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3 years ago

Simplify12e^5 ÷ 3e^3

Mathematics

1 answer:

Andru [333]3 years ago

8 0

Answer:

$4 {e}^{2}$

Step-by-step explanation:

$12e^5 ÷ 3e^3 \\ \\ = \frac{\cancel {12} {e}^{5} }{\cancel 3 {e}^{3} } \\ \\ = 4 {e}^{5 - 3} \\ \\ = 4 {e}^{2}$

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emeril used a total of 7 1/4 cups of flour to make three pastries. he used 2 1/4 cups of flour for the first and 2 1/3 cups for

inysia [295]

2 1/3 + 2 1/4
= 4 7/12
7 1/4 - 4 7/12
=2 2/3

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3 years ago

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(2.9X10^5)X(3.4X10^3 in standard form

Evgesh-ka [11]

By using exponent, it can be verified that

$(2.9 \times 10^5) \times (3.4 \times 10^3)$ in standard form is $9.86 \times 10^8$

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In $2^4 = 2 \times 2 \times 2 \times 2$

Here, 2 is multiplied by itself 4 times.

If $a^m = a \times a \times a ... \times a$ (m times), a is the base and m is the index.

The laws of index are

$a^{m + n} = a^m \times a^n\\a^{m - n} = \frac{a^m}{a^n}\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\(ab)^m = a^m b^m\\a^0 = 1\\a^{-n} = \frac{1}{a^n}$

The given exponent is

$(2.9 \times 10^5) \times (3.4 \times 10^3)\\9.86 \times 10^{5+ 3}\\9.86 \times 10^8$

To learn more about exponent, refer to the link:

brainly.com/question/11975096

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2 years ago

Kendra flips a fair coin two times. What is the probability that she will flip tails both times?

wolverine [178]

Answer: 1/4 or 25%

Step-by-step explanation:

The chance of flipping tails is 1/2, so you multiply 1/2*1/2 (for the 2 flips) to get 1/4 (1/2^2=1/4).

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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

5 0

3 years ago

If 75% of a number is 285 and 10% of the same number is 38, find 85% of that number.

NemiM [27]

Answer:

323

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Simplify12e^5 ÷ 3e^3​

Simplify12e^5 ÷ 3e^3