Find the measures of the given angles or the lengths of the given sides. m<b=3y, m<e=6y-12

Mathematics

1 answer:

Mamont248 [21]3 years ago

5 0

The measure of the angles would be: m<b=12 and m<e=12.

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What's the difference between 126 1/4 78 2/3

Stels [109]

Difference means subtract, so we use subtraction:

*first we need to make the fractions have the same denominator

1/4 = 3/12
2/3 = 8/12

126(3/12) - 78(8/12)
*since the fraction in the first term is smaller than the second, make it improper

125(15/12) - 78(8/12)

now simply subtract:

125 - 78
= 47

15 - 8
= 7
* this is now (7/12)

now put them back together:

47(7/12)

That's the final answer!

3 0

4 years ago

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:

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