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3 years ago

What equation represents the proportional relationship displayed in the table?

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

3 0

Answer:

$y=6x$

Step-by-step explanation:

Given:

The table is given as:

x 0 4 7 8

y 0 24 42 48

The relationship between 'x' and 'y' is a proportional relationship.

A proportional relationship is one in which one variable varies directly with the other by a factor of 'k' also known as constant of proportionality and $k\ne 0$

A proportional relationship is given as:

$y=kx$

Now, we plug in 'x' and 'y' values and find the value of 'k'.

Let $x=4\ and\ y=24$

$24=k\times 4\\\\k=\frac{24}{4}=6$

Therefore, the constant of proportionality is 6. Hence the complete equation is given as:

$y=6x$

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What is the approximate volume of one refraction cup? What’s its formula ?

Marizza181 [45]

Answer:

Volume = 0.1696 L

The formula is Area of base of refraction cup × Depth of the refraction cup

Step-by-step explanation:

The dimensions of a refraction cup are;

Diameter = 120 mm

Depth = 30 mm

Therefore, volume of the refraction cup = Area of base × Depth

Volume of the refraction cup = (π×120²/4)/2 × 30 = 169646.003 mm³

1 L = 1000000 mm³

Therefore, 169646.003 mm³ = 169646.003/1000000 m³ = 0.1696 L

The formula is Area of base of refraction cup × Depth of the refraction cup.

6 0

3 years ago

When we test Upper H 0: muequals0 against Upper H Subscript a: mugreater than0, we get a P-value of 0.03. a. What would the

Anastasy [175]

Answer:

(a) The null hypothesis will be rejected.

(b) Type I error

Step-by-step explanation:

The hypothesis provided is:

$H_{0}: \mu = 0\\ H_{a} : \mu > 0$

The p-value of the test obtained is 0.03

(a)

Decision rule for hypothesis testing, based on p-value, states that if the p-value is less than the significance level (α) then the null hypothesis is rejected and vice versa.

The significance level is α = 0.10

Then,

$p-value = 0.03 < \alpha = 0.10$

Thus, the null hypothesis will be rejected.

Conclusion:

The null hypothesis is rejected stating that the value of μ is more than 0.

(b)

If the decision in (a) is an error, i.e. the null hypothesis is rejected when in fact it is true, this type of error is known as type I error.

(c)

The significance level is α = 0.01

Then,

$p-value = 0.03 > \alpha = 0.01$

Thus, the null hypothesis will not be rejected.

Conclusion:

The null hypothesis was not rejected stating that the value of μ is 0.

If this decision is an error, i.e. the null hypothesis was not rejected when in fact it is false, this type of error is known as type II error.

3 0

3 years ago

Which radical expression is in simplified form A. 11y/sqrt3 B. sqrt6/5y C. sqrt17/sqrt4 D. sqrt25/18

Mkey [24]

Answer: $\frac{\sqrt{6}}{5y}$

Step-by-step explanation:

The given radical expressions are:

$A. \frac{11y}{\sqrt{3}}\\\text{It is not completely simplified ,}\\\text{since denominator is radical, we need to rationalize it first to simplify. }\\\\B.\frac{\sqrt{6}}{5y}\\\text{It is completely simplified ,}\\\text{since its denominator is not radical and 6 is not a perfect square. }\\\\C. \frac{\sqrt{17}}{\sqrt{4}}\\\text{It is not completely simplified ,}\\\text{since denominator is radical, we need to rationalize it first to simplify. }\\\\$ $\\\\D. \frac{\sqrt{25}}{18}=\frac{5}{18}\\\text{Hence, expression D was not completely simplified .}$