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3 years ago

Y=1/3x-3 Y=-x+5 How do I solve

Mathematics

1 answer:

ehidna [41]3 years ago

4 0

Since both equations are equal to y, we can just combine them like this:

1/3x-3=-x+5

1/3x=-x+8

4/3x=8 (since x is 1x which is 3/3x)

x=6

Plug x back in:

y=-6+5

y=-1

So x=6 and y=-1

Hope this helped!

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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:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

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.

3 0

3 years ago

A composition of reflections across two intersecting lines is a _____

kogti [31]

A composition of reflections across two intersecting lines is a rotation.

I hope helped ^^

4 0

3 years ago

Someone help me please???

NeTakaya

Im thinking the 3rd one . I’m not 100 percent sure.

3 0

3 years ago

Some values of the linear function 'f' are shown in the table what is the value of 3?

Monica [59]

6 | 16 is the correct answer I believe

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3 years ago

$20 haircut with 10% and 7% tax

Anika [276]

20 * .10 = 2 (2 = 10% of 20)

20 + 2 = 22

20 x .07 = 1.4 (1.4 = 7% of 20)

20 + 1.4 = 21.4

The price of a 20$ haircut with a 10% tax would be $22.

The price of a 20$ haircut with a 7% tax would be $21.40.

4 0

3 years ago