A bag has 2 red marbles, 1 blue marble and 4 gold marbles. What is the probability of
drawing two gold marbles, if the first marble is replaced after it is drawn?
A. 2/7
B. 16/49
C. 4/7
D. 7/13

The answer for the given polynomial by synthetic division is 3x+16+(30/(x-3)).

Step-by-step explanation:

The given polynomial is (3x^2 +7x -18) divided by (x - 3)

Take (x-3)=0, then x=3

    3  |  3        7       -18  

                    9        48

           3       16       30

step 1: write the coefficients of x^2, x and constant in first row. The divisor 3 is written separately on outside.

step 2: Write down the coefficient of x^2= 3 in the answer row as it is without any change.

step 3: Multiply each number in the answer row with the divisor and fill the answers in the second row.

step 4: The final step is to add the first row and second row. After addition, the answers are written in answer row and the last number in the answer row is the Remainder.

step 5: The remainder is written by dividing it with the divisor (x-3). The answer in the descending powers of x is 3x + 16 + (30/(x-3)).

The result of the division (3x^2 + 7x - 18) by (x - 3) using synthetic division is obtained as (3x + 16 + 30/(x - 3)).

To perform the synthetic division, the divisor (x - 3) is represented by its root '3'. Write down the coefficients from the dividend polynomial (3, 7, -18) at the top of your division setup. Write '3' to the left, leave some space, and then write down '3', '7', -18.

Then, perform the synthetic division: step one, bring the first coefficient (3) straight down. Step two, multiply this number by the root of the divisor (3), which is also 3. Write this product (9) underneath the next coefficient (7). Add these two numbers (7 + 9) to get 16. Write this number under the line. Now, repeat the previous step by multiplying 16 by the root, 3, to get 48. Write this under -18, add to get 30.

The quotient of the division is the polynomials received from the synthetic division which is 3x + 16 with a remainder of 30. So, the result of division (3x^2 + 7x - 18) by (x - 3) is (3x + 16 + 30/(x - 3)).

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Answer:

Subtracting polynomials is simply subtracting the like terms

(x-2)-(6x-9)

First you want to subtract your x from 6x

x-6x= -5x

Than you would subtract -2 and -9

-2- -9=7

-2+9=7

Your final answer would be

-5x+7

Hope this helps ;)

Step-by-step explanation:

ANSWER: 182 inches

STEP-BY-STEP EXPLANATION:

Since, it is an isosceles trapezoid, then area of an isosceles triangle is given by: [tex]\frac{1 (a+b)}{2}[/tex] × h

where a and b are the two parallel sides of the triangle and h is the height of an isosceles triangle.

Now, a= 12 inches and b= 2+2+12=16 inches and h=13 inches.

[tex]\frac{1 (12+16)}{2}[/tex] × 13 = 182 inches

Answer:

f^-1 (x)=1/5x-4/5

Step-by-step explanation:

y=5x+4

x=5y+4

5y=x-4

y=1/5x-4/5

Answer:

I WOULD SAY THAT THE ANSWER IS C

Step-by-step explanation:

I GOT IT FROM A

                          P

                          E

                          X

Answer:

Step-by-step explanation:

x^2 - 6x - 40 = 0.....get the -40 to the other side

x^2 - 6x = 40....now take half of ur x term (6)....so its 3...then square it (3^2 = 9)...now add 9 to both sides

x^2 - 6x + 9 = 40 + 9

(x - 3)(x - 3) = 49

(x - 3)^2 = 49...take sqrt of both sides, eliminating the ^2

x - 3 = sqrt 49

x = 3 (+ - ) 7

x = 3 + 7 = 10 or x = 3 - 7 = -4

so x = 10 or x = -4

Answer:

A) Sin A  + Sin B  =  1.2 Sin C  

D) Sin C =  2.5 Sin A  = 1.25 Sin B

E)  Sin A  + Sin C  =  1.75 B

Step-by-step explanation:

Here, in the given triangle ABC

Base AC = 16 units, AB  = 2 units, and BC  = 8 units

Now, by Trigonometric Functions:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} =\frac{Sin C}{20}[/tex]

Comparing first two terms, we get:

[tex]\frac{Sin A}{8} = \frac{Sin B}{16} \\\implies 2Sin A = Sin B[/tex]                 ........... (1)

Also,

[tex]\frac{Sin B}{16} = \frac{Sin C}{20} \\\implies Sin C = 1.25 Sin B[/tex]   ....... (2)

Comparing first and last  terms, we get:

[tex]\frac{Sin C}{20} = \frac{Sin A}{8} \\\implies SinC = 2.5 Sin A[/tex]      ..........  (D)

Also, Sin A  = 0.5 Sin B

So, the given statement Sin A  = 2 Sin B is FALSE

⇒ 2.5 Sin A  = 1.25 Sin B   .......... (D)

Also,  Sin B  = 2 Sin A

⇒ Sin A  + Sin B =  Sin A + 2 Sin A =  3 Sin A

Also, Sin A  = 0.4 Sin C

⇒3 Sin A = 3 x (0.4) Sin C  = 1.2 Sin C  ..

