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3 years ago

What is the derivative of -5

Mathematics

1 answer:

ololo11 [35]3 years ago

8 0

The derivative of constant numbers is zero.

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Which situation is most likely to have a constant rate of change? A. Length of a bead necklace compared with the number of ident

Kipish [7]

Answer:

A. Length of a bead necklace compared with the number of identical beads

Step-by-step explanation:

Using identical beads in a necklace means that the length of the necklace will depend on the total number of identical beads in the necklace.

For each bead added, the length of the necklace will increase a given, constant, amount. This is a constant rate of change.

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3 years ago

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You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distrib

uysha [10]

Answer:

Step-by-step explanation:

Given that that (X) the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.

i.e. X is normal with mean = 15 and unknown std deviation $\sigma$

Given that $P(X$

i.e. P( $z$

z=-1.475 (from normal table)

Hence $\frac{13-15}{\sigma}=-1.475\\\sigma = 1.356$

Using this we find P(X>17) = $P(Z>\frac{17-15}{1.356} \\=P(Z>1.475)\\=0.5-0.428\\=0.072$

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3 years ago

Ship A receives a distress signal from the north, and ship B receives a distress signal from the same vessel from the southeast.

MrRissso [65]

Step-by-step explanation:

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3 years ago

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

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3 years ago

How is the formula for a triangle derived from a parallelogram? Please give a good explanation.

Katen [24]

Answer:

At first, we divide the parallelogram into two triangles by joining any two opposite vertices. These two triangles are exactly the same (congruent) and thus have equal areas. The area of the parallelogram is the summation of the individual areas of the two triangles. We drop a perpendicular from a vertex to its opposite side to get an expression for the height of the triangles. The area of the individual triangle is 12×base×height12×base×height .The area of the parallelogram being twice the area of the triangle, thus becomes after evaluation base×heightbase×height .

Complete step by step answer:

The parallelogram can be divided into two triangles by constructing a diagonal by joining any two opposite vertices.

In the above figure, ΔABDΔABD and ΔBCDΔBCDare the two such triangles. These two triangles have:

AB=CDAB=CD (as opposite sides of a parallelogram are equal)

AD=BCAD=BC (opposite sides of a parallelogram are equal)

BDBD is common

Thus, the two triangles are congruent to each other by SSS axiom of congruence. Since, the areas of two congruent triangles are equal,

⇒area(ΔABD)=area(ΔBCD)⇒area(ΔABD)=area(ΔBCD)

Now, we need to find the area of ΔABDΔABD . We draw a perpendicular from DD to the side ABAB and name it as DEDE . Thus, ΔABDΔABD is now a triangle with base ABAB and height DEDE .

Then, the area of the ΔABD

5 0

2 years ago