What is the EXACT area of a circle that has a radius of 1/2 inch?

Solve the simultaneous equation 3x²-xy=0, 2y-5x=1

ratelena [41]

Answer:

(x, y) = (0, 1/2) or (1, 3)

Step-by-step explanation:

The first equation factors as ...

x(3x -y) = 0

This has solutions x=0 and y=3x.

__

x = 0

Using this in the second equation gives ...

2y -0 = 1

y = 1/2

(x, y) = (0, 1/2) is a solution

__

y = 3x

Using the expression for y in the second equation, we get ...

2(3x) -5x = 1

x = 1 . . . . . . . . . simplify

y = 3x = 3 . . . . using x=1 in the first equation

(x, y) = (1, 3) is a solution

_____

Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be anything. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.

4 0

2 years ago

The smallest natural number divisible by 2,3,4,5,6,8 and 9 is____.

SVETLANKA909090 [29]

Answer:

360

Step-by-step explanation:

You will need 2 * 2 * 2 for the smallest number to be divisible by 8 with all the others.

You will need 3 * 3 for the smallest number to be divisible by 9 with all the others.

Finally you will need 1 five

The smallest number divisible by all of these is 2*2*2*3*3*5 = 360

360/2 = 180 works
360/3 = 120 works
360/5 = 72 works
360/6 = 60 works
360/8 = 45 works
360/9 = 40 works.

There is no smaller number below 360 which will work.

7 0

2 years ago

Which expression has the same value as -18÷(-9)

erma4kov [3.2K]

Negative dividing by negative gives positive,
so 18:9=2

6 0

2 years ago

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Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The

Harlamova29_29 [7]

Answer:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

We have the following data given:

$n_1 =20$ represent the sample size for group 1

$n_2 =20$ represent the sample size for group 2

$\bar X_1 =43.5$ represent the sample mean for the group 1

$\bar X_2 =40.1$ represent the sample mean for the group 2

$s_1=4.1$ represent the sample standard deviation for group 1

$s_2=3.2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525$

And the deviation would be just the square root of the variance:

$S_p=3.678$

The statistic is givne by:

$t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923$

The degrees of freedom are

$df=20+20-2=38$

And the p value is given by:

$p_v =2*P(t_{38}>2.923) =0.0058$

Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different

6 0

2 years ago

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours. At this rate of growth, how many bacteria will

Alik [6]

The number of bacteria grown in 32 hours is 15771

Step-by-step explanation:

It is given that,

Researchers recorded that a group of bacteria grew from 100 to 7,000 in 14 hours.

Therefore, the bacteria has grown from 100 to 7000 in 14 hours.

To calculate number of bacteria grown in 14 hours :

⇒ 7000 - 100 = 6900

6900 bacteria grows in 14 hours. We need to find out the growth of bacteria in 1 hour in order to calculate its growth in 32 hours.

To calculate number of bacteria grown in 1 hour :

⇒ Total bacteria growth in 14 hours / 14

⇒ 6900 / 14

⇒ 492.85

To calculate number of bacteria grown in 32 hours :

⇒ 492.85 × 32

⇒ 15771.2

⇒ 15771 (rounded to nearest whole number)

∴ The number of bacteria grown in 32 hours is 15771

6 0

2 years ago

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