simplify so that your answer contains only positive exponents.​

Answer:

LCM = 240

GCF = 8

Step-by-step explanation:

Least common multiple (LCM) is the smallest number that both 40 and 48 go into

Greatest common factor (GCF) is the largest number that can go into 40 and 48.

Answer: 9x^2-9x-10 ==> D

Step-by-step explanation:

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

3x*3x + (-5)(3x) + 2*3x + (-5)(2)=

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

9x^2-15x+6x-10=

9x^2-15x+6x-10= 9x^2-9x-10 ==> D

=================================================

Explanation:

Let's make

y = 3x+2

So we can replace the (3x+2) with y

We go from (3x+2)(3x-5) to y(3x-5)

Distribute that y term through

y(3x-5)

y(3x) + y(-5)

3xy - 5y

Then plug in y = 3x+2 and distribute two more times

3xy - 5y

3x( y ) - 5( y )

3x( 3x+2 ) - 5( 3x+2 )

3x(3x) + 3x(2) - 5(3x) - 5(2)

9x^2 + 6x - 15x - 10

9x^2 - 9x - 10

which seems to point to choice D assuming the -9 in the middle is supposed to be -9x

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

Side note: Alternative methods are the FOIL rule and the box method.

The option that would complete the given expression is; Option B: 10 to the fourth power

We are told that Juliana wants to write the number twenty thousand, one hundred ninety in expanded notation.

This can be broken down as;

20,190

This can be broken further down into;

20000 + 100 + 90

Writing in expanded notation gives;

(2 * 10⁴) + (1 * 10²) + (9 * 10¹)

Thus, we can say that the option that would complete the given expression is; Option B: 10 to the fourth power

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The amount of tax deductions in one payment period and one year based on a Social Security tax rate of 6.2% and Medicare tax rate of 1.45% are;

13. Kim's weekly Medicare deductions is $7.888

Her annual Medicare deductions is $410.176

14. Jeffrey's annual Social Security tax deductions is $3,517.0616

15. Kareem's annual Medicare tax deductions is $606.97

16. A. Parker's annual Social Security tax deductions is $4,836

B. His annual Medicare tax deductions is $1,131

According to the accounting firm BGM website,in the year 2022, an employee is expected to pay a tax of 6.2% of the first $147,000 of wages, for Social Security, and a Medicare tax of 1.45% of the first $200,000

13. Kim's gross weekly salary is $544.

Given that 544 × 52 = 28,288 < 200,000, we have;

Kim's Medicare deduction for one pay period is 0.0145 × $544 = $7.888

Kim receives her payment weekly, therefore, multiplying by 52 gives;

Annual Medicare tax;

52 × $7.888 = $410.176

14. Jeffrey's semimonthly salary = $2,181.80

Jeffrey's tax deductions for Social Security for one pay period is therefore;

0.062 × $2,181.80 = $135.27160

The number of semimonthly payment periods in a year = 26

Jeffrey's annual Social Security tax deductions is therefore;

15. Kareem's gross biweekly salary is $1,610

Kareem's Medicare deductions per pay period is therefore;

0.0145 × $1,610 = $23.345

The number of biweekly pay periods in a year is 26

Kareem's total Medicare deductions for the year is therefore;

16. Parker's gross monthly salary is $6,500

A. Parker's Social Security deductions for one month is therefore;

0.062 × $6,500 = $403

The deductions in a year is therefore;

B. Parker's Medicare deductions for one month is given by the equation;

0.0145 × $6,500 = $94.25

Parker's Medicare deductions for one year is therefore;

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Python is a computer programming language often used to build websites and software, automate tasks, and conduct data analysis. Python is a general-purpose language, meaning it can be used to create a variety of different programs and isn't specialized for any specific problems.

Python 3 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print(entry)

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print("Square of ", entry, " = ", entry*entry)

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

Sample Output:

12 10 32 3 66 17 42 99 20 Square of  12  =  144 Square of  10  =  100 Square of  32  =  1024 Square of  3  =  9 Square of  66  =  4356 Square of  17  =  289 Square of  42  =  1764 Square of  99  =  9801 Square of  20  =  400

Python 2.7 code:

function to print the numbers in list

def print_list(List):

 for entry in List:

   print entry

function to print the numbers and squares in list

def print_squares(List):

 for entry in List:

   print "Square of ", entry, " = ", entry*entry

Call the functions now

input_list = [12,10,32,3,66,17,42,99,20]

print_list(input_list)

print_squares(input_list)

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The domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The range is going to be a set of real numbers from 0 to 6.

The domain of a function is the set of input values that we are allowed to plug into our function. This set is the x-values in a function.

The range of a function is the set of output values that the function assumes.

Now, we are told that there is a set of ordered pairs (q, T), where T is the total value of q quarters in dollars, up to $1.50 in quarters

Now, from conversions, we know that 1 quarters is equal to 0.25 dollar.

Thus, the domain q is a set of real numbers as(0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50).

