What is the LARGEST number of real zeros a polynomial with degree n can have?

Answer:

When two events X and Y are independent,

Then, P(X ∩ Y) = P(X) × P(Y)

We know that,

[tex]P(\frac{X}{Y})=\frac{P(X\cap Y)}{P(Y)}\text{ and }P(\frac{Y}{X})=\frac{P(X\cap Y)}{P(X)}[/tex]

Thus, by substituting the value of P(X ∩ Y),

[tex]P(\frac{X}{Y})=P(X)\text{ and }P(\frac{Y}{X})=P(Y)[/tex]

Which is the required condition for independent events.

In first option,

P(A)=0.3, P(B)=0.5, P(A|B)=0.15

[tex]\implies P(\frac{A}{B})\neq P(A)[/tex]

⇒ A and B are not independent events

In second option,

P(A)=0.2, P(B)=0.4, P(A|B)=0.2

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

⇒ A and B are independent events.

In third option,

P(A)=0.6, P(B)=0.2, P(A|B)=0.3

[tex]\implies P(\frac{A}{B})\neq P(A)[/tex]

⇒ A and B are not independent events

First Part: Not independent

Second Part: Independent

Third Part: Not independent

Two events A and B are independent if:

[tex]P(A|B)=P(A|B') \\Or,P(B|A)=P(B|A')[/tex]

Given,

[tex]P(A)=0.3, P(B)=0.5, P(A|B)=0.15[/tex]

[tex]P(A)=0.2, P(B)=0.4, P(A|B)=0.2[/tex]

[tex]P(A)=0.6, P(B)=0.2, P(A|B)=0.3[/tex]

[tex]P(A\cap B)=P(A|B)P(B)[/tex]

Then by substituting we get,

[tex]P(A|B)=P(A)[/tex] and [tex]P(B|A)=P(B)[/tex]

Computation of First probability:

So, if the probability is independent it will follow the above conditions.

[tex]P(A|B)=0.15\\P(A)=0.3\\0.3\neq 0.15\\ P(A|B)\neq P(A)[/tex]

So, it is not independent

Computation of second probability:

So, if the probability is independent it will follow the above conditions.[tex]P(A|B)=0.2\\P(A)=0.2\\0.2=0.2\\ P(A|B)= P(A)[/tex]

So, it is independent

Computation of second probability:

So, if the probability is independent it will follow the above conditions.

[tex]P(A|B)=0.3\\P(A)=0.6\\0.3\neq 0.6\\ P(A|B)\neq P(A)[/tex]

So, it is not independent.

Learn More: https://brainly.com/question/11348505

Answer: popcorn = $5.75 per bag

Step-by-step explanation:  

Set up the equation for each person.

Let x represent the cost of one drink and y represent the cost of one bag of popcorn.

           drinks    popcorn       Cost                     EQUATION

Naomi:      9            8            $111.25                9x + 8y = 111.25

Sofia:         3            2           $33.25                 3x + 2y = 33.25

Next, solve the system:

9x + 8y = 111.25   →    1(9x + 8y = 111.25)   →    9x + 8y = 111.25

3x + 2y = 33.25   →  -3(3x + 2y = 33.25)   → -9x  - 6y = -99.75

                                                                                2y =  11.50

                                                                                  y =  5.75

Answer:

System of equations :

$111.25=$9x+$8y

$33.25=$3x+$2y

The cost of 1 drink = $x = $7.25

The cost of 1 popcorn bag = $y = $5.75

Step-by-step explanation:

Given :  

Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.

Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

To Find : A system of equations that can be used to find the price of one drink and the price of one bag of popcorn.

Solution :

Let cost of 1 drink = $x

⇒ cost of 9 drinks = $9x

⇒ cost of 3 drinks = $3x

Let cost of 1 popcorn bag = $y

⇒Cost of 8 popcorn bags = $8y

⇒Cost of 2 popcorn bags = $2y

Since Naomi spends a total of $111.25 on 9 drinks and 8 bags of popcorn.

So, equation will be : $111.25=$9x+$8y  --(A)

Since, Sofia spends a total of $33.25 on 3 drinks and 2 bags of popcorn.

