15+45 as a product of the GCF of the addends and another

If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105

Eduardwww [97]

Answer:

z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

y = kxz

We can find k from the given values.

40 = k(10)(9)

40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

y = (4/9)xz

9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

z = 9·105/(4·55)

z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)

4 0

3 years ago

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation

nydimaria [60]

y/x = k

6.4/4 = 1.6

11.2 / 7 =1.6

16/10 = 1.6

20.8 /13 =1.6

This is a direct variation and the constant is 1.6

y=1.6x

8 0

2 years ago

Read 2 more answers

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assig

Keith_Richards [23]

Answer:

1. Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

2. D. 36

3. C. 34

4. B. 1.059

5. B. 8.02

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part 1

The hypothesis for this case are:

Null hypothesis: $\mu_{A}=\mu_{B}=\mu_{C}$

Alternative hypothesis: Not all the means are equal $\mu_{i}\neq \mu_{j}, i,j=A,B,C$

Part 2

In order to find the mean square between treatments (MSTR), we need to find first the sum of squares and the degrees of freedom.

If we assume that we have $p$ groups and on each group from $j=1,\dots,p$ we have $n_j$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

And we have this property

$SST=SS_{between}+SS_{within}$

We need to find the mean for each group first and the grand mean.

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

If we apply the before formula we can find the mean for each group

$\bar X_A = 27$ , $\bar X_B = 24$ , $\bar X_C = 30$ . And the grand mean $\bar X = 27$

Now we can find the sum of squares between:

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2$

Each group have a sample size of 4 so then $n_j =4$

$SS_{between}=SS_{model}=4(27-27)^2 +4(24-27)^2 +4(30-27)^2=72$

The degrees of freedom for the variation Between is given by $df_{between}=k-1=3-1=2$ , Where k the number of groups k=3.

Now we can find the mean square between treatments (MSTR) we just need to use this formula:

$MSTR=\frac{SS_{between}}{k-1}=\frac{72}{2}=36$

D. 36

Part 3

For the mean square within treatments value first we need to find the sum of squares within and the degrees of freedom.

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2$

$SS_{error}=(20-27)^2 +(30-27)^2 +(25-27)^2 +(33-27)^2 +(22-24)^2 +(26-24)^2 +(20-24)^2 +(28-24)^2 +(40-30)^2 +(30-30)^2 +(28-30)^2 +(22-30)^2 =306$

And the degrees of freedom are given by:

$df_{within}=N-k =3*4 -3 = 12-3=9$ . N represent the total number of individuals we have 3 groups each one with a size of 4 individuals. And k the number of groups k=3.

And now we can find the mean square within treatments:

$MSE=\frac{SS_{within}}{N-k}=\frac{306}{9}=34$

C. 34

Part 4

The test statistic F is given by this formula:

$F=\frac{MSTR}{MSE}=\frac{36}{34}=1.059$

B. 1.059

Part 5

The critical value is from a F distribution with degrees of freedom in the numerator of 2 and on the denominator of 9 such that we have 0.01 of the area in the distribution on the right.

And we can use excel to find this critical value with this function:

"=F.INV(1-0.01,2,9)"

And we will see that the critical value is $F_{crit}=8.02$

B. 8.02

5 0

3 years ago

If a scow is towed at the rate of 3 miles an hour, how many hours will be needed to tow the scow 28 miles?

alexandr1967 [171]

You would divide 28/3 because that's how many miles it would take. 28/3=9 1/3. Also, to help understand better, 3 miles is equal to 1 hour. So the equation would look like this: 3/1=28/?. To solve it like this, you'd divide 28/3 or 3*?=28. Whatever the answer is(9.33)you do it to the bottom. So 1*9.33. that equal 9 hours 20 min

8 0

3 years ago

Mrs. Sweeney bought 4 spools of thread. Each spool of orange thread is 4 meters long and each spool of indigo thread is 10 meter

Evgen [1.6K]

1 spool of orange and 3 spoils of indigo

6 0

2 years ago