⇒Sin A  + Sin B  =  1.2 Sin C   ........ (A)

B)   Sin A  - Sin B  = 0.4 Sin C - 2 Sin A  =  0.4 Sin C - 2 (0.4 Sin C)  

= 0.4 Sin C  - 0.8 Sin C  = -0.4 Sin C

⇒Sin A  - Sin B  =  -0.4 Sin C   ........ (B)

So, the given statement is FALSE

E)   Sin A  + Sin C =  0.5 Sin B + 1.25 B =  1.75 B

⇒ Sin A  + Sin C  =  1.75 B  ....(E)

At least 2,000 students are expected to pursue a Social Sciences degree at Arizona State University. The most popular degree is Business Marketing, and about 6,000 students are estimated to enroll in the top two most popular programs (Business Marketing and Social Sciences) in the fall semester.

Based on the information provided about

Arizona State University's

most popular majors and their respective percentages, you can determine the minimum number of students expected to be working towards a Social Sciences degree. The

Social Sciences

program makes up 10% of the student body. Therefore, if the enrollment is expected to reach at least 20,000 students, you can expect that at least 2,000 students (10% of 20,000) will be working towards a

Social Sciences

degree. As for the most popular degree, Business Marketing is listed as comprising 20% of the student body, making it the most popular degree. The two most popular programs, Business Marketing and Social Sciences, make up 30% of the student body. So the university might expect that at least 6,000 students (30% of 20,000) will enroll in one of the two most popular programs in the fall semester.

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Answer:

12

Step-by-step explanation:

3[y+2]

2+2= 4

3 multiplied by 4 is 12

Answer: 12

Step-by-step explanation: Since y = +2, we simply plug a +2 in for y in the expression. So we have 3(2 + 2).

Following your order of operations, you should simplify what's inside the parentheses first so 2 + 2 simplifies to 4.

Bring down your 3 and you have 3(4) which equals 12.

Answer for Question 1 is option 2  

Answer for Question 2 is option 3  

Answer for Question 3 is option 3  

Step-by-step explanation:  

For question 1 by plotting the two points we get the coordinates as (-2, 3) and (2, 1) where the x values are -2, 2 and the y values are 3, 1 respectively.  By substituting values of x in the formula given we get that equation 2 satisfies the values of y as in the graph.  

For question 2 the plotted line is split into two parts where one half is for values of x <2 and the other half is for values of x>2. By finding out the coordinates we get them as (2,-2), (1,-2.5) and (0,-3) for x<2 and by substituting the values of x in the formula we get option 3 as our answer.  

For question 3 we need to find the value of y when x=3 and the first condition is only for values greater than 3 so we take the second condition and substitute the value of x=3 and we get the value of y as 5 so the answer is option 3  

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Step-by-step explanation:

Let,

Weight of large box = x

Weight of small box = y

According to given statement;

4x+8y=197      Eqn 1

2x+3y=83       Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+3y=83)\\4x+6y=166\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+8y)-(4x+6y)=197-166\\4x+8y-4x-6y=31\\2y=31[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{31}{2}\\y=15.5[/tex]

Putting y=15.5 in Eqn 2

[tex]2x+3(15.5)=83\\2x+46.5=83 \\2x=83-46.5\\2x=36.5[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{36.5}{2}\\x=18.25[/tex]

A large box of fruit weighs 18.25 kilograms and a small box weighs 15.5 kilograms.

