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3 years ago

Draw a plane, showing the three (non-linear) points that define it.

Mathematics

1 answer:

algol [13]3 years ago

6 0

Draw a plane, showing the three (non-linear) points that define it. $\boxed{\large{\bold{\blue{ANSWER~:) }}}}$

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Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now?

masha68 [24]

Let's call Maura's age now M and Cara's age now C.

We know Maura is five years younger than Cara. In symbols that is, M - 5 = C

We also know that 7 years ago Maura's age was half of Cara's. Maura's age 7 years ago was M-7 and Cara's age seven years ago was C-7. Since Maura's age (7 years ago) was half of Cara's we can write in symbols: $M-7= \frac{1}{2}(C-7)$

Let's take that last equation and substitute C - 5 for M (this is because according to our first equation these are equal). When we do this we get an equation with only C as the variable and solve for C as follows:

$M-7= \frac{1}{2}(C-7)$
$C-5-7= \frac{1}{2}(C-7)$
$C-12= \frac{1}{2}C-( \frac{1}{2})(7)$
$C-12= .5C-3.5$
$.5C-12= -3.5$
$.5C= 8.5$
$C= 17$

Cara is 17. Since Maura is 5 years younger she is 12.

As a check, seven years ago Cara was 10 and Maura was 5. It is the case that Maura was half Cara's age seven years ago.

4 0

3 years ago

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

$A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2$

3 0

3 years ago

7.1 cm

SIZIF [17.4K]

Answer:

Cylinder Volume = PI * radius^2 * height

Radius = Square Root [Volume / (PI * height)]

Radius = Square Root [ 134 / (3.14 * 7.1)]

Radius = 2.45103

Radius = 2.45

Step-by-step explanation:

5 0

3 years ago

Choose the fraction that has not been reduced 10-19, 15-16,19-38,21-34

BartSMP [9]

19/38 is not reduces. Numerator and denominator can be divided by 19.
It can be reduced to 1/2

4 0

3 years ago

A nationwide census is conducted and it is found that the mean number of hours of television watched per year by Americans is 35

Ber [7]

Answer:

Probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.

Step-by-step explanation:

We are given that a nationwide census is conducted and it is found that the mean number of hours of television watched per year by Americans is 350 with a standard deviation of 220.

A group of 4 Americans is selected.

Let $\bar X$ = sample mean number of hours of television watched per year

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 350

$\sigma$ = standard deviation = 220

n = sample of Americans = 4

Now, the probability that a group of 4 Americans watch more than 400 hours of television per year is given by = P( $\bar X$ > 400 hours)

P( $\bar X$ > 400) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{400-350}{\frac{220}{\sqrt{4} } }$ ) = P(Z > 0.45) = 1 - P(Z $\leq$ 0.45)

= 1 - 0.6736 = 0.3264

The above probability is calculated by looking at the value of x = 0.45 in the z table which has an area of 0.6736.

Hence, the probability that a group of 4 Americans watch more than 400 hours of television per year is 0.3264.

6 0

3 years ago

Draw a plane, showing the three (non-linear) points that define it.​

Draw a plane, showing the three (non-linear) points that define it.