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3 years ago

If y varies directly with x, find the constant of variation with x = 4 and y = -24

2 answers:

6 0

Use the formula y=kx for this equation.
so considering that Y equals -24 then X and K must also equal that number
we already know that X is -4 but we dont know what K is.
so we divide -24 by -4 and get an answer of a positive 6 but the answer is not proven yet.
-4 times 6 is -24 meaning that the answer is 6

Ivahew [28]3 years ago

6 0

Answer:

The constant of variation is -6.

A is correct.

Step-by-step explanation:

If y varies directly with x

$y\propto x$

y is directly proportional to x.

Equation: y=kx

where, k is constant of proportionality or constant of variation.

At x=4 , y=-24

Substitute x and y into equation and solve for k

$-24=4k$

$k=-6$

Hence, The constant of variation is -6.

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71, 80, 82, 78, 80, 91, 107, 121, 125, 131, and 142. The variance of this data set is?

adoni [48]

Answer:

636.41818

Step-by-step explanation:

^2=∑=1(−⎯⎯⎯)2−1

^2=−1

^2=6364.181811−1

^2=6364.181810

^2=636.41818

I hope this helps :)

7 0

3 years ago

Look at the picture below

Vadim26 [7]

= 2x + 11

Steps

(8x+9) -(6x-2)

Remove ( a ) = a

8x + 9 - 6x + 2

Simplify

8x+ 9 - 6x + 2: 2x + 11

= 2x + 11 <----- your answer

Please tell me if this was right

3 0

3 years ago

The function f(x)f(x) is a quartic function and the zeros of f(x)f(x) are -6−6, -5−5, -2−2 and 11. Assume the leading coefficien

Luden [163]

<h2>Answer: </h2>

$\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}$

<h2>Explanation: </h2>

A quartic function is a function given by the the following equation in standard form:

$f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}$

From the statement we must assume the leading coefficient of f(x) is 11, so:

$a_{4}=11$

The zeros are:

$x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11$

So, we can write:

$f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)$

$Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)$

$Expand: \left(x^3+13x^2+52x+60\right)\left(x-11\right):\ x^4+2x^3-91x^2-512x-660 \\ (Distributive \ property)$

Finally:

$f(x) = 11(x^4 + 2x^3 - 91x^2 - 512x - 660) \\ \\ \boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}$

3 0

3 years ago

A simple random sample of 60 households in city 1 is taken. In the sample, there are 45 households that decorate their houses wi

murzikaleks [220]

Answer:

The calculated value of z = - 0.197 falls in the critical region therefore we reject the null hypothesis and conclude that at the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays

against Ha : p1≠ p2 (claim) ( two sided)

The significance level is set at ∝= 0.05

The critical value for two tailed test at alpha=0.05 is ± 1.96

or Z∝= 0.05/2= ± 1.96

The test statistic is

Z = p1-p2/√pq(1/n1 +1/n2)

p1= proportions of households decorating in city 1 = 45/60=0.75

p2= proportions of households decorating in city 2 = 40/50= 0.8

p = the common proportion on the assumption that the two proportion are same.

p = $\frac{n_1p_1 +n_2p_2}{n_1+n_2}$

Calculating

p =60 (0.75) + 50 (0.8) / 110

p= 45+ 40/110= 85/110 = 0.772

so q = 1-p= 1- 0.772= 0.227

Putting the values in the test statistic and calculating

z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)

z= -0.05/√ 0.175244 ( 110/300)

z= -0.05/0.25348

z= -0.197

4 0

3 years ago

Find the hypotenuse of each Isosceles right triangle when the legs are of the given measure.

ludmilkaskok [199]

Answer:

Step-by-step explanation:

We can use the pythagorean theorem giving us:

a^2+b^2=c^2

(6sqr2)^2 + (6sqr2)^2 = c^2

72+72=c^2

144=c^2

12=c

6 0

3 years ago