The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations.

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

[tex]x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm[/tex]

Let the total length of the 9 adults' big finger = T

[tex]x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm[/tex]

The total length of the 13 people's big finger = t + T

                                                                           = 56 + 144.9

                                                                            =200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

Answer:

-19

Step-by-step explanation:

-19 is the absolute value of 19

hope this helps

Answer:

sum = +13

Step-by-step explanation:

The possible factors of 48 are

{1,2,3,4,6,8,12,16,24,48}

Of these, the pair 3,16 gives a sum of 19 and a product of 48.

We are given that 16 (greater absolute value) is positive, so 3 is negative.

The sum of the two is therefore 16-3 = 13

Answer:

A, B, and E are all less than 1/8

Answer:

72

Step-by-step explanation:

We are assuming that all girls in the group bought the same number of items.

Therefore, we need to find the highest common factor of 72, 144 and 216.

HCF

72 = 2 * 2 * 2 * 3 * 3

144 = 2 * 2 * 2 * 2 * 3 * 3

216 = 2 * 2 * 2 * 3 * 3 * 3

The product of the emboldened numbers is the highest common factor.

That is:

2 * 2 * 2 * 3 * 3 = 72

Therefore, the largest possible number of girls in the group is 72.

Answer:

a) [tex]\angle G = 125^\circ[/tex]

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units

Step-by-step explanation:

Given:

Polygon ROTFL ~ Polygon SUBAG

Similar polygons mean they have similar angles and the ratio of corresponding sides and ratio of their perimeter are equal.

Part A:

Given that

[tex]m\angle R = 100^\circ\\m\angle O = 120^\circ\\m\angle T = 75^\circ\\M\angle L = 60^\circ[/tex]

[tex]m\angle L+M\angle L = 180^\circ\\\Rightarrow m\angle L=180-60=120^\circ[/tex]

Sum of all interior angles of a pentagon is [tex]540^\circ[/tex]

[tex]m\angle R+m\angle O+m\angle T+m\angle F+m\angle L=540^\circ\\\Rightarrow 100+120+75+m\angle F+120=540^\circ\\\Rightarrow m\angle F=125^\circ\\[/tex]

Due to similarity property of the two pentagons, [tex]\angle F =\angle G = 125^\circ[/tex]

Part B:

Ratio of corresponding sides is equal.

Given the sides SU = 12, RO = 8 and FL = 10 units respectively.

[tex]\dfrac{SU}{RO}=\dfrac{AG}{FL}\\\dfrac{12}{8}=\dfrac{AG}{10}\\\Rightarrow AG = 15\ units[/tex]

Part C:

Ratio of corresponding sides must be equal to ratio of perimeter of the two polygons:

[tex]\dfrac{RO}{SU} = \dfrac{\text{perimeter of ROTFL}}{\text{perimeter of SUBAG}}\\\Rightarrow \dfrac{8}{12} = \dfrac{52}{\text{perimeter of SUBAG}}\\\Rightarrow \text{perimeter of SUBAG} = 52 \times 1.5\\\Rightarrow \text{perimeter of SUBAG} = 78\ units[/tex]

So, the answers are:

a) [tex]\angle G = 125^\circ[/tex]

b) AG = 15 units

c) Perimeter of polygon SUBAG = 78 units

Answer:

y=-3

Step-by-step explanation:

This is a horizontal line

Horizontal lines are of the form

y=

The y value is -3

y=-3

━━━━━━━☆☆━━━━━━━

▹ Answer

A. y = -3

▹ Step-by-Step Explanation

Y is represented by a horizontal line and it passes through the point -3 therefore, the answer is y = -3.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

y = 10 - 0.5x for 0 ≤  x ≤ 20

Step-by-step explanation:

Initial value = (0,10)

final value = (20,0)

Cost per trip = debit of 0.50 = slope

equation : y = 10 - 0.5x for 0 <=  x <= 20

Distribute the sum:

[tex]\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1[/tex]

Use the following formulas:

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]

[tex]\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}[/tex]

In case you don't know where those formulas came from:

The first one is obvious; you're just adding n copies of 1, so 1 + 1 + ... + 1 = n.

The second can be proved in this way: let S be the sum 1 + 2 + 3 + ... + n. Rearrange it as S = n + (n - 1) + (n - 2) + ... + 1. Then 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1), or n copies of n + 1. So 2S = n(n + 1). Divide both sides by 2 and we're done.

Answer:

A. The triangles are congruent by SAS.

Step-by-step explanation:

Two sides of one triangle are congruent to two sides of the other triangle. The included angles of the two triangles are congruent.

The triangles are congruent by SAS.

