Which number does the blue dot represent on the number line?

a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.

b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.

Therefore,

g(x) = 4x(x² - 6) - 1(x² - 6).

g(x) = (4x - 1)(x² - 6).

g(x) = (4x - 1)(x + √6)(x - √6).

Hence, x = 1/4, ± √6.

So, The roots of the polynomial are 1/4 and ± √6.

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She expects to have $2710591.78 when she retires at age 65 with the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3 by the concept of compound interest.

Interest that is paid on the principal and interest at regular periods is known as compound interest. The interest is calculated for the new principal at regular intervals after the interest that has already accumulated has been combined with the existing principal amount. The initial principal plus the interest that has accrued thus far are added together to form the new principal.

Interest on the principal + periodic compound = compound interest.

According to the question the principal amount is 398100, the interest rate is 8%, time period is 24 and number of times interest applied is 3.

Here the interest is compounded every 4 months

So, the formula of compound interest is as follows:

A=p (1+ [tex]\frac{r}{n}[/tex]) ∧ (n× t)

Where P is the principal balance, r is the interest rate, n is the number of times interest is compounded per year and t is the number of years.

Here the interest is compounded every 4 months hence the value of n is 12/4 which is equal too 3.

Insert the values of p, n, t, r in above equation,

A=398100(1+[tex]\frac{8}{300}[/tex]) ∧ (3×24)

A=398100× (1.027) ∧ (72)

A=398100×6.809

A=2710591.78

She expects to have amount $2710591.78 when she retires at age 65.

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An equivalent fraction of 36/48 having denominator 6 could be 6/6 only.

A fraction represents a part of a number or any number of equal parts.

we are given a fraction as 36/48.

We can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.

We have to only multiply or divide, never add or subtract, to get an equivalent fraction. Only divide when the top and bottom stay as whole numbers.

In this case we have a clue which is 48,

6 x 8 = 48

Then we would want to take the 6 and times it by the denominator which is 6

So 6 x 6 = 36

An equivalent fraction of 36/48 is 6/6.

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The required number of new boys in a sports team is 62.

As mentioned in the question,  A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50

Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys

Thus, the required number of new boys in a sports team is 62.

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80% is her free throw shooting percentage.

Fractions are used to represent smaller pieces (or parts) of a whole. The parts might make up one thing, or more than one thing. Either way, altogether, they make up what's called a whole.

Given that, Jeremiah makes 4/5 of the free throw shots he attempts in basketball. Jeremiah likes to shoot free throws until he misses one. Let F be the number of shots it takes Jeremiah to miss his first free throw.

We can construct a fraction in which the numerator is how many shots she makes, and the denominator is how many shots she took overall.

We now have the following fraction:4/5

To convert this to a percentage, we want the denominator to be 20/20

= 4/5×20/20

= 80/100

= 0.8

Now multiply 0.8 with 100

= 0.8×100=80

Hence, 80% is her free throw shooting percentage.

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Step-by-step explanation:

this is a college question ? and you don't know how to do that ?

think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.

Focus !

g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.

g(3) = 4×3 - 5 = 12 - 5 = 7

that's all to it.

The list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces.

Given triangles are,

ΔABC and ΔNOP

And also given that they are similar triangles.

The pairs of the congruent angles are:

∠A≅∠N

∠B≅∠O

∠C≅∠P

Therefore, the list of pairs of triangles are ∠A≅∠N, ∠B≅∠O, ∠C≅∠P for the given similar triangles.

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The answer is option 3: approval ratings tended to fall as stock prices rose.

This means that when stock prices rose, the approval ratings of George Bush's presidency decreased. This can be interpreted as an indication that people were not satisfied with the performance of the stock market during the Bush presidency. This could be because the stock market was not performing as well as expected or because the people were not satisfied with the decisions made by the Bush presidency that impacted the stock market.

Whatever the reason, the negative correlation between the stock market performance and Bush's approval ratings shows that when stock prices rose, approval ratings tended to fall.

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The option that best describes the data is The data is band numerical

This kind of data just has one variable. Since there is only one variable that varies, univariate data analysis is the most straightforward type of analysis.

In this case the one variable is World History scores exam

Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.

Numerical data, also known as quantitative data, is gathered in number form and differs from all other sorts of number data because it can be calculated mathematically and statistically.

