Please answer this correctly

Answer:

The simplified expression is:

[tex]\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

Step-by-step explanation:

To find:

[tex]-\dfrac{1}{2}p^{2} q^{2} r+\dfrac{1}{3}p q^{2} r-\dfrac{1}{4}p q r^{2}-\dfrac{1}{5}rq^{2} p^{2} +\dfrac{1}{6}rq^{2} p-\dfrac{1}{7}r^{2}pq+\dfrac{1}{8}rp^{2}q[/tex]

Solution:

We can see that pqr having power 1 is common throughout.

Let us take it common to make the expression simpler and then we will add by taking LCM:

[tex]\Rightarrow pqr(-\dfrac{1}{2}p q+\dfrac{1}{3}q-\dfrac{1}{4}r-\dfrac{1}{5}pq+\dfrac{1}{6}q-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(-\dfrac{1}{2}p q-\dfrac{1}{5}pq+\dfrac{1}{3}q+\dfrac{1}{6}q-\dfrac{1}{4}r-\dfrac{1}{7}r+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-5pq-2pq}{2\times 5}+\dfrac{2q+q}{2 \times 3}+\dfrac{-7r-4r}{7 \times 4}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7pq}{10}+\dfrac{3q}{6}+\dfrac{-11r}{28}+\dfrac{1}{8}p)\\\Rightarrow pqr(\dfrac{-7}{10}pq+\dfrac{1}{2}q+\dfrac{-11}{28}r+\dfrac{1}{8}p)[/tex]

Now, multiplying pqr again to the expression:

[tex]\Rightarrow \dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

So, the answer is:

[tex]\dfrac{-7}{10}p^2q^2r+\dfrac{1}{2}pq^2r-\dfrac{11}{28}pqr^2+\dfrac{1}{8}p^2qr[/tex]

Answer:

110 = 16 + 10h

110 - 16 = 10h

Step-by-step explanation:

Sylvie needs a total of $110, which is the number she is working towards.

She already has $16, which is what we call a constant, or a number that will not change in the equation.

We are told that if she works 10 hours, she will earn enough money to buy the concert ticket. The amount that she is paid per hour is the variable, which would be signified by the letter "h" in this case.

Set the equation:

(amount of hours) * (pay per hour) + (amount she starts out with) = (total she needs).

Or, to put into numerical & variable terms, plug in the corresponding number (or variable) to the corresponding part.

10 * h + 16 = 110

(10h) + 16 = 110

Another way to solve is to do the first step in isolating the variable, h. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation & =

Parenthesis

Exponents & roots

Multiplication

Division

Addition

Subtraction

First, subtract 16 from both sides:

10h + 16 (-16) = 110 (-16)

10h = 110 - 16

10h = 94

Next, divide 10 from both sides:

(10h)/10 = (94)/10

h = 94/10

h = 9.4

The function is f(x)= 2x+1/x+3.

A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.

The function domain f (x) is a set of all values ​​defined by the function, and the scope of the function is a set of all values ​​taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.

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Answer:

B

Step-by-step explanation:

i got it right! :)

Answer:

The answer is explained below

Step-by-step explanation:

What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.

The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.

Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.

Step-by-step explanation:

The difference between. Each numbers is 5 so, it's answer is 22 and 27

Answer:

Length= 30 in

Width= 10 in

Step-by-step explanation:

Let the width of the rectangle be x in.

Length of rectangle

= 3 (width)

= 3x

Perimeter of rectangle= 2(length) +2(width)

80= 2(3x) +2(x)

80= 6x +2x

8x= 80 (simplify)

x= 80 ÷8 (÷8 on both sides)

x= 10

Thus width of rectangle= 10 in

Length of rectangle

= 3(10)

= 30 in

Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.

Step-by-step explanation:

Answer:

x= (30 -15)/3

Step-by-step explanation:

If we call x the number each friend gets, then the equation is:

Solving this we get:

Each friend gets 5 folders

Answer:

P-value =0.062

At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

The significance level is 0.05.