The maximum output value will be; 1.5/0.25 = 6

Meanwhile, the range is going to be a set of real numbers from 0 to 6.

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By using simple rule of three, a period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

One year on Earth is equivalent to 365.3 days and one year on Venus is equivalent to 224.7 days, the equivalent terrestrial time of 9.5 years on Venus is found by simple rule of three:

x = 9.5 yr × (224.7 days / 1 yr)

x = 2134.65 days

A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

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Answer:

64 and 13 I hope this helps

Step-by-step explanation:

Answer:

-3x>24

Step-by-step explanation:

-3x-10>14

now we add 10 to both sides, 10+14 is 24

so, the missing step is -3x>24

The equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18

The question has to do with linear equation

A linear equation is a mathematical expression in which the highest power of the unknown is 1.

Let

Given that the maximum speed, in miles per hour, of a cheetah is 18 more than 3 times  the maximum speed of the hippopotamus

Now, since the maximum speed of the hippopotamus is h, 3 times the maximum speed of the hippopotamus is 3h.

Since the cheetah is 18 more than 3 times  the maximum speed of the hippopotamus, we have that

x = 3h + 18

Substituting x = 75 into the equation, we have

75 = 3h + 18

So, the equation could be used to find the maximum speed of a hippopotamus h is C. 75 = 3h + 18

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The given bounded region is the set

[tex]R = \left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^4 \le y \le x^{1/4} \right\}[/tex]

assuming the curves are [tex]y=x^4[/tex] and [tex]x=y^4\implies y=x^{1/4}[/tex] (since [tex]x>0[/tex] in the first quadrant).

The coordinates of the centroid are [tex](\bar x, \bar y)[/tex] where [tex]\bar x[/tex] and [tex]\bar y[/tex] are the average values of [tex]x[/tex] and [tex]y[/tex], respectively, over the region [tex]R[/tex]. These are given by the ratios

[tex]\bar x = \dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \bar y = \dfrac{\displaystyle \iint_R y\,dA}{\displaystyle \iint_R dA}[/tex]

Compute the area of [tex]R[/tex].

[tex]\displaystyle \iint_R dA = \int_0^1 \int_{x^4}^{x^{1/4}} dy \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \frac45 - \frac15 = \frac35[/tex]

Integrate [tex]x[/tex] and [tex]y[/tex] over [tex]R[/tex].

[tex]\displaystyle \iint_R x \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} x \, dy \, dx \\\\ ~~~~~~~~ = \int_0^1 x \left(x^{1/4} - x^4\right) \, dx \\\\ ~~~~~~~~ = \int_0^1 \left(x^{5/4} - x^5\right) \, dx \\\\ ~~~~~~~~ = \frac49 - \frac16 = \frac5{18}[/tex]

[tex]\displaystyle \iint_R y \, dA = \int_0^1 \int_{x^4}^{x^{1/4}} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left((x^{1/4})^2 - (x^4)^2\right) \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^1 \left(x^{1/2} - x^8\right) \, dx \\\\ ~~~~~~~~ = \frac12 \left(\frac23 - \frac19\right) = \frac5{18}[/tex]

Then the centroid's coordinates are

[tex]\bar x = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}} \approx 0.463[/tex]

[tex]\bar y = \dfrac{\frac5{18}}{\frac35} = \boxed{\frac{25}{54}}[/tex]

Answer:

It would be 3710.

Step-by-step explanation:

The polynomial function will be y = (x⁴-14x³+70x²-144x+104)

2 and 5+i are the roots of the given polynomial and the multiplicity of 2 and 5+i are 2 and 1 respectively.

Thus, the general form of the polynomial will be given as:

y = (x-2)² (x-(5+i)) (x-(5-i))                                  [as (5-i) is conjugate of (5+i)]

y = (x²+4-4x) (x-5-i) (x-5+i)

y = (x²-4x+4) (x²-5x+xi-5x+25-5i-xi+5i-i²)

y = (x²-4x+4) (x²-10x+25+1)                                            [as i²= -1]

y = (x²-4x+4) (x²-10x+26)  

y = (x⁴-10x³+26x²-4x³+40x²-104x+4x²-40x+104)

y = (x⁴-14x³+70x²-144x+104)

Thus, the polynomial is y = (x⁴-14x³+70x²-144x+104)

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20/100

That is the answer if u want it simplified it is 1/5

Answer:

20/100 simplified is 1/5

Step-by-step explanation:

it is the fraction form

The correct option is A) The 99% confidence interval ranges from 53.73 to 56.27 hours.

The 99% confidence interval for the mean hours devoted to social networking in January ranges from 53.73 to 56.27 hours.