Keywords: linear equation, elimination method

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Answer:

Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Step-by-step explanation:

Given that the points are A(-3,13), B(15,7) and C(-3,11)​

To find the mid points :

To find midpoint of AB

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points A(-3,13),B(15,7) respectively

Midpoint of AB[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3+15}{2},\frac{13+7}{2})[/tex]

[tex]=(\frac{12}{2},\frac{20}{2})[/tex]

[tex]=(6,10)[/tex]

Midpoint of AB=(6,10)

To find midpoint of BC

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points B(15,7),C(-3,11) respectively

Midpoint of BC[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{15-3}{2},\frac{7+11}{2})[/tex]

[tex]=(\frac{12}{2},\frac{18}{2})[/tex]

[tex]=(6,9)[/tex]

Midpoint of BC=(6,9)

To find midpoint of CA

Let [tex](x_1,y_1) and (x_2,y_2)[/tex] be the points C(-3,11),A(-3,13),respectively

Midpoint of CA[tex]=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

[tex]=(\frac{-3-3}{2},\frac{11+13}{2})[/tex]

[tex]=(\frac{-6}{2},\frac{24}{2})[/tex]

[tex]=(-3,12)[/tex]

Midpoint of CA=(-3,12)

Therefore Midpoint of AB=(6,10) ,Midpoint of BC=(6,9) and Midpoint of CA=(-3,12)

Answer:

Emily decides marbles the ratio of marbles is 2 to 3 she adds 3 times more to that.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I have 2/3 of milk and I need 6/3 so my neighbor gave me 3

Answer: C

Step-by-step explanation:

to be a good graph the x axis and y axis need labeled

The graph could be misleading because it does not indicate if the free throws were made at home or away, it is missing the scale on the y-axis, and it doesn't specify if all team members are included.

The statement that best describes why this graph could be misleading is A. The graph does not indicate if the free throws were made at home or away. The graph may show higher or lower percentages for certain players based on the location of the game. For example, a player may have a higher free throw percentage when playing at home compared to playing away.

Additionally, statement C is also correct. The graph is missing the scale on the y-axis, which makes it unclear how much higher or lower the free throw percentages are for each player.

Lastly, statement D is another reason why the graph could be misleading. Without knowing if all the people on the team are included, the graph may not provide an accurate representation of the overall free throw percentages of the team.

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Answer:

it will always be 1

Step-by-step explanation:

lets make an equation

pick a number : x

add 2 : x+2

multiply by 3 : (x+2)*3

subtract 3 : (x+2)*3-3

divide by 3 : ((x+2)*3-3)/3

if you simplify, you will get 1

step by step simplification

(x+2)*3 = 3x+6

3x+6-3=3x+3

(3x+3)/3 = x+1

x+1-x=1

Final answer:

The algebraic equation for the given math trick is: (((((x + 2) * 3) - 3) / 3) - x).

Explanation:

To represent the math trick you described algebraically, we can use the variable x to represent the initial number you pick. Following the steps you provided, the algebraic equation would be: ((((x + 2) * 3) - 3) / 3) - x. Let's break down each step:

Answer:

Miguel traveled 0.2 mile per minute.

Step-by-step explanation:

3÷15=0.2

Speed can be interpreted from a graph's slope in a distance versus time plot. Comparing this to Molly's speed of 0.15 mile per minute, we could establish who is faster or slower. However, without the actual graph of Miguel's bicycling, we can't make a specific comparison.

This question relates to graph interpretation and the concept of speed. Here, we're trying to compare the cycling speed of Miguel and Molly. Molly's speed is given as 0.15 mile per minute. Without the graph available, we cannot definitively compare their speeds. But let's briefly explain what we'd look for.

If we had Miguel's graph, we'd specifically examine the slope of the graph. In a distance vs. time plot, speed is represented by the slope of the graph. Therefore, if the slope of Miguel's graph indicated a value higher than 0.15 mile per minute (steep slope), Miguel was going faster. Conversely, if it showed a lesser value (gentle slope), Miguel was going slower.

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Answer:

C

Step-by-step explanation:

Answer:  C ) No, Hugo forgot to multiply both sides of the first equation in step one.

Step-by-step explanation:

Answer:

4 11/20

Step-by-step explanation:

The length of road unpaved is 7 3/10 less 2 3/4 miles  The LCD of the fractions is 20 (both 10 and 4 divide evenly into 20).

Thus, the problem becomes 7 6/20 - 2 15/20.

We have to borrow 1 from that 7 because 15/20 is larger than 6/20.  This results in

6 26/20 - 2 15/20, or

4 11/20  

The total length of the main road in Belleville is [tex]7^{(3/10)}[/tex] miles. So far, [tex]2^{3/4}[/tex] miles have been repaved, leaving [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex] miles that have not been repaved.

1. The total length of the main road is given as [tex]7^{(3/10)}[/tex] miles. In mathematical notation, [tex]7^{(3/10)}[/tex] represents the cube root of 7, which is then raised to the power of 3. So, the total length of the road is the cube root of 7, and then that result is cubed.

2. The length of the repaved portion is given as [tex]2^{3/4}[/tex] miles. In mathematical notation, [tex]2^{3/4}[/tex] represents the fourth root of 2, which is then raised to the power of 3. So, the repaved length is the fourth root of 2, and then that result is cubed.

