Use the Order of Operations to evaluate this expression

Divide and simplify<br> ax + ay + bx + by/<br> x+y

Kisachek [45]

Answer:

a + b

Step-by-step explanation:

ax + ay + bx + by

a(x +y) +b(x + y)

(a + b) ( x + y)

therefore (a + b) ( x + y) divide x+y

x + y is canceled out both in the denominator and numerator

= a+b

4 0

3 years ago

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To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certai

Nataliya [291]

Answer:

a

$\frac{\alpha }{2} = 2.5 \%$

b

$N = 25$

Step-by-step explanation:

From the question we are told that

The number of bootstrap samples is n = 1000

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally the percentage of values that must be chopped off from each tail for a 95% confidence interval is mathematically evaluated as

$\frac{\alpha }{2} = \frac{0.05}{2} = 0.025 = 2.5 \%$

=> $\frac{\alpha }{2} = 2.5 \%$

Generally the number of the bootstrap sample that must be chopped off to produce a 95% confidence interval is

$N = 1000 * \frac{\alpha }{2}$

=> $N = 1000 * 0.025$

=> $N = 25$

4 0

4 years ago

Use a triple integral to find the volume of the tetrahedron T bounded by the planes x+2y+z=2, x=2y, x=0 and z=0

Tanzania [10]

Answer:

Volume of the Tetrahedron T = $\frac{1}{3}$

Step-by-step explanation:

As given, The tetrahedron T is bounded by the planes x + 2y + z = 2, x = 2y, x = 0, and z = 0

We have,

z = 0 and x + 2y + z = 2

⇒ z = 2 - x - 2y

∴ The limits of z are :

0 ≤ z ≤ 2 - x - 2y

Now, in the xy- plane , the equations becomes

x + 2y = 2 , x = 2y , x = 0 ( As in xy- plane , z = 0)

Firstly , we find the intersection between the lines x = 2y and x + 2y = 2

∴ we get

2y + 2y = 2

⇒4y = 2

⇒y = $\frac{2}{4} = \frac{1}{2}$ = 0.5

⇒x = 2( $\frac{1}{2}$ ) = 1

So, the intersection point is ( 1, 0.5)

As we have x = 0 and x = 1

∴ The limits of x are :

0 ≤ x ≤ 1

Also,

x = 2y

⇒y = $\frac{x}{2}$

and x + 2y = 2

⇒2y = 2 - x

⇒y = 1 - $\frac{x}{2}$

∴ The limits of y are :

$\frac{x}{2}$ ≤ y ≤ 1 - $\frac{x}{2}$

So, we get

Volume = $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}\int\limits^{2-x-2y}_{z=0} {dz} \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{[z]}\limits^{2-x-2y}_0 {} \, \, dy \, dx$

= $\int\limits^1_0 {\int\limits^{1-\frac{x}{2}}_{y = \frac{x}{2}}{(2-x-2y)} \, \, dy \, dx$

= $\int\limits^1_0 {[2y-xy-y^{2} ]}\limits^{1-\frac{x}{2}} _{\frac{x}{2} } {} \, \, dx$

= $\int\limits^1_0 {[2(1-\frac{x}{2} - \frac{x}{2}) -x(1-\frac{x}{2} - \frac{x}{2}) -(1-\frac{x}{2}) ^{2} + (\frac{x}{2} )^{2} ] {} \, \, dx$

= $\int\limits^1_0 {(1 - 2x + x^{2} )} \, \, dx$

= ${(x - x^{2} + \frac{x^{3}}{3} )}\limits^1_0$

= 1 - 1² + $\frac{1^{3} }{3}$ - 0 + 0 - 0

= 1 - 1 + $\frac{1 }{3}$ = $\frac{1}{3}$

So, we get

Volume = $\frac{1}{3}$

7 0

3 years ago

A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 38 centimeters, and the l

Goryan [66]

Answer:

Hi!

Your answer here is 39 cm.

7 0

3 years ago

You bought a $7.00 meal and 3 cookies. You spent a total of $10.00. How much did each cookie cost?

nadya68 [22]

Answer:

A dollar

Step-by-step explanation:

7+3 is 10

3 divided by 1 is 3

3 0

3 years ago

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