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Nata [24]
3 years ago
9

(Algebra II) Extra points!!Determine whether y varies directly with x

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0

Answer:

  • k = 1.6
  • y = 1.6x

Step-by-step explanation:

If the variation is proportional dividing the y-value by the x-value will give the same result for all table entries. That quotient is the constant of variation (k).

Here 6.4/4 = 11.2/7 = 16/10 = 20.8/13 = 1.6

The value of y varies directly as x, and the constant of variation is 1.6. The equation is ...

  y = 1.6x

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Rewrite 1/3 book - 5/6 hour as a unit rate.
insens350 [35]

Answer:

2/5

Step-by-step explanation:

The answer is 2/5 as a fraction or 0.40 as a decimal. To get the answer all you have to do is 1/3÷5/6

6 0
3 years ago
F(x)=2x+1 and g(x)=x^2-7, find (f g) (x)
hodyreva [135]

The answer is (f o g)(x) = 2x^2 - 13

In order to find a composite function, you take the first letter (in this case f) and use that equation. You then remove the variable and put in the second letter (g).

f(x) = 2x + 1 ----> Remove variable.

f(x) = 2(      ) + 1 ----> Insert g(x)

(f o g)(x) = 2(x^2 - 7) + 1 ----> Distribute

(f o g)(x) = 2x^2 - 14 + 1 ----> Simplify

(f o g)(x) = 2x^2 - 13

5 0
3 years ago
In the proportion 2:3 = 16:24 ,the product of the two middle values is __.
klio [65]

Answer:

48 and 48

Step-by-step explanation:

product means multiplication

two middle values are 3 and 16

3*16 = 48

two outside values are 2 and 24

2*24 = 48

4 0
3 years ago
What is the radius and center of the circle given by the equation (x-5)^{2}+(y+2)^{2} = 81/4
artcher [175]

Answer:

The center is (5, -2) and the radius is 9/2

Step-by-step explanation:

The equation of a circle can be written by

(x-h) ^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-5)^{2}+(y+2)^{2} = 81/4

( (x-5)^{2}+(y- -2)^{2} = (9/2)^2

The center is (5, -2) and the radius is 9/2

6 0
3 years ago
In 1990, 1000 adults were randomly selected and each was asked if they smoked, 300
Oduvanchick [21]

Answer:

 The proportion of smokers was higher in 1990 than in 2000

Step-by-step explanation:

Solution

Recall that,

The total number of sample 1 (n1) = 1000

Total  sample 2 number  (n2) = 2000

The number of favourable events (X1) = 300

The number of favourable events (X2) = 500

so,

p₁ = X₁/n₁ = 300/1000 = 0.3

p₂ = X₂/n₂ =500/2000 =0.25

α = 0.05

We are interested in testing the hypothesis.

The  hypothesis (Null) ....>  H₀ : p₁ = p₂

Alternate hypothesis------ > H₁ : p₁ > p₂

Thus,

P = X₁ + X₂/ n₁ + n₂

P =300 + 500/1000 +2000

P =800/3000

=0.2667

Now,

Z₀ = P₁ - P₂/√ P (1 -P) (1/n₁ + 1/n₂)

Z₀ =  0.3 - 0.25/√0.2667  (1 - 0.2667) (1/1000 + 1/2000)

Z₀ = 0.4999999999999999/√ 0.2667 (0.7333000000000001) (0.001 +0.0005)

Then,

Z₀ = 0.4999999999999999/√0.00029335666500000004

Z₀ = 2.9193

so,

zα/2 = z0.05/2 =z0.025

zα/2 = 1.6448536269514722

Now, we apply the decision rule:

Decision Rule: Reject the null hypothesis if the statistic value test is higher than the critical value 1.6448536269514722

The statistic value, 2.9193 is greater than the critical value 1.6448536269514722,  then we will reject the null hypothesis.

Therefore, the proportion of smokers was higher in 1990 than in 2000

3 0
3 years ago
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