The sample has a size n=1500.

The sample proportion is p=0.041.

[tex]p=X/n=61/1500=0.041[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]

As the P-value (0.062) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the unemployment rate is less than 5%.

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

Answer:

Step-by-step explanation:

We assume you want the integral ...

  [tex]\displaystyle\int_4^{14}{\sqrt{\ln{x}}}\,dx[/tex]

The width of each interval is 1/6 of the difference between the limits, so is ...

  interval width = (14 -4)/6 = 10/6 = 5/3

Then the point p[n] at the left end of each interval is ...

  p[n] = 4 +(5/3)n

__

Trapezoidal Rule

The area of a trapezoid is the product of its average base length multiplied by the width of the trapezoid. Here, the "bases" are the function values at each end of the interval. The integral according to the trapezoidal rule can be figured as ...

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}\left(\dfrac{f(p[n])+f(p[n+1])}{2}\right)[/tex]

  integral ≈ 14.559027

If you're doing this on a spreadsheet, you can avoid evaluating the function twice at the same point by using a weighted sum. Weights are 1, 2, 2, ..., 2, 1.

__

Midpoint Rule

This rule uses the area of the rectangle whose height is the function value at the midpoint of the interval.

  [tex]\dfrac{5}{3}\sum\limits_{n=0}^{5}{f(p[n+\frac{1}{2}])}[/tex]

  integral ≈ 14.587831

__

Simpson's Rule

This rule gives the result of approximating the function over each double-interval by a parabola. It is like the trapezoidal rule in that the sum is a weighted sum of function values. However, the weights are different. Again, multiple evaluations of the function can be avoided by using a weighted sum in a spreadsheet. Weights for 6 intervals are 1, 4, 2, 4, 2, 4, 1. The sum of areas is ...

  [tex]\dfrac{10}{3}\sum\limits_{n=0}^{2}{\left(\dfrac{f(p[2n])+4f(p[2n+1])+f(p[2n+2])}{6}\right)}[/tex]

  integral ≈ 14.577542

Answer:

Point estimate is 16 and Margin of error is 9

Step-by-step explanation:

The point estimate is given by the following formula:

Point estimate = (Lower Bound + Upper Bound) / 2

Replacing we have:

Point estimate = (7 + 25) / 2 = 32/2

Point estimate = 16

Now, the margin of error is given by the following equation:

Margin of error = (Upper Bound - Lower Bound) / 2

Margin of error = (25 -7) / 2 = 18/2

Margin of error = 9

Answer:

the answer is b

Step-by-step explanation:

Answer:

- 2 1/4

Step-by-step explanation:

Methods for solving multiplication problems

I will go into details and give methods to solve with and the final answer.

: 1\3 × −6 3\4 = -1/3 ×( (6*4)+3)/4

1/3 × -6 3/4 = -1/3 ×(24+3)/4

1/3 × -6 3/4 =- 1/3 ×(27/4)

1/3 × -6 3/4 = -27/(3*4)

1/3 × -6 3/4 = -27/(12)

1/3 × -6 3/4 =-( 9/4) * 3/3

1/3 × -6 3/4 = -9/4

1/3 × -6 3/4 =- 2 1/4

OR by direct division

1/3 × -6 3/4 =( -6 3/4)/3

1/3 × -6 3/4 = -6/3 (3/4)/3

1/3 × -6 3/4 = -2 1/4

Answer:

39°

Step-by-step explanation:

==>Given:

Shadow length = 20ft

Flag height = 16ft

==>Required:

Angle of elevation of sun (θ)

==>Solution:

To calculate the angle of elevation of the sun, recall the trigonometry formula SOHCAHTOA.

