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3 years ago

12

The membership of Imua Gym is $30/ month plus a one-time fee of $100 while Planet Fit is $50/ month and no one-time fee. How do

I set up a system of equations to represent the membership costs at both gyms?

1 answer:

LekaFEV [45]3 years ago

5 0

The equarion to this problem is 30 + 100 + 50x = x

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Me!! whats your favorite song?

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3 years ago

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In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>The significance level is 0.05.</em>

<em>The data is:</em>

<em>Brand X: 91, 100, 88, 89</em>

<em>Brand Y: 99, 96, 94, 99</em>

<em>Brand Z: 83, 88, 89, 76</em>

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$

Now we calculate the F statistic as:

$F=MSB/MSE=172/23.78=7.23$

The degrees of freedom of the numerator are:

$dfn=a-1=3-1=2$

The degrees of freedom of the denominator are:

$dfd=N-a=3*4-3=12-3=9$

The P-value of F=7.23, dfn=2 and dfd=9 is:

$P-value=P(F>7.23)=0.01342$

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

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3 years ago

What is the unit rate of 9 strikes in 3 innings?

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4 years ago

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The sum of the digits of a two digit number is 8.if the ten digit is 4 more than the units digit what is the number

PIT_PIT [208]

Answer:

The number is 62.

Step-by-step explanation:

If the number is xy then x + y = 8.

Also x - y = 4.

x + y = 8

Adding the above 2 equations eliminates y:

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and y = 8-6 = 2.

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3 years ago

Use synthetic division to completely factor y=x^3-3x^2-10x+24 by x – 2.A. y = (x – 2)(x – 4)(x – 3)B. y = (x – 2)(x + 4)(x + 3)C

PIT_PIT [208]

Answer:

D. y = (x – 2)(x – 4)(x + 3)

Explanation:

We want to completely factor the polynomial.

First, given the division of polynomials below:

$\frac{x^3-3x^2-10x+24}{x-2}$

To use synthetic division, set the denominator equal to 0 and solve for x:

$x-2=0\implies x=2$

Next, write the result(2) outside and the coefficients of the numerator inside as shown below:

Carry down the leading coefficient as shown below:

Multiply the carry down value(1) by the number outside (2) and write the number under the next column:

Repeat until it gets to the last column:

Therefore:

$\frac{x^{3}-3x^{2}-10x+24}{x-2}=x^2-x-12$

We factor the resulting quadratic expression:

$\begin{gathered} x^2-x-12=x^2-4x+3x-12 \\ =x(x-4)+3(x-4) \\ =(x+3)(x-4) \end{gathered}$

So, we have:

$\begin{gathered} \frac{x^{3}-3x^{2}-10x+24}{x-2}=(x+3)(x-4) \\ \implies x^3-3x^2-10x+24=(x-2)\left(x-4\right)(x+3) \end{gathered}$

Thus:

$y=(x-2)\left(x-4\right)(x+3)$

Option D is correct.

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2 years ago