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lord [1]
2 years ago
10

I REALLY NEED HELP

Mathematics
2 answers:
ch4aika [34]2 years ago
6 0

9514 1404 393

Answer:

  108 ft²

Step-by-step explanation:

The length of the other side of the rectangle can be found using the Pythagorean theorem.

  15² = 12² + x²

  x = √(225 -144) = √81 = 9

So, the rectangle is 9 ft by 12 ft. Its area is the product of those dimensions:

  A = bh

  A = (12 ft)(9 ft)

  A = 108 ft² . . . . area of the rectangle

alex41 [277]2 years ago
4 0
The area is 180ft I think. You can do (15*12)/2 = 90. Since it’s two triangles you then do 90*2. I hope I am right
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Answer:

  • a = 3/2
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Step-by-step explanation:

  \dfrac{\sqrt{5}-1}{\sqrt{5}+1}=\dfrac{(\sqrt{5}-1)(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)}\\\\=\dfrac{5-2\sqrt{5}+1}{5-1}=\dfrac{6-2\sqrt{5}}{4}\\\\=\dfrac{3}{2}-\dfrac{1}{2}\sqrt{5}

Comparing this to the form a+b√5, we see that ...

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Step-by-step explanation:

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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.

3 0
3 years ago
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