So, equation will be :  $33.25=$3x+$2y--(B)

SOLVING A and B by using substitution method

finding value of x from equation B :

[tex]x=\frac{33.25-2y}{3}[/tex]

Putting this value in Equation (A)

⇒[tex]111.25=9(\frac{33.25-2y}{3})+8y[/tex]

⇒[tex]111.25=99.75-6y+8y[/tex]

⇒[tex]111.25=99.75+2y[/tex]

⇒[tex]y = 5.75[/tex]

Thus, cost of 1 popcorn bag =y = $5.75

Now put this value of y in equation A to get value of x

⇒$111.25=$9x+$8(5.75)

⇒$111.25-$46 = 9x

⇒$65.25 = 9x

⇒65.25/9 = x

⇒$7.25 = x

Thus, The cost of 1 drink = $x = $7.25

Answer:

30 girls

Step-by-step explanation:

10 x 2= 20

15x2=30

For every 10 boys there are 15 girls. since 20 is just 10 multiplied by 2 you can multiply 15 by 2

Answer:

your number is n= -3

Step-by-step explanation:

Answer:

n=-3

Step-by-step explanation:

4n-2n=-6

2n=-6

2 x n / 2 = 6 / 2 then simplify to get the answer! Hope this is Helpful! ;3

[tex]\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&7020\\ P=\textit{original amount deposited}\dotfill & \$4500\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill \end{cases}[/tex]

[tex]\bf 7020\geqslant 4500(1+0.03t)\implies \cfrac{7020}{4500}\geqslant 1+0.03t\implies \cfrac{39}{25}\geqslant 1+0.03t \\\\\\ \cfrac{39}{25}-1\geqslant 0.03t\implies \cfrac{14}{25}\geqslant 0.03t\implies \cfrac{~~\frac{14}{25}~~}{0.03}\geqslant t\implies \cfrac{56}{3}\geqslant t \\\\\\ 18\frac{2}{3}\geqslant t\impliedby \textit{18 years and 8 months}~\hfill \boxed{0 \leqslant t \leqslant 18\frac{2}{3}} \\\\\\ ~\hspace{34em}[/tex]

check the picture below.

bearing in mind that "t" cannot be less than 0.

Answer:

C

5(10)+10=60

-2(-5)+7=17

Step-by-step explanation:

Answer:

35[tex]\pi[/tex]

Answer:

C = 35 * pi

Step-by-step explanation:

The circumference is pi * d

The new diameter is 5 cm longer than the given one.

d = 30 + 5

d = 35

C = 35 * pi

Answer: Your answer will be 1,416

Step-by-step explanation: First you see how many day March and February had March had 31 days and 31 days= 744 hours and February has 28 days and 28 days= 672 hours so know I add the two numbers 744 + 672 = 1,416.

Answer:

You should multiply with the days in March which is 744 hours. And then you have to multiply with the days in February witch is 696 and then you have to subtract them.

Step-by-step explanation:

have a nice day.

Answer:

7.81

Step-by-step explanation:

Given points (-2,-2)  and (3, 4)

To find distance between points we apply distance formula

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

(x1,y1) is (-2,-2)  and (x2,y2) is (3,4)

Plug in the values in the formula

[tex]D = \sqrt{(3-(-2))^2+(4-(-2))^2}[/tex]

[tex]D = \sqrt{(5)^2+(6)^2}[/tex]

[tex]D = \sqrt{25+36}[/tex]

[tex]D = \sqrt{61}[/tex]

D= 7.810249676

Round to nearest hundredth

So distance = 7.81

Since we know that there are exactly 180 degrees in any triangle, and if each angle is equal to 45 degrees, we must add 45 to 45 and then subtract the result from 180 to find the 3rd angle. Since 45+45=90,we subtract 180-90 and get 90 degrees or a right angle.

The measure of the third angle is 90° a right angle isosceles triangle.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles in a triangle is 180°.'

Given, a triangle with a measure of its two angles is 45° and 45°.

∴ The measure of the third angle is 180° - (45 + 45)°.

= 180° - 90°.

= 90°.

