{20}$ = 0.65, which equals 65%.

6 0

3 years ago