We are given adjacent side = 20ft, and opposite side = 16ft

Therefore, we would use TOA, which is:

tan θ = Opposite/Adjacent

tan θ = 16/20

tan θ = 0.8

θ = 38.6598083 ≈ 39°

Angle of elevation of the sun = 39°

Answer:

For 3x^2+4x+4=0

Discriminant= = -32

The solutions are

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= -44

The solutions

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= -36

The solutions

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a= (1-√-1)/3

Step-by-step explanation:

Formula for the discriminant = b²-4ac

let the discriminant be = x for the equations

The solution of the equations

= (-b+√x)/2a and = (-b-√x)/2a

For 3x^2+4x+4=0

Discriminant= 4²-4(3)(4)

Discriminant= 16-48

Discriminant= = -32

The solutions

(-b+√x)/2a =( -4+√-32)/6

(-b+√x)/2a= (-4 +4√-2)/6

(-b+√x)/2a= (-2+2√-2)/3

(-b-√x)/2a =( -4-√-32)/6

(-b-√x)/2a= (-4 -4√-2)/6

(-b-√x)/2a= (-2-2√-2)/3

For 3x^2+2x+4=0

Discriminant= 2²-4(3)(4)

Discriminant= 4-48

Discriminant= -44

The solutions

(-b+√x)/2a =( -2+√-44)/6

(-b+√x)/2a= (-2 +2√-11)/6

(-b+√x)/2a= (-1+√-11)/3

(-b-√x)/2a =( -2-√-44)/6

(-b-√x)/2a= (-2 -2√-11)/6

(-b-√x)/2a= (-1-√-11)/3

For 9x^2-6x+2=0

Discriminant= (-6)²-4(9)(2)

Discriminant= 36 -72

Discriminant= -36

The solutions

(-b+√x)/2a =( 6+√-36)/18

(-b+√x)/2a= (6 +6√-1)/18

(-b+√x)/2a= (1+√-1)/3

(-b-√x)/2a =( 6-√-36)/18

(-b-√x)/2a= (6 -6√-1)/18

(-b-√x)/2a= (1-√-1)/3

Answer:

equation: 3x²+4x+4=0 value: -32   solutions: -2±2i√2 / 3

equation: 3x²+2x+4=0 value: -44   solutions: -1±i√11 / 3

equation: 9x²−6x+2=0 value: -36   solutions: 1±i / 3

Answer:

y-1 = 3(x +2)

Step-by-step explanation:

Ok, so the point-slope form is:

y-k = m(x-h)  where m is the slope and (h,k) is the given point.

Since you are given  m = 3 ,  and (h,k) = (-2,1)

y-1 = 3(x +2)

Since your question specified using the point-slope form, make sure you use this equation when answering it. Otherwise, you may get it wrong.

Answer:

see below

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

  = 4/3 pi ( 7)^3

  = 1372/3 pi in^3

Using 3.14 for pi

V =1436.0266666 in^3

Using the pi button

1436.75504 in^3

Answer:

Step-by-step explanation:

Product of 5 and a number:  5n

Six more than that would be 5n + 6

Finally, "six more than the product of 5 and a number, decreased by one" would be

5n + 6 - 1, or 5n + 5

Answer: A) 6 + 5n - 1

Step-by-step explanation: edge. 2022

Answer:

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14

Answer:

0

Step-by-step explanation:

√12 can be rewritten as √2²·3 = 2√3

√75 can be rewritten as √5²·3 = 5√3

2/5 * 5 = 2

so

2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0

Answer:

0

Step-by-step explanation:

Answer:

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.

so the expression actually is:

∛(16)/e

Answer:

  13.636

Step-by-step explanation:

The area can be found using Heron's formula:

  A = √(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2.

For the given triangle, ...

  a=9, b=4, c=12, s=(9+4+12)/2 = 12.5

  A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636

The area of the triangle is about 13.636 square units.

Answer:

24 units\

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

Total Cards = 5

Even Numbers = 3

P(even) = 3/5

In %age:

=> 60%

Answer:

60%

Step-by-step explanation:

The numbers that are even from the list are 2, 4, and 6.

3 numbers are even out of 5 total numbers.

3/5 = 0.6

P(even) = 60%

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

Answer:

9.392

Step-by-step explanation:

3.1415 + 6.25 = 9.3915

Rounded to the thousandths place, this would be ≈ 9.392

The sum of the given decimal numbers is rounded to the nearest thousandths place as 9.392.