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Answer:

6 rows to 7 steal in each rows

Answer:

8/33

p(d'c')

not having a cat=12/18

not a dog =4/11

12/18×4/11=8/33

Ans=8/33

Answer:

h = 6

Step-by-step explanation:

h is the short leg for AD in ΔADC: AD = 12

h is the long leg for DB in ΔCDB: DB = 3

Hence:

12/h = h/3

3 * 12/h = 3 * h/3  ==> isolate h by multiplying 3 on both sides

36/h = h

h * 36/h = h*h  ==> multiply by h on both sides to remove fractions

36 = h^2

h = [tex]\sqrt{36}[/tex]

h = 6

The expression as a rounded decimal  is 1.23

From the question, we have the following parameters that can be used in our computation:

27/22

To start with, we evaluate the expression using a calculator

So, we have the following representation

27/22 = 1.22727272727

Next, we approximate to the nearest hundredth

So, we have the following representation

27/22 = 1.23

Hence, the approximated expression is 1.23

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The piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).

On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).

That line passes through (-1, 0) and (0, 1), then the slope is:

a = (1 - 0)/(0 -(-1)) = 1

And the y-intercept is y = 1, then the equation of the line is:

y = x + 1

The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)

The slope is:

a = (0 - 7)/(6 -5) = -7

Then the line is something like:

y = -7*x + b

To find b, we use the point (6, 0)

0 = -7*6 + b

7*6 = 42 = b

Then this line is:

y = -7x + 42

Concluding, the piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.

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The same cost of both of the plan of the gym will be in 5 visits. And plan B is better than Plan A as B is cheaper than A.

In mathematics, expression is the combining of variables with the application of operations and prescribed rules. It could take the shape of an equation, some numbers, etc.

We have,

plan A consists of :

Amount for monthly membership fee = $50

Cost per visit = $10

The expression of total fees would be:

50+10x,

where x is the number of times Jim visits the gym.

Plan B consists of :

Amount for monthly one time membership fee = $25

Cost per visit = 15

The expression of total fees would be:

25 + 15x,

where x is the number of times Jim visits the gym.

Here, x denotes the number of visits.

Let us suppose x = 1

Then, fees for plan A would be:

50 + 10 x1 = $60

Fees for plan B would be:

25 + 15 x1 = $40

To find the same cost in x number of visits:

We equate both the expressions.

50+10x = 25 + 15x

15x - 10x = 50 - 25

5x = 25

x = 5

That means, if Jim visits 5 times, the gym, then he would have the similar cost for both of the plans.

Hence, Plan B is better than Plan A as B is cheaper than A. The same cost of both of the gym will be in 5 visits.

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So the expected value of the remainder when M is divided by 64 is approximately 0.2080.

To find the expected value of the remainder when M is divided by 64, we can find the probability that M is congruent to each possible remainder modulo 64 and then sum these probabilities multiplied by the corresponding remainders.

For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then

P(0) = P(64) = P(128) = ... = 1/100

P(1) = P(65) = P(129) = ... = 1/100

P(63) = P(127) = P(191) = ... = 1/100

Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.

Therefore, the expected value of the remainder when M is divided by 64 is

E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6

= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6

= (0 + 1 + 2 + ... + 63) * P(0)^6

= 2080 * (1/100)^6

= 0.2080

So the expected value of the remainder when M is divided by 64 is approximately 0.2080.

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For a positive integer n, let P(n) denote the probability that a positive integer chosen from the set {1, 2, . . . , 100} is congruent to n modulo 64. Then

P(0) = P(64) = P(128) = ... = 1/100

P(1) = P(65) = P(129) = ... = 1/100

P(63) = P(127) = P(191) = ... = 1/100

Since the integers a, b, c, d, e, and f are chosen independently and uniformly at random from the set {1, 2, . . . , 100}, the probability that M is congruent to n modulo 64 is P(n)^6.

Therefore, the expected value of the remainder when M is divided by 64 is

E = 0 * P(0)^6 + 1 * P(1)^6 + 2 * P(2)^6 + ... + 63 * P(63)^6

= (0^6 + 1^6 + 2^6 + ... + 63^6) * P(0)^6

= (0 + 1 + 2 + ... + 63) * P(0)^6

= 2080 * (1/100)^6

= 0.2080

This sample a simple random sample. It v a random sample.