Answer:

B(3.5, 0.5)

Step-by-step explanation:

Given:

A(5,5), Xa=5, Ya=5

C(3,-1), Xc=3, Yc=-1

To find point B, we can use the partition rule, where AB = 3BC, so AB occupies k=3/4 of the distance AC.

B(x,y) = ((1-k)Xa+kXc, (1-k)Ya+kYc)

=(Xa/4+3Xc/4, Ya/4+3Yc/4), substitute values

=(5/4+3*3/4, 5/4+3*(-1)/4)

=(14/4,2/4)

=(3.5, 0.5)

Answer:

(3.5, 0.5) or A

Step-by-step explanation:

Got it right

Step-by-step explanation:

_22greater than minus 2 x minus minus 72 minus 3

72 minus 22 minus 3greathan than 2x

49greatern than 2 x

Answer:

Option B

Step-by-step explanation:

With a scale factor of 1/2, the dilated shape should be smaller because of the scale factor, So in Option B the dilated shape is smaller than the real one.

1) Option A is an enlargement

2) Option B is reduction

3) Option C is equality

Answer:

e)  (3.77%, 8.70%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 369

Sample proportion

                              [tex]p = \frac{x}{n} = \frac{23}{369} = 0.0623[/tex]

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.0623 - 1.96 \sqrt{\frac{0.0623(1-0.0623)}{369} } , 0.0623 + 1.96\sqrt{\frac{0.0623(1-0.0623)}{369} })[/tex]

(0.0623 - 0.0246 , 0.0623 + 0.0246)

(0.0383 , 0.0869)

(3.83% , 8.69%)

95% confidence interval for the percentage of all medical students who plan to work in a rural community

(3.83% , 8.69%)

Step(ii):-

Given 43% of those polled blamed of companies the most for the recent increase in gasoline prices

sample proportion 'p' = 0.43

Given Margin of error (M.E) = 0.024

95% confidence intervals are determined by

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.43 - 0.024 } , 0.43 +0.024 )[/tex]

(0.406 , 0.454)

Final answer:-

95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices

(0.406 , 0.454)

Answer:

living organism

Step-by-step explanation:

soil particals and decad crops living organism

Hey there! :)

Answer:

B. The volume of Cylinder B is larger.

Step-by-step explanation:

Find the volumes of each cylinder using the formula V = πr²h:

Cylinder A:

V = π3² · 5

V = 9π · 5

V = 45π units³

Cylinder B:

V = π5²· 3

V = 25π · 3

V = 75π units³

75π u³ > 45π u³, so the volume of Cylinder B is larger.

Answer:

The missing reason in step 5 is;

The linear pair postulate

Step-by-step explanation:

The information given are;

Column 1,                                                 Column 2

Statements,                                             Reasons

Line AB intersect DE at C,                      Given

∠DCB and ∠BCE are linear pair,           Definition of linear pair

∠DCB is supplementary to ∠BCE,         Linear pair postulate

∠BCE and ∠ECA are linear pair,           Definition of linear pair

∠BCE is supplementary to ∠ECA,         Linear pair postulate

∠DCB ≅ ∠ECA,                                      Congruent to supplementary theorem  

Therefore, the missing reason in step 5 is the linear pair postulate.

Answer:

itS A

Step-by-step explanation:

Answer:

(a) Shown below.

(b) Shown below.

(c) The probability that a person does not learn Spanish is 0.18.

(d) The probability that method B was used given that a student learned the Spanish successfully is 0.83.

Step-by-step explanation:

(a)

Consider the provided data.

[tex]P(A)=0.20\\P(B)=0.80\\P(L|A)=0.70\\P(L|B)=0.85[/tex]

Then the probability of not learning Spanish using the respective methods are:

[tex]P(L'|A)=1-P(L|A)=1-0.70=0.30\\\\P(L'|B)=1-P(L|B)=1-0.70=0.15[/tex]

(b)

The Probability Tree representing each of the probabilities mentioned above is attached below.

(c)

Compute the probability that a person does not learn Spanish as follows:

[tex]P(L')=P(L'|A)P(A)+P(L'|B)P(B)[/tex]

         [tex]=(0.30\times 0.20)+(0.15\times 0.80)\\\\=0.06+0.12\\\\=0.18[/tex]

Thus, the probability that a person does not learn Spanish is 0.18.

(d)

Compute the probability that method B was used given that a student learned the Spanish successfully as follows:

[tex]P(B|L)=\frac{P(L|B)P(B)}{P(L|A)P(A)+P(L|B)P(B)}[/tex]

            [tex]=\frac{(0.85\times 0.80)}{(0.70\times 0.20)+(0.85\times 0.80)}\\\\=\frac{0.68}{0.14+0.68}\\\\=0.82927\\\\\approx 0.83[/tex]

Thus, the probability that method B was used given that a student learned the Spanish successfully is 0.83.