In statistics, a confidence interval denotes the likelihood that a population parameter would then fall between two specified values.

sample size 'n' =200

Mean 'x'  = 55 hours

Standard deviation (Population) = 7 hours

For 99% confidence level

Z critical value = 2.58

Margin of error = ±2.58(std error)

Now, compute the standard error

Standard error = 7/√n

              =7/√200

               = 0.495

Thus, margin of error = ±0.495(258) = 1.28

Now, calculate the Confidence interval;

Confidence interval = (55 - 1.28, 55 + 1.28)

                                  = (53.72, 56.28)

Confidence interval = (53.73, 56.27) [approx.]

Therefore, the confidence level lies between 53.73, 56.27) [approx.]

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The correct question is-

In a sample of 200 households, the mean number of hours spent on social networking sites during the month of January was 55 hours. In a much larger study, the standard deviation was determined to be 7 hours. Assume the population standard deviation is the same. What is the 99% confidence interval for the mean hours devoted to social networking in January?

A) The 99% confidence interval ranges from 53.73 to 56.27 hours.

B) The 99% confidence interval ranges from 7 to 55 hours.

C) The 99% confidence interval ranges from 54.51 to 55.49 hours.

D) The 99% confidence interval ranges from 55 to 60 hours.

(2x6)^3/2  in it's simplest form is equal to 41.56. See the computation below.

Using BODMAS, we say

(2 x 6) = 12

12^(3/2)

= 41.5692

[tex]$\approx$[/tex] 41.56

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We get the values of m as 1 and n as 0.

We are given a function:

f(x) = m / (x - 1) + n

We are also given that:

f (-2) = 1 and f (4) = 3

We have to find the value of m and n.

f (-2) = m (2 - 1) + n

1 = m + n

n = 1 - m

f (4) = m / (4 - 1) + n

3 = 3 m + n

3 = 3 m + 1 - m

3 = 2 m + 1

2 m = 3 - 1

2 m = 2

m = 2 / 2

m = 1

m + n = 1

1 + n = 1

n = 0.

Therefore, we get the values of m as 1 and n as 0.

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Please check the image attached aside with the graph of the quadratic equation.

In this problem we have a quadratic equation, of which we should plot the graph by matching five points. We can make use of its vertex, two roots, y-intercept and other point. First, determine the vertex of the quadratic function:

- x² - 12 · x - (35 + y) = 0

x² + 12 · x + (35 + y) = 0

12² - 4 · 1 · (35 + y) = 0

144 - 4 · (35 + y) = 0

144 - 140 - 4 · y = 0

4 · y = 4

y = 1

- x² - 12 · x = 36

x² + 12 · x + 36 = 0

(x + 6)² = 0

x = - 6

The vertex of the quadratic equation is (x, y) = (- 6, 1).

Second, calculate the roots of the quadratic equation:

- x² - 12 · x - 35 = 0

x² + 12 · x + 35 = 0

(x + 5) · (x + 7) = 0

The roots of the quadratic equation are (x, y) = (- 5, 0) and (x, y) = (- 7, 0).

Third, determine the y-intercept of the quadratic equation:

y = - 0² - 12 · 0 - 35

y = - 35

The y-intercept of the quadratic equation is (x, y) = (0, - 35).

And fourth, find another point by evaluating the quadratic equation:

y = - 1² - 12 · 1 - 35

y = - 48

The remaining point is (x, y) = (1, - 48).

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Answer:

B

Step-by-step explanation:

Answer B is the result of simplifying

The ratio of circumference/diameter for all circles is π. And the ratio of force/mass for all freely-falling bodies will be g.

Let d be the diameter of the circle. The circumference of the circle will be

C = πd units

The ratio of circumference to diameter for all circles is pie.

C/D = πd / d

C/D = π

Then the ratio of force to mass for all freely-falling bodies will be

The force acting on a free-falling body of mass (m) is mg. Then we have

Force/Mass = mg / m

Force/Mass = g

Where g is the acceleration due to gravity.

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The range of the situation is 30 to 55.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used when you do not know the exact number in a calculation.

Given:

A vinyl decal shop charges a set-up fee of $25.00

$5.00 for each decal printed.

as, f(x)=5x+25 represents the total cost of the set-up fee

we have 6 cheerleaders

put x= 1

5x+25 = 5+25 = 30

and x=6

5x+25= 5*6+25= 30+25= 55

Hence, the range is 30 to 55.

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The correct family is option D.

To understand this problem we must be aware of the concept of addition and subtraction and also BODMAS rules which applies in an linear equation.

The numbers given here are 4,2 and 6.

We can see here that on adding 4 and 2 we get 6;

4+2=6

And on subtracting 2 from 6 we get 4;

6-2=4

Also we can see here that on subtracting 4 from 6 we get 2;

6-4=2.

These three relations are true for the given numbers.

And we can see that option D clearly fits the answer.

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Answer:

The cost per unit of an item is called unit cost

The slope of the line shown is 1/5, and being parallel means having the same slope. So it’s either a or b.

Next, you plug in (-2, 2) into y=1/5x+b to find b.

Solving you get: 2=1/5 * -2 +b

2=-2/5+b

B=2 2/5

12/5 = 2 2/5

So the answer is b.

Hope this helps!