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Answer: n = 15

Step-by-step explanation:

9 + n - 6 = 18

3 + n = 18

n = 15

Rick's deposit in first 3 weeks is  $39  

1. Rick's deposit in the second week = 3  times($3)

                                                             = 3(3)

                                                             = 9

                                                             = [tex]3^{2}[/tex]

The exponential expression for Rick's 2nd week deposit = [tex]3^{2}[/tex]

Where,  Base  = 3

              Exponent = 2                                

2. Rick's deposit in 1st week = $3  

   Rick's deposit in 2nd week = 3 (3) = $9

   Rick's deposit in 3rd week =  3 (9) = $27  

   Rick's deposit in first 3 weeks = 3+9+27

                                                      = $39      

  Rick's deposit in all in the first 3 weeks is  $39  

3.   Rick's deposit for 15 weeks = [tex]3^{15}[/tex]

                                                    = $1,43,48,907.

We know, no. of weeks in a year = 52

Rick's deposit for 52 weeks ( 1 year ) = 52 times of 3

                                                             [tex]=3^{52}\\= 6.4610819e+24[/tex]

Since this is a huge number , Rick cannot keep up this savings plan for a year.

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The number from the expression is 22. 3

An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.

These expressions are also seen to be made up of mathematical or arithmetic operation, such as;

Some examples of algebraic expressions;

2x + 6

3x + 8

From the information given;

Let the number be x

Then'

3x - 17 = - 50

collect like terms

3x = 67

Make 'x' the subject

x = 22. 3

Hence, the value is 22. 3

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The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The principal amount, p = $5000,

The amount, A = $8300

The rate of interest, r = 7.5 %,

Calculate the time as shown below,

[tex]A = p(1 + r / 400)^{4n}[/tex]

8300 = 5000 (1 + 7.5 / 400)⁴ⁿ

8300 / 5000 = (1 + 0.01875)⁴ⁿ

1.66  = (1.0188)⁴ⁿ

1.66 = (1.077)ⁿ

(1.077)⁷ = (1.077)ⁿ

n = 7

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Answer:

h(x) = (x-2)^2

Step-by-step explanation:

The equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

What is equation?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation

3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Consider the given equation

5/6 x + 2/3 = -9

Subtract 2/3 from both sides,

5/6x + 2/3 - 2/3 = -9 - 2/3

5/6x = -29/3

[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]

The value of x is -11.6.

Hence, the equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

After solving above these equations we get the same value of x which is -11.6.

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Complete question:

Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9

6(5/6x + 2/3) = -9(6)

5 x + 4 = -54 5 x + 4 = -9

5 x = -13

5 x = negative 58

The dimensions are 12 meter by 18 meter .

perimeter of rectangle = 2(length + width)

length and width of the  Luis plot by L and W, respectively.

We know that the perimeter, is 60 meters. So we can write:

2L + 2W = 60

Simplifying this equation, we can divide both sides by 2:

L + W = 30

now , area of the plot is 216 square meters:

L x W = 216

use substitution to solve for one of the variables. Let's solve for L in the first equation:

L = 30 - W

We can substitute this expression for L into the second equation:

(30 - W) x W = 216

[tex]W^2 - 30W + 216 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2

Simplifying:

W = [30 ± 6] / 2

So  W = 18 or W = 12.

If W = 18, then L = 30 - 18 = 12.

If W = 12, then L = 30 - 12 = 18.

Therefore, the dimensions  are 18 meters by 12 meters or 12 meters by 18 meters.

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Answer:

4

Step-by-step explanation:

Based on the given conditions, formulate:

16/6 ÷ 2/3

Divide a fraction by multiplying its reciprocal:

16/6 × 3/2

(16 × 3) ÷ (6 × 2)

48/12 = 4

Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.

The value of x is 7/3 and the value of y is -11/3 for the given equations.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equations are 2x - 2y = 12 and -8x -y = -15. The value of x and y will be calculated as,

2x - 2y = 12

-8x - y = -15

Solve the above equation,

2x - 2(-8x + 15) = 12

2x + 16x - 30 = 12

18x = 42

x = 42 / 18

x = 7 / 3

The value of y is calculated as,

-8x - y = -15

y = ( -8 x 7 / 3 ) +15

y = (-56 + 45) /3

y = -11 / 3

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Kate and Miley sold 60 boxes of cookies in one hour.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b.

Given that,

Cookies sold by Kate in 45 minutes = 27 boxes.

Also,

Cookies sold by Miley in 30 minutes = 12 boxes.

To find the total boxes of cookies sold by girls in one hour,

Use ratio method,

Cookies sold by Kate in 3/4 hours = 27 boxes,

Cookies sold by Kate in 1 hour = 27 x (4/3) = 36

Cookies sold by Miley in 1/2 hours = 12 boxes,

Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes

Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60

There are 60 boxes of cookies sold by the girls in one hour.

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