Expand and simplify 5(2x-1) + 2(3x-6)

David uses 1/4 bag of potting soil to plant 6 tomato plants. If he uses the same amount of potting soil for each plant, what fra

Schach [20]

Answer:

Step-by-step explanation:

A

8 0

3 years ago

The first term in a geometric series is 64 and the common ratio is 0.75. Find the sum of the first 4 terms in the series.

maks197457 [2]

Answer:

195.25

Step-by-step explanation:

Consider geometric series S(n) where initial term is a

So S(n)=a+ar^1+...ar^n

Factor out a

S(n)=a(1+r+r^2...+r^n)

Multiply by r

S(n)r=a(r+r^2+r^3...+r^n+r^n+1)

Subtract S(n) from S(n)r

Note that only 1 and rn^1 remain.

S(n)r-S(n)=a(r^n+1 -1)

Factor out S(n)

S(n)(r-1)=a(r^n+1 -1)

The formula now shows S(n)=a(r^n+1 -1)/(r-1)

Now use the formula for the problem

4 0

3 years ago

What is the length of ST?

defon

Answer:

5 cm

Step-by-step explanation:

Let's assume this is a number line were given.

Distance of S from 0 = 4 units

Distance of T from 0 = 9 units

Length of ST = the difference between T and S

ST = |9 - 4| = 5 units = 5 cm

This means S and T are 5 cm apart.

3 0

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

The scatter plot shows the relationship between the test scores of a group of students and the number of hours they exercise in

Y_Kistochka [10]

Answer: Part A: Group p is called a cluster. Group T is called an outlier.

Part B: it seems that as the hours of exercise increases, their test scores increases.

Step-by-step explanation:

5 0

3 years ago

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