Product and Quotient Functions

x = some unknown number

x+8 = sum of the number and 8

2(x+8) = product of 2 and the sum of a number and 8

Answer: 13.71

Step-by-step explanation:

20+6+17+10+19+15+9=96

96/7=13.71

Answer:

100,000

Step-by-step explanation:

89678 rounded to the nearest hundred thousand is 100,000.

Answer:

The values are missing in the question. They are : 16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

Step-by-step explanation:

16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

We calculate sample mean and std deviation from given data.

Sample Mean, [tex]$ {\overset{-}X} =\frac{\Sigma (X)}{n} $[/tex]   =269.8/10=26.98

Sample Variance, [tex]$s^2= \frac{\Sigma(X-{\overset{-}X})^2}{(n-1)}$[/tex]    =1859.496/9=206.610667

Sample std dev,s=[tex]$\sqrt{s^2}$[/tex]=√206.610667≈14.373958

We want to test two tailed hypothesis:

[tex]$H_0$[/tex] : σ=12

[tex]$H_2$[/tex] : σ≠12

Given: s=14.373958⇒ [tex]$s^2$[/tex] =206.610667,n=10

Significance level, a=0.1 Degrees of freedom, df=n-1=9

Since this is two tailed test, we need area of α=0.1 on either side of critical value. This means area of 0.05 on right of positive critical value.

Critical values are given by [tex]$ X_{1-\alpha/2}^2 =X_{0.95}^2 \text{ and}\ X_{1-\alpha/2}^2 =X_{0.95}^2 $[/tex]  with 9 degrees of freedom.

We can use chi-square table or following excel commands:

CHISQ. INV(0.95,9)=3.32511284307

CHISQ. INV (0.05,9)=16.9189776046

Critical Values, [tex]$X_L^2$[/tex]=3.325  and [tex]$X_R^2$[/tex]=16.919

Since this is two tailed test, the decision rule or rejection criteria is:

Reject null hypothesis if test statistic is less than or equal to left critical value OR more than or equal to right critical value, i.e,

Reject [tex]$H_0$[/tex]   if [tex]$x^2$[/tex]≤3.325  OR [tex]$x^2$[/tex]≥16.919

Test statistic is given by [tex]$X^2=\frac{(n-1)s^2}{\sigma^2}$[/tex] =((9)*206.610667)/144=12.913167    

Test statistic, [tex]$x^2$[/tex]=12.913

since test statistic is between two critical values, we (do not reject [tex]$H_0$[/tex]) (i.e, we fail to reject [tex]$H_0$[/tex].

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is not equal to 12 .

Alternatively, we can use p-value approach. The decision rule or rejection criteria is: reject null hypothesis if p-value is less than or equal to significance level (α), i.e, reject [tex]$H_0$[/tex] if p-value ≤0.1

P-value is twice the (smaller) tail area of test statistic because this is two tailed test. We can use excel function to find this. 2*M IN (CHISQ.DIST (12.913167,9,  TRUE ) 1-CHISQ.DIST 12.913167,9,  TRUE ) =0.333149809868

P-value =0.3331

since p-value is greater than significance level (α),we (do not reject [tex]$H_0$[/tex]) (i.e, we fail to reject [tex]$H_0$[/tex]).

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is different from 12 .

Answer:

D

Step-by-step explanation:

Perpendicular lines intersect at a 90 degree angle.

Answer:

3

Step-by-step explanation:

First, subtract 9 from 27:

27 - 9 = 18

Next, divide 6 from 18:

18/6 = 3

3 is Hugo's age.

~

Answer:

= -2

-7(5+3)+216/4

-7(8)+216/4

-56+54

= -2

Answer:

$1672.68

Step-by-step explanation:

Answer:

dssds 8900

Step-by-step explanation:

dwdwdmunayaynd

Answer:

34

Step-by-step explanation:

b+115°+31°= 180° (sumof all angles of triangle)

b=146°-180°

b=34°

hope it helps you!

steffie matt

Answer: Constant

Step-by-step explanation: It is a straight horizontal line with no dips or curves, so it is constant.

Hope this helps!

Please mark Brainliest!

Answer:

Constant

Step-by-step explanation:

It must be constant because the line is neither increasing or decreasing

Answer:

3

Step-by-step explanation:

Each of the lines lengths multiply by 3.

Answer: 512/9 and 6,144/81

Step-by-step explanation:

The sequence is:

18, 24, 32, 128/3, ...

Now, is easy to see that it is not an arithmetic sequence, so we can jump to see if this is a geometric sequence.

To see this, we must see at the quotient of two consecutive numbers in the sequence, and that quotient must be the same for any pair of consecutive elements.

24/18 = 1.33...

32/24 = 1.33...

(128/3)/32 = 1.33....

The quotient is constant, then this is a geometric sequence.

Then we can write the n-th term as:

Aₙ = Aₙ₋₁*1.33...

And we first should write 1.33 in a way that is easier to use:

1.33... = 1 + 0.33...

