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3 years ago

What is the value of the fourth term in a geometric sequence for which a=15 and r= 1/3

Mathematics

1 answer:

Andreyy893 years ago

6 0

Answer:

Step-by-step explanation:

hello :

the n-ieme term is : An=A1×r^(n-1)

A1 the first term r : the common ratio

in this exercice : A1 =15 r = 1/3 n = 4

A4=15×(1/3)^(4) =15×4^4 =3840

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The value of n for the equation 5n = 5 11 × 5 3

ExtremeBDS [4]

If you add the two terms on the right, you will get 5^14. 14 is your answer.

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3 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:

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

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

Pls help I’ll brainlest ASAP

Burka [1]

So, and, but, but, or, nor, so. Im pretty sure this is correct.

5 0

3 years ago

Cassidy wrote the linear equation y = 5 x + 4. Then, she wrote the equation of the line that is parallel to y = 5 x + 4 and that

Kryger [21]

Answer:

b=−5x+y

Step-by-step explanation:

Let's solve for b.

y=5x+b

Step 1: Flip the equation.

b+5x=y

Step 2: Add -5x to both sides.

b+5x+−5x=y+−5x

b=−5x+y

3 0

2 years ago

For all the functions of the form f(x) = ac^2 + bx + c, which is true when b=0

bixtya [17]

You didn't show us the choices.
The graph of that function would be centered on the y-axis.

4 0

3 years ago

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