15 ) 2,145 please help I cant understand it

A ball is thrown into the air. The height in feet of the ball can be modeled by the equation h = -16t2 + 20t + 6 where t is the

makkiz [27]

$f(t)=h=-16t^2+20t+6

$

a=-16, b=20, c =6

Δ= $b^2-4ac=20^2-4*(-16)*6=400+384=784$

$\sqrt{Δ}=\sqrt{784}=28$

max:

$p=-\frac{b}{2a}=-\frac{20}{-32}=\frac{20}{32}=\frac{5}{8}$

max heigh: $h=-16(\frac{5}{8})^2+20*\frac{5}{8}+6=-16\frac{25}{64}+\frac{100}{8}+6$

$h=-\frac{25}{4}+\frac{50}{4}+6=\frac{-25+50+24}{4}=\frac{49}{4}$

$h=\frac{49}{4}$ at $t=\frac{5}{8}s$

will fall down at t:

$t=\frac{-20-28}{-32}=\frac{-48}{-32}=\frac{3}{2}=1.5$

$t=1.5s$

8 0

2 years ago

A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performanc

Anni [7]

Answer:

A.) At α = 0.05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline.

B.)The advantage of attempting to remove the block effect is

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

Step-by-step explanation:

Using Two-way ANOVA method

Given problem

Observation I II III Row total (xr)

A 18 21 20 59

B 24 26 27 77

C 30 29 34 93

D 22 25 24 71

E 20 23 24 63

Col total (xc) 114 124 129 367

∑x²=9233→(A)

∑x²c/r

=1/5(114²+124²+129²)

=1/5(12996+15376+16641)

=1/5(45013)

=9002.6→(B)

∑x²r/c

=1/3(59²+77²+93²+71²+67²)

=1/3(3481+5929+8649+5041+4489)

=1/3(27589)

=9196.3333→(C)

(∑x)²/n

=(367)²/15

=134689/15

=8979.2667→(D)

Sum of squares total

SST=∑x²-(∑x)²/n

=(A)-(D)

=9233-8979.2667

=253.7333

Sum of squares between rows

SSR=∑x²r/c-(∑x)²/n

=(C)-(D)

=9196.3333-8979.2667

=217.0667

Sum of squares between columns

SSC=∑x²c/r-(∑x)²/n

=(B)-(D)

=9002.6-8979.2667

=23.3333

Sum of squares Error (residual)

SSE=SST-SSR-SSC

=253.7333-217.0667-23.3333

=13.3333

ANOVA table

Source Sums Degrees Mean Squares

of Variation of Squares of freedom

SS DF MS F p-value

B/ w SSR=217.0667 4 MSR=54.2667 32.56 0.0001

rows

B/w SSC=23.3333 c-1=2 MSC=11.6667 7 0.01

columns

Error (residual)SSE=13.3333 (r-1)(c-1)=8 MSE=1.6667

Total SST=253.7333 rc-1=14

Conclusion:

1. F for between Rows

The critical region for F(4,8) at 0.05 level of significance=3.8379

The calculated F for Rows=32.56>3.8379

Therefore H0 is rejected

2. F for between Columns

The critical region for F(2,8) at 0.05 level of significance=4.459

We see that the calculated F for Colums=7>4.459

therefore H0 is rejected,and concluded that there is significant differentiating between columns

Part B:

To analyze the data for completely randomized designs click on anova two factor without replication in the data analysis dialog box of the excel spreadsheet.

The following table is obtained

Source DF Sum Mean F Statistic

(df1,df2) of Square (SS) Square (MS) P-value

Factor A 1 1496.5444 1496.5444 769.6514 0.001297

Rows

Factor B - 2 19.4444 9.7222 5 0.1667

Columns

Interaction

AB 2 3.8889 1.9444 0.1013 0.9045

Error 12 230.4 19.2

Total 17 1750.2778 102.9575

Factor - A- Rows

Since p-value < α, H0 is rejected.

Factor - B- Columns

Since p-value > α, H0 can not be rejected.

The averages of all groups assume to be equal.

Interaction AB

Since p-value > α, H0 can not be rejected.

