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4 years ago

PLEASE HELP ASAP

1 answer:

3 0

Real numbers are "closed" under addition Integers are "not closed" under division. Irrational numbers are "not closed" under multiplication. Rational numbers are "closed" under subtraction. If an operation is closed under a set of numbers that means that the result of the operation will always be within that same set of numbers. If that's not true, then the operation is not closed. So with that in mind, let's look at the problems. Real numbers are (closed,not closed) under addition * Since a real number plus a real number always results in another real number, then real numbers are closed under addition. So the answer is "closed" Integers are ( closed, not closed) under division. * Let's try this counter example. 1 divided by 2 = 1/2. 1/2 is NOT an integer, therefore integers are not closed under division. The answer is "not closed" Irrational numbers are (closed, not closed) under multiplication. * This is a tricky one. You may give an impulsive answer and say "closed". After all, how could you possibly multiply one non repeating infinite sequence by another and get something rational?. But what's pi multiplied by the reciprocal of pi? Both pi and 1/pi are irrational. Yet when you multiply them together you get 1 which is quite rational. So the answer is "not closed" Rational numbers are ( closed, not closed) under subtraction. * Since rational numbers are all numbers that can be expressed as a fraction consisting on an integer numerator and divisor, we can express subtraction as a/b - c/d = ad/bd - bc/bd = (ad-bc)/bd and since all we're doing is adding, subtracting, and multiplying integers which is closed under those operations, that means that rational numbers are also closed under subtraction. So the answer is "closed".

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What is the vertex of the graph of y = x + 12 -10?

statuscvo [17]

Answer:

y=x+12-10

Step-by-step explanation:

0=x+12-10

-x=2

x=-2

4 0

3 years ago

The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in

Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

P.Q. = $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }$ = 5.063

$\sigma$ = population standard deviation

n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, $\sigma$ is ;

P(11.59 < $\chi^{2}__2_1$ < 32.67) = 0.90 {As the critical value of chi at 21 degrees

of freedom are 11.59 & 32.67}

P(11.59 < $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ < 32.67) = 0.90

P( $\frac{ 11.59}{(n-1) \times s^{2}}$ < $\frac{1}{\sigma^{2} }$ < $\frac{ 32.67}{(n-1) \times s^{2}}$ ) = 0.90

P( $\frac{(n-1) \times s^{2} }{32.67 }$ < $\sigma^{2}$ < $\frac{(n-1) \times s^{2} }{11.59 }$ ) = 0.90

90% confidence interval for $\sigma^{2}$ = [ $\frac{(n-1) \times s^{2} }{32.67 }$ , $\frac{(n-1) \times s^{2} }{11.59 }$ ]

= [ $\frac{21 \times 5.063^{2} }{32.67 }$ , $\frac{21 \times 5.063^{2} }{11.59 }$ ]

= [16.48 , 46.45]

90% confidence interval for $\sigma$ = [ $\sqrt{16.48}$ , $\sqrt{46.45}$ ]

= [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

5 0

3 years ago

A recipe calls for 12 oz of flour for every 11 oz of milk. Let x be the amount of milk used. Let y be the amount of flour used.

nekit [7.7K]

17 and 1/2 oz of flour

4 0

3 years ago

El tamaño de cierto cultivo de bacterias se multiplica por 2 cada 30 minutos. Si suponemos que el cultivo tiene inicialmente 256

Oduvanchick [21]

Answer:

La población de bacterias después de tres horas es de $2^{14}$ bacterias.

Step-by-step explanation:

En este enunciado observamos un caso de progresión geométrica, en donde la población de bacterias se duplica cada treinta minutos, es decir:

$\frac{p(n\cdot\Delta t)}{p(0)} = 2^{n}$ (1)

Donde:

$\Delta t$ - Intervalo de tiempo requerido para el incremento geométrico de la población, en minutos.

$n$ - Número de períodos para incremento geométrico, sin unidad.

Sabemos que la población inicial de bacterias es 256 y que 3 horas son 6 veces 30 minutos. Entonces, tenemos la siguiente razón:

$\frac{p(6\cdot \Delta t)}{p(0)} = 2^{6}$ (2)

Si sabemos que $p(0) = 256$ , entonces $p(6\cdot \Delta t)$ es:

$p(6\cdot \Delta t) = 2^{6}\cdot p(0)$

$p(6\cdot \Delta t) = 2^{6}\cdot (256)$

$p(6\cdot \Delta t) = 2^{6}\cdot 2^{8}$

$p(6\cdot \Delta t) = 2^{14}$

La población de bacterias después de tres horas es de $2^{14}$ bacterias.

4 0

3 years ago

Find the slope of the line joining the points (-1,5) and (6,-2). Also find the equation of that straight line. Find the intercep

Nesterboy [21]

The slope of the line joining the points (-1,5) and (6,-2) is -1

x + y = 4 is the equation of line

x intercept is (-4, 0)

y intercept is (0, 4)

Solution:

Given that,

Points are (-1,5) and (6,-2)

The slope of line is given as:

$m = \frac{y_2-y_1}{x_2-x_1}$

From given,

$(x_1, y_1) = (-1, 5)\\\\(x_2, y_2) = (6, -2)$

Substituting the values we get,

$m = \frac{-2-5}{6+1}\\\\m = \frac{-7}{7}\\\\m = -1$

Thus slope of line is -1

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where,

m is the slope

c is the y intercept

Substitute m = -1 and (x, y) = (-1, 5) in eqn 1

5 = -1(-1) + c

5 = 1 + c

c = 4

Substitute m = -1 and c = 4 in eqn 1

y = -x + 4

In standard form,

x + y = 4 is the equation of line

Find x intercept:

Substitute y = 0

x + 0 = 4

x = -4

Thus x intercept is (-4, 0)

Find y intercept:

Substitute x = 0

0 + y = 4

y = 4

Thus y intercept is (0, 4)

7 0

3 years ago