It is an isosceles right-angle triangle.

learn more about triangles here :

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#SPJ2

Answer:

Take it slowly

Step-by-step explanation:

[tex]\bf 5(x-5)^2-9=6\implies 5(x-5)^2=15\implies (x-5)^2=\cfrac{15}{5}\implies (x-5)^2=3 \\\\\\ \sqrt{(x-5)^2}=\sqrt{3}\implies x-5=\sqrt{3}\implies x=\sqrt{3}+5[/tex]

Answer:

             = 1092 people/ sq mile  

Step-by-step explanation:

Population density is the number of people per unit of area.

We know the population is 1627260

The are is 1490 mi ^2

Population density = 1627260/1490

                                 =1092.120805  people / sq mile

Round to the nearest whole number

                                  = 1092 people/ sq mile  

Answer:

70

Step-by-step explanation:

Range is the difference between the lowest and the hist number

Range=max-min

120-50=70

since 120 is the highest number and 50 is the lowest you subtract and get 70

Hope this helps!

I got 83.48 so i think it's B 85%

Answer:

1/12

Step-by-step explanation:

6 x 2 = 12

6 = the original amount of slices

2 = it was cut in half so multiply by 2

each slice now represents 1/12

Answer:

Each slice represents 1/12th of the total pizza.

Step-by-step explanation:

1 = 1/6 = 1/12

Put the vales of x and y to the expression:

[tex]x=-1;\ y=3\\\\\dfrac{5x^{-6}y^{-2}}{y}=\dfrac{5(-1)^{-6}(3)^{-2}}{3}=\dfrac{5(-1)^6\left(\dfrac{1}{3}\right)^2}{3}=\dfrac{5(1)\left(\dfrac{1}{9}\right)}{3}=\dfrac{\dfrac{5}{9}}{3}\\\\=\dfrac{5}{9}\cdot\dfrac{1}{3}=\boxed{\dfrac{5}{27}}[/tex]

Answer:D)66

Step-by-step explanation:

55 /x = 5/ 6

Step 1: Cross-multiply.

55 /x = 5/ 6

(55)*(6)=5*x

330=5x

Step 2: Flip the equation.

5x=330

Step 3: Divide both sides by 5.

5x /5 = 330 /5

x=66

Answer:

d

Step-by-step explanation:

Answer:

[tex]a_{52}[/tex] = - 394

Step-by-step explanation:

these are the terms of an arithmetic sequence with nth term

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

where d is the common difference and [tex]a_{1}[/tex] the first term

d = - 18 - (- 10) = - 10 - (- 2) = - 2 - 6 = - 8 and [tex]a_{1}[/tex] = 14, hence

[tex]a_{52}[/tex] = 14 + (51 × - 8) = 14 - 408 = - 394

Answer:

(x-1) x-12

Step-by-step explanation:

Step 1 :  Multiply first term of the first bracket to the first term of the other bracket

Step 2 :  Then multiply the first term of the first bracket to the last term of the second bracket.

Step 3 :  Now come to the second term of first bracket, multiply second term with first term of second bracket.

Step 4 :  Finally multiply last term of first bracket with the last term of the second bracket.

Step 5 :  Adding all the answers got from the steps, we get the final answer.

Final answer:

The FOIL method is an algebraic technique for multiplying two binomials, represented as (First, Outer, Inner, Last). For the expression (X+3)(x-4), we apply this method to get x^2 - x - 12 after combining like terms.

Explanation:

The FOIL method is a technique used in algebra to multiply two binomials. The acronym FOIL stands for First, Outer, Inner, Last and refers to the order in which you multiply the terms in the binomials. Applying the FOIL method to the expression (X+3)(x-4), we multiply the First terms (x × x), the Outer terms (x × -4), the Inner terms (3 × x), and the Last terms (3 × -4), then sum them all.

Step-by-step, this looks like:

First: x × x = x^2

Outer: x × (-4) = -4x

Inner: 3 × x = 3x

Last: 3 × (-4) = -12

Now, combine these results to get the final expression:

x^2 - 4x + 3x - 12

Combining like terms, we have:

x^2 - x - 12

Answer:n^2/(n+1)

Step-by-step explanation:

n=1

1^2/(1+1) = 1/2

n=2

2^2/(2+1) = 4/3

n=3

3^2/(3+1) = 9/4

Answer:

n^2/(n + 1)

Step-by-step explanation:

The numerators are the squares of the sequence numbers 1^1  2^2  3^2....

