Ask question

Ask question

All categories

3 years ago

5

Ann has 14 socks. tom has 6 socks. how many more socks does ann have than tom

1 answer:

Readme [11.4K]3 years ago

4 0

Ann has 8 more socks then tom

You might be interested in

If a pond has a major axis of 68 feet and a minor axis of 32 feet how far apart are the foci

Bogdan [553]

Answer:

The distance between foci is 60 feet

Step-by-step explanation:

we are given

a pond has a major axis of 68 feet

so, $a=\frac{68}{2} =34$

a minor axis of 32 feet

so, $b=\frac{32}{2} =16$

now, we know ellipse formula

$c^2=a^2-b^2$

where

c is the distance between center and focus

so, we can plug it and find c

$c^2=34^2-16^2$

$c=30$

Distance between foci is

$=2c$

$=2\times 30$

$=60$

6 0

4 years ago

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

svetlana [45]

Answer:

The equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

Given

The equation of ellipsoid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation of tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ ( Given)

The equation of hyperboloid

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The equation of tangent plane at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The equation of tangent plane to the hyperboloid

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The equation of tangent plane

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required equation of tangent plane to the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

3 years ago

Bess [88]

Website 1

y=1.50x+30

Website 2

y=2x+30

Hope this helps!

4 0

3 years ago

Back of last questions answer as many as possible

daser333 [38]

13) 0.352

16) is A and B

3 0

3 years ago

Emissions of sulfur dioxide by industry sett off chemical changes in the atmosphere that result in "acid rain". The acidity of l

horsena [70]

Answer:

Case n =5

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894$

Case n =15

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549$

Case n = 40

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530$

P value

Case n =5

$p_v =P(z$

Case n =15

$p_v =P(z$

Case n =40

$p_v =P(z$

Step-by-step explanation:

Data given and notation

$\bar X=4.8$ represent the sample mean

$\sigma=0.5$ represent the population standard deviation

$n$ sample size

$\mu_o =5$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is lower than 5, the system of hypothesis would be:

Null hypothesis: $\mu \geq 5$

Alternative hypothesis: $\mu < 5$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

Case n =5

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894$

Case n =15

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549$

Case n = 40

$z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530$

P-value

Since is a left tailed test the p value would be:

Case n =5

$p_v =P(z$

Case n =15

$p_v =P(z$

Case n =40

$p_v =P(z$

5 0

3 years ago