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3 years ago

Simplify using suitable properties 2/5 × 7/6 + 7/6 × 7/2

Mathematics

1 answer:

natta225 [31]3 years ago

3 0

Answer:

4 11/20

Step-by-step explanation:

Using bidMAs Multiplication comes first before addition

2/5 * 7/6 = 14/30

7/6 * 7/2 = 49/12

Make denominators equal

14/30 * 2 = 28/60

49/12 * 5 = 245/60

Then add

28/60 + 245/60 = 273/60

Finally convert improper into mixed fraction

4 11/20

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Use the identity (x+y)(x−y)=x2−y2 to find the difference of two numbers if the sum of the numbers is 12 and the difference of th

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Answer:

The difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$ is 4.

Step-by-step explanation:

Given: The sum of the numbers is 12 and the difference of the squares of the numbers is 48.

To find the difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$

Let the two numbers be a and b, then

Given that the sum of the numbers is 12

that is a + b = 12 .........(1)

Also, given the difference of the squares of the numbers is 48.

that is $a^2-b^2=48$ ..........(2)

Using given identity $(x+y)(x-y)=x^2-y^2$

We have $(a+b)(a-b)=a^2-b^2$

Substitute the known values, we have,

$12(a-b)=48$

Divide both side 12 , we have,

$(a-b)=4$

Thus, the difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$ is 4.

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3 years ago

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3 years ago

The opposite of the opposite of 17, or -(-17), is equivalent to which of the following?

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Step-by-step explanation:

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3 years ago

find the coordinates of the point P on the parabola y=1-x^2 with domain 0≤x≤1 that minimize the area of the triangle enclosed by

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Let point P be with coordinates $(x_0,y_0).$ Find the equation of the tangent line.

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2. The equation of the tangent line at point P is

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Find x-intercept and y-intercept of this line:

when x=0, then $y=y_0+2x_0^2;$
when y=0, then $x=\dfrac{y_0}{2x_0}+x_0=\dfrac{y_0+2x_0^2}{2x_0}.$

The area of the triangle enclosed by the tangent line at P, the x-axis, and y-axis is

$A=\dfrac{1}{2}\cdot (2x_0^2+y_0)\cdot \left(\dfrac{y_0+2x_0^2}{2x_0}\right)=\dfrac{(y_0+2x_0^2)^2}{4x_0}.$

Since point P is on the parabola, then $y_0=1-x_0^2$ and

$A=\dfrac{(1-x_0^2+2x_0^2)^2}{4x_0}=\dfrac{(1+x_0^2)^2}{4x_0}.$

Find the derivative A':

$A'=\dfrac{2(1+x_0^2)\cdot 2x_0\cdot 4x_0-4(1+x_0^2)^2}{16x_0^2}=\dfrac{12x_0^4+8x_0^2-4}{16x_0^2}.$

Equate this derivative to 0, then

$12x_0^4+8x_0^2-4=0,\\ \\3x_0^4+2x_0^2-1=0,\\ \\D=2^2-4\cdot 3\cdot (-1)=16,\ \sqrt{D}=4,\\ \\x_0^2_{1,2}=\dfrac{-2\pm4}{6}=-1,\dfrac{1}{3},\\ \\x_0^2=\dfrac{1}{3}\Rightarrow x_0_{1,2}=\pm\dfrac{1}{\sqrt{3}}.$

And

$y_0=1-\left(\pm\dfrac{1}{\sqrt{3}}\right)^2=\dfrac{2}{3}.$

Answer: two points: $P_1\left(-\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right), P_2\left(\dfrac{1}{\sqrt{3}},\dfrac{2}{3}\right).$

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3 years ago

A survey asks, "If the husband in a family wants children, but the wife decides that she does not want any children, is it all r

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a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).

D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.

b. The 99% confidence interval would be wider than a 95% confidence interval.

As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.8241.

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The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143$

The critical z-value for a 99% confidence interval is z=2.5758.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610$

The 99% confidence interval for the population proportion is (0.7872, 0.8610).

We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.

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3 years ago

Simplify using suitable properties 2/5 × 7/6 + 7/6 × 7/2​

Simplify using suitable properties 2/5 × 7/6 + 7/6 × 7/2