The denominators are the  sequence numbers + 1, so the nth term is

n^2/(n + 1).

The Percentage of Sally's Team Wins :

[tex]\bf{\implies (\frac{Number\;of\;Games\;won\;by\;the\;Team}{Total\;Number\;of\;Games\;the\;Team\;Played}) \times 100}[/tex]

Given : Total Number of Games the Team Played = 25

Given : Number of Games won by the Team = 17

[tex]\bf{The\;Percentage\;of\;Team\;Wins = (\frac{17}{25}) \times 100}[/tex]

⇒ The Percentage of Sally's Team Wins = (17 × 4) = 68%

Sally's soccer team played 25 games and the team won 17 games. What percent of games did the team win?

The fraction [tex]\frac{17}{25}[/tex] represents the number of games that Sally's soccer team won out of all the games the team played.

To find what percent of games the team won, we can turn the fraction [tex]\frac{17}{25}[/tex] into a percent.

17 ÷ 25 = 0.68

0.68 × 100 = 68%

Therefore, Sally's soccer team won 68% of the games they played.

Answer:

A. 33/56

Step-by-step explanation:

Make them have the same denominator of 56

so you get for the first one 49/56

the second one will be 16/56

subtract both and you get your answer of 33/56

Answer: A. 33/56

Step-by-step explanation:

To get the number of pages left, all we need to do is to subtract 2/7 from 7/8

number of pages left = 7/8 - 2/7

=49 - 16 / 56

= 33/56

Answer:

152/7=21.714 hrs

152/8=19

It took the whale between 19 and 21.7 hours to swim 152 kilometers

Step-by-step explanation:

Answer:

C x-3

Step-by-step explanation:

3 less than x - 49

Is means =

less than means -  (reversing the order)

x-3 = 49

Answer: C) x - 3 = 49

Step-by-step explanation: X represents the number that we are subtracting things from. 3 is how much (the number that we are) subtracting. 49 is the difference/answer. The problem is pretty much asking us to subtract 3 from x and get 49 as the answer. So, if you wrote that mathematically, the answer would be x - 3 = 49.

Hope that helped, fam!

-Une :D

Answer:

We will need 5 1/3 lbs  of hamburger

Step-by-step explanation:

We can use ratio's to solve this problem.  We will put breadcrumbs on top and hamburger on bottom.

1/4 c         1 1/3 c

--------- = -----------

1 lb             x lbs

Using cross products

1/4 *x = 1 * 1 1/3

1/4x = 1 1/3

Multiply each side by 4

4 * 1/4 x = 4 * (1 1/3)

x = 4 * 1 1/3

We need to convert 1 1/3 to an improper fraction

1 1/3 = (3*1+1)/3 = 4/3

x = 4 * 4/3

x = 16/3

Now we need to convert it back to a mixed number

3 goes into 16 5 times with 1 left over

x = 5 1/3 lbs

To find the better buy, calculate the unit price of each item by dividing the cost by the weight, and compare them. The first item at $1.50 for 5 oz has a lower unit price ($0.30 per oz) than the second item at $1.20 for 3 oz ($0.40 per oz), so it is the better buy.

To determine which is the better buy between two products, you need to calculate the unit price for each and then compare them.

The unit price is the cost per unit of weight or volume.

Final answer:

To find the better buy between $1.50 for 5 oz and $1.20 for 3 oz, calculate the cost per ounce for each and compare. The first option is cheaper at $0.30 per ounce compared to the second option at $0.40 per ounce.

Explanation:

To determine which is the better buy between $1.50 for 5 oz and $1.20 for 3 oz, we need to calculate the cost per ounce for each option.

Step-by-step Comparison

Therefore, the better buy is the first option, $1.50 for 5 oz, since it has a lower cost per ounce.

Answer:

14.99

Step-by-step explanation:

20.02=50-2t

20.02-50= -2t

-29.98= -2t