All categories

3 years ago

Find k, the constant of proportionality, for the data in this table. Then write an equation for the relationship.

Mathematics

1 answer:

VashaNatasha [74]3 years ago

7 0

Answer:

$k=\frac{32}{5}$ , $y=\frac{32}{5}x$

$k=6.4$ , $y=6.4x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

Find the value of the constant of proportionality k

take any ordered pair from the data

For x=25, y=160

$k=\frac{y}{x}$

substitute the values of x and y

$k=\frac{160}{25}$

simplify

$k=\frac{32}{5}$

The linear equation is equal to

$y=\frac{32}{5}x$

$y=6.4x$

You might be interested in

The extensions of the legs AB and CD of a trapezoid ABCD intersect at point E. Find the lengths of the sides of △AED if AB=5cm,

Lynna [10]

Answer:

AE = 15 cm; ED = 18 cm; AD = 15 cm (given)

Step-by-step explanation:

ΔBEC ~ ΔAED so ...

AD/BC = AE/BE = (BE+AB)/BE = 1 + AB/BE

Substituting given numbers (lengths in centimeters), we have ...

15/10 = 1 + 5/BE

1/2 = 5/BE

BE = 10

Similarly, ...

1/2 = 6/CE

CE = 12

Then the unknown sides are ...

AE = AB + BE = 5 + 10 = 15 . . . cm

ED = CE + CD = 12 + 6 = 18 . . . cm

8 0

3 years ago

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

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

where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

$\sigma$ = population standard deviation = 0.001 g

n = sample of specimen = 3

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]

= [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

6 0

3 years ago

Felicia drew a triangle with side lengths that measured 15 cm, 18 cm and 27 cm. To determine if Felicia drew a right triangle, s

Charra [1.4K]

Answer:

The equation should be h²=P²+b²

27²=15²+18²

729=225+324

729=549

thus, it is not right angle triangle

3 0

3 years ago

What is 34 divided by the square root of 5

Margaret [11]

Answer:

15.205

Step-by-step explanation:

simplemathdbdjjsjdi

5 0

3 years ago

Read 2 more answers

Simplify (x^3/x^2)^2 . Explain your steps.

Helen [10]

Answer:

Step-by-step explanation:

(x^3

x^2)^2

X³ )²

X²

X³*²

X²*²

X ⁶

X⁴

X ⁶-⁴ = X²

8 0

3 years ago