Answer:

35

Step-by-step explanation:

f(x)=5x^3-2x^2+3

f(2)=5x2^3-2x2^2+3

=5x8-2x4+3

=40-8+3

=40-5

=35

Answer:

35

Step-by-step explanation:

F(x) = 5x^3 -2x^2 + 3

Let x=2

F(2) = 5(2)^3 -2(2)^2 + 3

       = 5*8 -2(4) +3

       = 40 -8+3

       = 32+3

      = 35

Answer:

63m

Step-by-step explanation:

Answer:

1/2 or 0.5

Step-by-step explanation:

Saying that there is a 50-50 chance of an event happening is equivalent to saying there is a 1 in 2 chance. Therefore, expressing that degree of likelihood as a value between 0 and 1:

[tex]\frac{1}{2}=0.50[/tex]

There is a 1/2 or 0.5 chance that a randomly selected adult has pierced ears.

Answer:

1/2 or 0.5

Step-by-step explanation:

50-50 chance between 0-1 means half of 0-1 which is 1/2 or 0.5

1/2 or 0.5!

Answer:

The history instructor has made a computational error.

Step-by-step explanation:

We have that the data represents the linear correlation coefficient and notes it is 1.15

The linear correlation coefficient value which is 1.15 does tell the instructor that the history instructor has made a computational error due to the linear correlation coefficient value falls in the range -1 to +1.

Therefore, the history instructor has made a computational error.

Answer:

992

Step-by-step explanation:

You must convert the meter the kilometer by miltiplying by 1000

and when you do it you must multiply 0.992 by 1000 since it is a fraction .

or you can work it this way :

Answer:

Step-by-step explanation:

hello,

how many students ? 14 + 2 + 5 +3 = 24

how many students who had C and S ? 14 + 2 + 5 = 21

so P(C∪S)=21/24=(7*3)/(8*3)=7/8

hope this helps

Answer:

$261,500

Step-by-step explanation:

What amount should Nash report as its December 31 inventory?

Item                                                             Amount

Goods on hand as per physical count    $208,000

(+) Goods purchased from Swifty             $30,000

Corporation FOB shipping point    

(+) Goods sold to Marigold Corp               $23,500

FOB destination (at cost value)

Ending inventory                                        $261,500

Notes:

1) In case of FOB shipping point, the ownership of goods is transferred to the buyer when the goods are shipped and hence in the case of purchases from Swifty corporation, the goods should be included in the inventory of Nash's Trading Post as the goods are shipped and are in transit.

2) In case of FOB destination, the ownership of goods is transferred to the buyer when the goods reaches to the buyer, hence in the case of sales made to Marigold Corp, the goods are still in transit and the ownership is not transferred to Marigold Corp, hence Nash's Trading Post should included that goods in its inventory.

Answer:

[tex](fof^{-1})(x)=x[/tex]

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ [tex]-\frac{8}{6}[/tex]]

Another function is the inverse of f(x),

[tex]f^{-1}(x)=-\frac{\sqrt{x}+8}{6}[/tex]

Now composite function of these functions will be,

[tex](fof^{-1})(x)=f[f^{-1}(x)][/tex]

                  = [tex][-6(\frac{\sqrt{x}+8}{6})-8]^{2}[/tex]

                  = [tex][-\sqrt{x}+8-8]^2[/tex]

                  = [tex](-\sqrt{x})^2[/tex]

                  = x

Therefore, [tex](fof^{-1})(x)=x[/tex]

Answer:

Step-by-step explanation:

hello,

for [tex]ax^2+bx+c=0[/tex]

[tex]\Delta = b^2-4ac[/tex]

so here

[tex]\Delta = b^2-4*(-4)*(-11)=b^2-176[/tex]

to have two complex solutions we need [tex]\Delta < 0\\[/tex]

so [tex]b^2<176[/tex]

[tex]<=> b < \sqrt{176}=13.266...[/tex]

for instance we can take b = 0

hope this helps

Answer:

The correct answer is 12.

Step-by-step explanation:

i got it correct on my test, thanks to comment on the question above.

