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3 years ago

Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

8 0

Answer:

y = 6x direct variation

Step-by-step explanation:

Remember that direct variation is y = kx and inverse variation is y = k/x where k is a constant

x= 1 2 5 10

y= 6 12 30 60

First look at direct y = kx solving for k y/x =k

y/x from the table is 6/1 =6 12/2 = 6 30/5 =6 60/10 =6 so k=6

This is a direct variation with k=6

y = 6x

GarryVolchara [31]3 years ago

6 0

c. y=6x direct variation

Answer:

the table represent a direct variation

Step-by-step explanation:

as when x=1

y=2

and

x=10

y=60

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A right triangle with two congruent legs is always a 45-45-90 triangle.

saw5 [17]

Answer:

True

Step-by-step explanation:

I think this is a true or false question and this is a true statement.

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3 years ago

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Yo! Solving linear equations with integers! These are just some practice exercises I need help with! So they should probably be

drek231 [11]

Answer:

Step-by-step explanation:

<h3>Solving linear equation with one variable:</h3>

1) -4 + 3x = 4x - 8

Add 4 to both sides

-4 + 3x + 4 = 4x - 8 + 4

3x = 4x - 4

Subtract 4x from both sides,

3x - 4x = -4x + 4x - 4

-x = -4

$\sf \boxed{\bf x = 4}$

2) -5x - 8 = 2

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-5x - 8 + 8 = 2 + 8

-5x = 10

Divide both sides by (-5)

$\sf \dfrac{-5}{-5}x =\dfrac{10}{-5}$

$\sf \boxed{\bf x = -2}$

3) 12r - 14 = 5(2-r)

12r - 14 = 5*2 - 5*r

12r - 14 = 10 - 5r

Add 14 to both sides

12r - 14 + 14 = 10 - 5r + 14

12r = 24 - 5r

Add 5r to both sides

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17r = 24

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r = 24/17

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3x - 8 = -17 - 2x

Add 8 to both sides

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2 years ago

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kolezko [41]

There are officially two people aboard the space station
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3 years ago

Find each function value 1. f(7) if (x)=5x 2. f(4) if f(x)=3x-1

Inessa [10]

ANSWER

$1. \: \: f(7) = 35$

$2. \: f(4) = 11$

EXPLANATION

To find the value of a function, f(x) at a given value x=a, we plug in x=a into f(x) to obtain f(a) in simplified form.

The first function is

$f(x) = 5x$

To find f(7), we substitute x=7, into the function.

$\implies f(7) =5(7) = 5 \times 7 = 35$

The second function is

$f(x) = 3x - 1$

To find f(4), we replace x with 4 to obtain,

$f(4) = 3(4) - 1$

$f(4) = 12 - 1 = 11$

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3 years ago

A study was conducted to determine if the salaries of elementary school teachers from two neighboring districts were equal. A sa

Semenov [28]

Answer:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

(–2975, 175)

Do not reject H₀

Step-by-step explanation:

Hello!

The objective of this experiment is to test if the salaries of elementary school teachers are equal in two districts. You can test this trough the population means of the salaries of the teachers if they are either equal or different or directly test if the difference between the salaries of the two districts is cero or not, symbolically: μ₁ - μ₂ = 0

Remember, in the null hypothesis is usually stated the known information, is the "no change" premise and always carries the = symbol.

The hypothesis is:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

You have two normally distributed variables and you are studying the difference of the means. You can use a pooled Z to make the interval, the formula is:

X[bar]₁-X[bar]₂ ± $Z_{1-\alpha /2}$ *(√(σ₁²/n₁+σ₂²/n₂)

Since the test is two-tailed and at a signification level of 5% I've made the interval at the complementary confidence level of 95% so that I can use it to decide over the hypothesis.

X[bar]₁-X[bar]₂ ± $Z_{1-\alpha /2}$ *(√(σ₁²/n₁+σ₂²/n₂)

$Z_{1-\alpha /2}$ = $Z_{0,975}$ = 1,96

[28900-30300 ± 1.96*(√((2300)²/15+(2100)²/15)]

[-1400 ± 1576,15]

[-2976.15;176,15]

Since I've approximated to two decimal units in the intermediate calculations, the values differ slightly, but the interval is:

(–2975, 175)Now, since the 0 is contained in the Confidence interval, the decision is to not reject the null hypothesis. In other words, the difference in average salaries between the two districts is cero.

I hope it helps!

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3 years ago