The advantage of attempting to remove the block effect is

The completely randomized designs does not prove that H0 is incorrect only that it cannot be rejected.

3 0

2 years ago

The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = (x – 1). What is the slope-i

joja [24]

Y + 3 = x - 1
- 3 - 3
y = x - 4

The slope-intercept form of the equation of the line is y = x - 4.

8 0

3 years ago

Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreas

o-na [289]

Answers:

(a) f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing at $(-2,2)$ .

(c) f is concave up at $(2, \infty)$

(d) f is concave down at $(-\infty, 2)$

Explanations:

(a) f is increasing when the derivative is positive. So, we find values of x such that the derivative is positive. Note that

$f'(x) = 15x^2 - 60
$

So,

$
f'(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 15x^2 - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 15(x - 2)(x + 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textgreater \ 0} \text{ (1)}$

The zeroes of (x - 2)(x + 2) are 2 and -2. So we can obtain sign of (x - 2)(x + 2) by considering the following possible values of x:

-->> x < -2
-->> -2 < x < 2
--->> x > 2

If x < -2, then (x - 2) and (x + 2) are both negative. Thus, (x - 2)(x + 2) > 0.

If -2 < x < 2, then x + 2 is positive but x - 2 is negative. So, (x - 2)(x + 2) < 0.
If x > 2, then (x - 2) and (x + 2) are both positive. Thus, (x - 2)(x + 2) > 0.

So, (x - 2)(x + 2) is positive when x < -2 or x > 2. Since

$f'(x) \ \textgreater \ 0 \Leftrightarrow (x - 2)(x + 2) \ \textgreater \ 0$

Thus, f'(x) > 0 only when x < -2 or x > 2. Hence f is increasing at $(-\infty,-2) \cup (2,\infty)$ .

(b) f is decreasing only when the derivative of f is negative. Since

$f'(x) = 15x^2 - 60$

Using the similar computation in (a),

$f'(x) \ \textless \ \ 0 \\ \\ \Leftrightarrow 15x^2 - 60 \ \textless \ 0 \\ \\ \Leftrightarrow 15(x - 2)(x + 2) \ \ \textless \ 0 \\ \\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textless \ 0} \text{ (2)}$

Based on the computation in (a), (x - 2)(x + 2) < 0 only when -2 < x < 2.

Thus, f'(x) < 0 if and only if -2 < x < 2. Hence f is decreasing at (-2, 2)

(c) f is concave up if and only if the second derivative of f is positive. Note that

$f''(x) = 30x - 60$

Since,

$f''(x) \ \textgreater \ 0
\\
\\ \Leftrightarrow 30x - 60 \ \textgreater \ 0
\\
\\ \Leftrightarrow 30(x - 2) \ \textgreater \ 0
\\
\\ \Leftrightarrow x - 2 \ \textgreater \ 0
\\
\\ \Leftrightarrow \boxed{x \ \textgreater \ 2}$

Therefore, f is concave up at $(2, \infty)$ .

(d) Note that f is concave down if and only if the second derivative of f is negative. Since,

$f''(x) = 30x - 60$

Using the similar computation in (c),

$f''(x) \ \textless \ 0 
\\ \\ \Leftrightarrow 30x - 60 \ \textless \ 0 
\\ \\ \Leftrightarrow 30(x - 2) \ \textless \ 0 
\\ \\ \Leftrightarrow x - 2 \ \textless \ 0 
\\ \\ \Leftrightarrow \boxed{x \ \textless \ 2}$

Therefore, f is concave down at $(-\infty, 2)$ .

3 0

3 years ago

9.) A new basketball is $10.95 and is 20% off. The sales tax is 7%.

blagie [28]

If you are trying to find the cost of the basket ball, it is $8.15.

Step 1: Find 20% of 10.95- which is 2.19- and subtract 2.19 from 10.95-which is 8.76.

Step 2: Find 7% of 8.76-which is 0.6132- and subtract 0.6132 from 8.76-which is 8.1468

Step 3: Round to the nearest hundredth, which gives you 8.15.

Thus, $8.15 is your answer.

4 0

3 years ago

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15 ) 2,145 please help I cant understand it​

15 ) 2,145 please help I cant understand it