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3 years ago

Rafael is going for a walk. he takes 3 hours to walk 7.5 miles. What is his speed

Mathematics

2 answers:

irina [24]3 years ago

8 0

He speed maybe be 2.5

ra1l [238]3 years ago

5 0

Answer:

2.5 miles per hour

Step-by-step explanation:

7.5 divided by 3

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Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured across a line (x + 2)/3 = (2y + 3)/4

dimaraw [331]

Answer:

Distance of the point from its image = 8.56 units

Step-by-step explanation:

Given,

Co-ordinates of point is (-2, 3,-4)

Let's say

$x_1\ =\ -2$

$y_1\ =\ 3$

$z_1\ =\ -4$

Distance is measure across the line

$\dfrac{x+2}{3}\ =\ \dfrac{2y+3}{4}\ =\ \dfrac{3z+4}{5}$

So, we can write

$\dfrac{x-x_1+2}{3}\ =\ \dfrac{2(y-y_1)+3}{4}\ =\ \dfrac{3(z-z_1)+4}{5}\ =\ k$

$=>\ \dfrac{x-(-2)+2}{3}\ =\ \dfrac{2(y-3)+3}{4}\ =\ \dfrac{3(z-(-4))+4}{5}\ =\ k$

$=>\ \dfrac{x+4}{3}\ =\ \dfrac{2y-3}{4}\ =\ \dfrac{3z+16}{5}\ =\ k$

$=>\ x\ =\ 3k-4,\ y\ =\ \dfrac{4k+3}{2},\ z\ =\ \dfrac{5k-16}{3}$

Since, the equation of plane is given by

x+y+z=3

The point which intersect the point will satisfy the equation of plane.

So, we can write

$3k-4+\dfrac{4k+3}{2}+\dfrac{5k-16}{3}\ =\ 3$

$=>6(3k-4)+3(4k+3)+2(5k-16)\ =\ 18$

$=>18k-24+12k+9+10k-32\ =\ 18$

$=>\ k\ =\dfrac{13}{8}$

So,

$x\ =\ 3k-4$

$=\ 3\times \dfrac{13}{8}-4$

$=\ \dfrac{7}{4}$

$y\ =\ \dfrac{4k+3}{2}$

$=\ \dfrac{4\times \dfrac{13}{8}+3}{2}$

$=\ \dfrac{19}{4}$

$z\ =\ \dfrac{5k-16}{3}$

$=\ \dfrac{5\times \dfrac{13}{8}-16}{3}$

$=\ \dfrac{-21}{8}$

Now, the distance of point from the plane is given by,

$d\ =\ \sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}$

$=\ \sqrt{(-2-\dfrac{7}{4})^2+(3-\dfrac{19}{4})^2+(-4+\dfrac{21}{8})^2}$

$=\ \sqrt{(\dfrac{-15}{4})^2+(\dfrac{-7}{4})^2+(\dfrac{9}{8})^2}$

$=\ \sqrt{\dfrac{225}{16}+\dfrac{49}{16}+\dfrac{81}{64}}$

$=\ \sqrt{\dfrac{1177}{64}}$

$=\ 4.28$

So, the distance of the point from its image can be given by,

D = 2d = 2 x 4.28

= 8.56 unit

So, the distance of a point from it's image is 8.56 units.

4 0

3 years ago

In 2006 Edison, NJ had a population of 100,500. Livermore, CA had a population of 78,400. What was the total population of these

forsale [732]

The answer is simple:
Just add the two populations together.

100,500 + 78,400 = 178,900

ANSWER: A. 178,900

Hope this helps! Have a good night and God bless (:

7 0

3 years ago

Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research

kolbaska11 [484]

Complete Question

The complete question is shown on the first uploaded image

Answer:

Yes the researcher can conclude that the supplement has a significant effect on cognitive skill

$d = 0.5778$

The result of this hypothesis test shows that there is sufficient evidence to that the supplement had significant effect.The measure of effect size is large due to the large value of Cohen's d (0.5778 > 0.30 )

Step-by-step explanation:

From the question we are told that

The sample size is n=16

The sample mean is $M = 50.2$

The standard deviation is $\sigma = 9$

The population mean is $\mu = 45$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o \mu =45$

The alternative hypothesis is $H_a \mu \ne 45$

Generally the test statistics is mathematically represented as

$z = \frac{M - \mu}{\frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{50.2 - 45}{\frac{9}{\sqrt{16} } }$

=> $z = 2.31$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > z )$

$p-value = 2 * P(Z > 2.31 )$

From the z-table

$P(Z > 2.31 ) = 0.010444$

=> $p-value = 2 * 0.010444$

=> $p-value = 0.021$

From the obtained values we see that $p-value < 0.05$

Decision Rule

Reject the null hypothesis

Conclusion

There is sufficient evidence to conclude that the supplement has a significant effect on the cognitive skill of elderly adults

Generally the Cohen's d for this study is mathematically represented as

$d = \frac{M - \mu}{\sigma }$

=> $d = \frac{50.2 -45}{9 }$

=> $d = 0.5778$

3 0

3 years ago

Prime numbers up to 30

Mrrafil [7]

Answer:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Step-by-step explanation:

Google

6 0

2 years ago

Read 2 more answers

The intercepts of the equation x^2 + 4y^2 = 16 are ___<br> PLEASE HELP

Eva8 [605]

Yintercepts are where x=0
set to zero to solve

0^2+4y^2=16
4y^2=16
divide 4
y^2=4
sqrt both sides
y=+/-2

xintercept is where y=0

x^2+4(0)^2=16
x^2+0=16
x^2=16
sdqrtboth sides
x=+/-4

yintercepts are (0,2) and (0,-2)
xintercepts are (4,0) and (-4,0)

3 0

3 years ago