Answer:

a) Probability that haul time will be at least 10 min = P(X ≥ 10) ≈ P(X > 10) = 0.0455

b) Probability that haul time be exceed 15 min = P(X > 15) = 0.000

c) Probability that haul time will be between 8 and 10 min = P(8 < X < 10) = 0.6460

d) The value of c is such that 98% of all haul times are in the interval from (8.46 - c) to (8.46 + c)

c = 2.12

e) If four haul times are independently selected, the probability that at least one of them exceeds 10 min = 0.1700

Step-by-step explanation:

This is a normal distribution problem with

Mean = μ = 8.46 min

Standard deviation = σ = 0.913 min

a) Probability that haul time will be at least 10 min = P(X ≥ 10)

We first normalize/standardize 10 minutes

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (10 - 8.46)/0.913 = 1.69

To determine the required probability

P(X ≥ 10) = P(z ≥ 1.69)

We'll use data from the normal distribution table for these probabilities

P(X ≥ 10) = P(z ≥ 1.69) = 1 - (z < 1.69)

= 1 - 0.95449 = 0.04551

The probability that the haul time will exceed 10 min is approximately the same as the probability that the haul time will be at least 10 mins = 0.0455

b) Probability that haul time will exceed 15 min = P(X > 15)

We first normalize 15 minutes.

z = (x - μ)/σ = (15 - 8.46)/0.913 = 7.16

To determine the required probability

P(X > 15) = P(z > 7.16)

We'll use data from the normal distribution table for these probabilities

P(X > 15) = P(z > 7.16) = 1 - (z ≤ 7.16)

= 1 - 1.000 = 0.000

c) Probability that haul time will be between 8 and 10 min = P(8 < X < 10)

We normalize or standardize 8 and 10 minutes

For 8 minutes

z = (x - μ)/σ = (8 - 8.46)/0.913 = -0.50

For 10 minutes

z = (x - μ)/σ = (10 - 8.46)/0.913 = 1.69

The required probability

P(8 < X < 10) = P(-0.50 < z < 1.69)

We'll use data from the normal distribution table for these probabilities

P(8 < X < 10) = P(-0.50 < z < 1.69)

= P(z < 1.69) - P(z < -0.50)

= 0.95449 - 0.30854

= 0.64595 = 0.6460 to 4 d.p.

d) What value c is such that 98% of all haul times are in the interval from (8.46 - c) to (8.46 + c)?

98% of the haul times in the middle of the distribution will have a lower limit greater than only the bottom 1% of the distribution and the upper limit will be lesser than the top 1% of the distribution but greater than 99% of fhe distribution.

Let the lower limit be x'

Let the upper limit be x"

P(x' < X < x") = 0.98

P(X < x') = 0.01

P(X < x") = 0.99

Let the corresponding z-scores for the lower and upper limit be z' and z"

P(X < x') = P(z < z') = 0.01

P(X < x") = P(z < z") = 0.99

Using the normal distribution tables

z' = -2.326

z" = 2.326

z' = (x' - μ)/σ

-2.326 = (x' - 8.46)/0.913

x' = (-2.326×0.913) + 8.46 = -2.123638 + 8.46 = 6.336362 = 6.34

z" = (x" - μ)/σ

2.326 = (x" - 8.46)/0.913

x" = (2.326×0.913) + 8.46 = 2.123638 + 8.46 = 10.583638 = 10.58

Therefore, P(6.34 < X < 10.58) = 98%

8.46 - c = 6.34

8.46 + c = 10.58

c = 2.12

e) If four haul times are independently selected, what is the probability that at least one of them exceeds 10 min?

This is a binomial distribution problem because:

- A binomial experiment is one in which the probability of success doesn't change with every run or number of trials. (4 haul times are independently selected)

- It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (Only 4 haul times are selected)

- The outcome of each trial/run of a binomial experiment is independent of one another. (The probability that each haul time exceeds 10 minutes = 0.0455)

Probability that at least one of them exceeds 10 mins = P(X ≥ 1)

= P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 1 - P(X = 0)

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 4 haul times are independently selected

x = Number of successes required = 0

p = probability of success = probability that each haul time exceeds 10 minutes = 0.0455

q = probability of failure = probability that each haul time does NOT exceeds 10 minutes = 1 - p = 1 - 0.0455 = 0.9545

P(X = 0) = ⁴C₀ (0.0455)⁰ (0.9545)⁴⁻⁰ = 0.83004900044

P(X ≥ 1) = 1 - P(X = 0)

= 1 - 0.83004900044 = 0.16995099956 = 0.1700

Hope this Helps!!!

Answer:

2

Step-by-step explanation:

-(1-√2) -(2-√3) + 1/√3 + 2+1/2+√5-(√5-√6)-(√6-√7)+ 1/√7+2√2+1/2√2+3

-1+√2-√2+√3-(√3-2)-(2-√5)-√5+√6-√6+√7-(√7-2√2)-(2√2-3)

-1+√2-√2+√3-√3+2-2+√5-√5+√6-√6+√7-√7+2√2-2√2+3

2

Answer:

(x+6)(x^2+8)

D

Step-by-step explanation:

x^3 + 6x^2 + 8x + 48=

x2(x+6)+8(x+6)= take x+6 common factor

(x+6)(x^2+8)