The left side can be writen as:

0.33... = 0.33...*(10/10) = (3.3.../10)

Now we can subtract the initial number:

(3.33..../10) - 0.33... = 3/10 = 0.33...*(9/10)

0.33... = (3*10)/(9*10) = 30/90 = 3/9

then we have:

1.33... = (1 + 3/9) = (9/9 + 3/9) = (12/9)

Then the two next terms are:

(128/3)*(12/9) = 128*4/9 = (512/9)

And the next term is:

(512/9)*(12/9) = (6,144/81)

Then the first six terms are:

18, 24, 32, 128/3, 512/9, 6,144/81

Answer:

please put the full question

Step-by-step explanation:

For a quadratic equation y = ax² + bx + c, the vertex (the maximum or minimum point) is at x = -b/(2a).

1) y = -0.5t² + 2t + 38

The maximum is at:

t = -2 / (2 × -0.5)

t = 2

The maximum height is:

y = -0.5(2)² + 2(2) + 38

y = 40

The coordinates of the vertex are (2, 40).  That means the missile reaches a maximum height of 40 km after 2 minutes.

2) y = -4.9t² + 12t + 1.6

The maximum is at:

t = -12 / (2 × -4.9)

t = 1.22

The maximum height is:

y = -4.9(1.22)² + 12(1.22) + 1.6

y = 8.95

The coordinates of the vertex are (1.22, 8.95).  That means the missile reaches a maximum height of 8.95 m after 1.22 seconds.

3) y = -0.04x² + 0.88x

The maximum is at:

x = -0.88 / (2 × -0.04)

x = 11

The maximum height is:

y = -0.04(11)² + 0.88(11)

y = 4.84

The maximum height of the tunnel is 4.84 meters.

The maximum width is when y = 0.

0 = -0.04x² + 0.88x

0 = -0.04x (x − 22)

x = 22

The maximum width is 22 feet.

28x + 44y = 964.40

21x + 33y = 723.30

Let's multiply the first equation by 4 and the second by -4

84x + 176y = 3857.6

-84x - 132y = -2893.2

Add the equations together.

0 + 44y = 964.4

Simplify

44y = 964.4

Divide both sides by 44

y = 964.4/44

Since we have the value of y, let's plug 964.4/44 into y for the first equation.

28x + 44(964.4/44) = 964.40

Simplify the left side

28x + 964.4 = 964.4

Subtract 964.4 from both sides

28x = 0

Divide both sides by 0

x = 0

In conclusion,

y = 964.4/44

x = 0

Answer:

Well one do the square root of 16

Answer:

1 and 9

Step-by-step explanation:

[tex]5-\sqrt{16}[/tex]

[tex]5+\sqrt{16\\[/tex]

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Zero, One, Two

Step-by-step explanation:

when it's like

[tex]y=a|x-b|+c[/tex]

with

[tex]c>0[/tex]

it will be upward

[tex]y=a|x-b|[/tex]

it will touch it in  [tex](b,0)[/tex]

[tex]y=a|x-b|-c[/tex]

with

[tex]c>0[/tex]

the equations are just an example, there can be other ways too

have three or more it's impossible, because the absolute value graph is the union of two lines, and each line at most can touch the x-axis once

Answer:

198 degrees

Step-by-step explanation:

Such a shape is called a 20-gon, such shapes have an interior angle of 162. Hence, the exterior angle = 360 (Complete angle) - 162 (The interior anlge) = 198 degrees, Hope my answer helps you, Thank you, and please add me as brainliest! Thanks

Answer:

Step-by-step explanation:

Such a shape is called a 20-gon, such shapes have an interior angle of 162. Hence, the exterior angle = 360 (Complete angle) - 162 (The interior anlge) = 198 degrees, Hope my answer helps you, Thank you, and please add me as brainliest! Thanks and Godbless

Answer:

Yes it is.

Step-by-step explanation:

-(5/12) = -*5/12 = -5/12

5/-12 = -5/12

Best of Luck!

Answer:8 pounds to make 20 apple pies

Answer:

x=1+√334, x=1−√334

Step-by-step explanation:

ANSWER is C on edge for those of you looking

Step-by-step explanation:

Answer:

175°

Step-by-step explanation:

Since, [tex] \overrightarrow{BD} [/tex] is in the interior of [tex] \angle ABC[/tex]

[tex] \therefore m\angle ABC = m\angle ABD + m\angle CBD\\

\therefore (14x + 21)\degree = (2x + 3)\degree + 150\degree \\

\therefore (14x + 21)\degree = (2x + 153)\degree\\

\therefore 14x + 21 = 2x + 153\\

\therefore 14x - 2x = 153 - 21\\

\therefore 12x = 132\\

\therefore x = \frac{132}{12}\\

\therefore x = 11\\\\

m\angle ABC = (14x + 21)\degree\\

m\angle ABC = (14\times 11+ 21)\degree\\

m\angle ABC = (154+ 21)\degree\\

\huge\red {\boxed {m\angle ABC = 175\degree}} \\[/tex]

Answer:

i think its p ≤ 85 or p ≥ 125

Step-by-step explanation:

p can be 85 and higher but can be passed 125 but it can be 125 which makes the equality signs have the line under them meaning less than or equal to, and could also mean greater than or equal to.

The  inequality that represents P the scores for students who are eligible for tutoring or extension activities ​is p ≤ 85 or p ≥ 125.

Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.

The average score is 105

The score required for tutoring is at least 20 points higher than average

The score required for extension activities is at least 20 points lower than average

P is the scores for students who are eligible for tutoring or extension activities ​

Then p ≤ 105 -20 = p ≤ 85

p ≥ 105+20 = p ≥125

p ≤ 85 or p ≥ 125

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