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kondor19780726 [428]

2 years ago

8

Jack was so frustrated with his slow laptop that he threw it out of his second story window. The height, h, of the laptop at tim

e t seconds can be given by the equation h(t)= -16t^2 + 28t + 17. Assuming the laptop hits the ground below, find the domain of the function.

1 answer:

jeyben [28]2 years ago

5 0

Answer:

The domain of the function is the interval [0,2.23]

see the explanation

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> the height of the laptop in units

we have

$h(t)=-16t^{2}+28t+17$

we know that

When the laptop hits the ground, the value of h(t) is equal to zero

so

For h(t)=0

$-16t^{2}+28t+17=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+28t+17=0$

so

$a=-16\\b=28\\c=17$

substitute in the formula

$x=\frac{-28(+/-)\sqrt{28^{2}-4(-16)(17)}} {2(-16)}$

$x=\frac{-28(+/-)\sqrt{1,872}} {-32}$

$x=\frac{-28(+/-)12\sqrt{13}} {-32}$

$x_1=\frac{-28(+)12\sqrt{13}} {-32}=-0.477$

$x_1=\frac{28(-)12\sqrt{13}} {32}=-0.477$ ---> is not a solution

$x_2=\frac{-28(-)12\sqrt{13}} {-32}$

$x_2=\frac{28(+)12\sqrt{13}} {32}=2.23\ sec$

therefore

The domain of the function is the interval [0,2.23]

All real numbers greater than or equal to 0 seconds and less than or equal to 2.23 seconds

$0\ sec \leq x \leq 2.23\ sec$

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1 year ago

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Give an example of a qualitative variable and an example of a quantitative variable (discrete or continuous.) Explain the common

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Answer:

Example of qualitative variable: hair colour.

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Step-by-step explanation:

A qualitative variable expresses a non-numerical quality of an object or person. For example, hair colour (brown, blonde, red...) or eye colour (green, blue, brown...).

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1 year ago

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Izumi is running on a quarter-mile oval track. After running 110 yards, his coach records his time as 16 seconds.

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Answer:

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1 year ago

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Answer:

<em>The amount of animal feed left was 86.4 kilograms.</em>

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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

1 year ago