3. To find the remaining length that has not been repaved, we simply subtract the repaved length from the total length:

  Remaining length = [tex]7^{(3/10)}[/tex] - [tex]2^{3/4}[/tex]

Calculating the values, the total length is approximately 2.262 miles (rounded to three decimal places) and the repaved length is approximately 1.682 miles (rounded to three decimal places). Now, subtracting the repaved length from the total length, we get approximately 0.580 miles (rounded to three decimal places) as the length that has not been repaved.

Therefore, the remaining length that has not been repaved is approximately 0.580 miles (rounded to three decimal places).

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Answer:

option (2)

Step-by-step explanation:

Given the area (A) of a circle is

A = πr² ← r is the radius ( divide both sides by π )

[tex]\frac{A}{\pi }[/tex] = r² ( take the square root of both sides )

[tex]\sqrt{\frac{A}{\pi } }[/tex] = r → option (2)

Answer:

(negative infinity, 2)

Step-by-step explanation:

The two functions are given by f(x) = x - 3 and g(x) = - 0.5x

So, (f - g)(x) = x - 3 - ( - 0.5x) = 1.5x - 3

Then, for (f - g)(x) to be negative (1.5x - 3) < 0

⇒ 1.5x < 3

⇒ x < 2

Therefore, the interval will be (negative infinity, 2) for which the function (f - g)(x) will be negative. (Answer)

Answer:

negative infinity 2

Step-by-step explanation:

just did the test

Answer:

100 boxes

Step-by-step explanation:

Divide 1,198 with 12 because if there are 1,198 paperweights and each box holds 12 then how many boxes can hold these paperweights. Answer us 100 boxes

In a day, there are 24 hours. Then the number of hours in d days and 6 hours is 24d + 6.

Algebra is the study of mathematical symbols and the rule involves manipulating these mathematical symbols.

The number of hours in d days and 6 hours. Then the algebraic expression will be

We know that in a day, there are 24 hours.

Let the number of the days be d. Then the algebraic expression will be

→ 24 d + 6

Then the number of hours in d days and 6 hours is 24d + 6.

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Answer:

The square root of 49 is 7. 7*7=49

Hope this helps,

:)

Answer:

f(x) = x³ - 3x² - 10x

Step-by-step explanation:

Given that the zeros are x = - 2, x = 5 and x = 0 then the factors are

(x + 2), (x - 5) and (x - 0) = x

The polynomial is the product of it's factors, thus

f(x) = x(x + 2)(x - 5) ← expand factors using FOIL

     = x(x² - 3x - 10) ← distribute parenthesis by x

     = x³ - 3x² - 10x

Answer:

[tex]\large \boxed{\text{39 ft}}[/tex]

Step-by-step explanation:

Let x be the distance from the foot of the ladder to the base of the building.

We have a right triangle, so we can use Pythagoras' Theorem.

[tex]\begin{array}{rcl}80^{2} + x^{2}& = & 89^{2} \\6400+ x^{2} & = & 7921\\x^{2} & = & 1521\\x & = & \sqrt{1521}\\& = &\mathbf{39}\\\end{array}\\\text{The foot of the ladder will be $\large \boxed{\textbf{39 ft}}$ from the base of the building,}[/tex]

Answer: x-intercept(6,0) & y-intercept(0,3)

Step-by-step explanation: To find the x-intercept, subsitutue zero in for y and solve for x, and vice versa to solve for y.

----------------------

Now you know the answer as well as the formula. Hope this helps, have a BLESSED AND WONDERFUL DAY!

- Cutiepatutie ☺❀❤

Answer:

Step-by-step explanation:

Answer:

y = 5/2 , x= 7/2

Step-by-step explanation:

5x - 3y = 10…....(1)

3x + 3y = 3......(2)

solving by elimination, we subtract equation (2) from equation (1)

so, 2x = 7

dividing both sides by 2

x= 7/2

substitute x=7/2 for the value of y in equation (1)

5(7/2) - 3y = 10

multiply both sides by 2

35 - 6y = 20

rearranging

-6y = -15

dividing both sides by -6

y = 5/2

Answer:

Step-by-step explanation:

I need help

Answer:

28 girls

Step-by-step explanation:

Given girls : boys ===> 7 : 12

i.e.

fraction all children who are girls = 7 / (7 + 12) = 7 / 19

fraction all children who are boys = 12 / (7 + 12) = 12 / 19

given that there are 76 children

number of girls = fraction of all children who are girls x total number of children

= 7/19   x   76

= 28 girls