Given that, 3.1415 + 6.25.

Here, sum of the given decimals is 9.3915.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

To round 9.3915 to the nearest thousandths consider the ten thousandths' digit of 9.3915, which is 5. So, the thousandths place value of 9.3915 increase by 1 and ten thousandths place becomes 0.

That, 9.392

Therefore, the sum of the given decimal numbers is rounded to the nearest thousandths place as 9.392.

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Answer:

option 1 both statements are true

Step-by-step explanation:

Prove by PMI -- Principle of Mathematical  Induction

1) n³ + 2n

n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1   ---->divisible by 3

n = 2 ; 2³ + 2*2 = 8+4 = 12  = 3*4  ----> is divisible by 3

Assume that It is valid for n = k ;  

[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N

We have to prove for n =k +1 , the statement is true.

n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]

                                           = k³ + 3k² + 3k + 3 + 2k

                                           =  k³ +  2k + 3k² + 3k + 3

                                           = 3m + 3 (k² + k + 1)

                                          = 3(3 + [k² + k + 1] ) is divisible by 3

Therefore, this statement is true

2) [tex]5^{2n}-1\\[/tex]

[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]

This statement is also true

Answer:

Area = 7 square units

Perimeter = 14 units

Step-by-step explanation:

The shape is made up of 7 identical squares and, we are told the side length of each square is 1 unit.

==>Find area of the shape by calculating the area of 1 square, then multiply by the number of square used in the construction.

Thus, area of 1 square = s² = 1² = 1 square units.

Area of shape = 7 × 1 square units = 7 square units

==>Find the Perimeter of the shape by adding all the lengths of the boundary formed by the square to make up the shape.

(Check attachment to understand how we got the measurement of the boundary)

The perimeter = 1 + 1 + 1 + ½ + ½ + 1 + 1 + 1½ + ½ + 1 + 1 + 4 = 14 units

Answer:

solution,

[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

The value of y is 4

Step-by-step explanation:

What is similarity ?

In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given,

ΔACB~ΔEFD

The proportional sides are equal.

[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]

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Answer:

solution,

[tex]48 > 2x - 10 \\ 48 + 10 > 2x \\ \frac{58}{2} > \frac{2x}{2} \\ 29 > x \\ x < 29[/tex]

but,

[tex]2x - 10 > 0 \\ \frac{2x}{2} > \frac{10}{2} \\ x > 5 \\ \\ 5 < x < 29 \: is \: the \: answer.[/tex]

Hope this helps...

Good luck on your assignment..

The range of value of x is 5 < x < 29.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given:

A quadrilateral ABCD.

From the diagram,

2x - 10 < 48

2x < 58

x < 29.

And 0 < 2x - 10

10 < 2x

5 < x

Therefore, the range is 5 < x < 29.

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Answer:

The relative frequency distributions would be more preferable to use when we want to measure the weight of a particular category or also when we want to compare different categories of data within a table. Moreover, relative frequency is often used for the probability calculations.

Step-by-step explanation:

Frequency distribution:

A frequency distribution simply tells us how many times an event has occurred or in other words, it is the rate of occurrence.

Relative frequency distribution:

On the other hand, the relative frequency tells us the fraction of how many times an event has occurred with respect to the total number of trials.

For example:

Consider a bag of marbles having marbles of different colors. We randomly pick marbles from the bag and got the following results.

Event    |   Frequency

Red       |        2

Blue      |        4

Green   |        6

Grey     |        3

The frequency of Red marbles is 2 which means that the red marble came up two times. Similarly, the blue marble came up four times.

The relative frequency of red marble is 2/15 = 0.133 = 13.3%

The relative frequency of green marble is 6/15 = 0.40 = 40%

This means that the green marbles came up 40% of the time.

When relative frequency distributions is preferred?

The relative frequency distributions would be more preferable to use when we want to measure the weight of a particular event or also when we want to compare different categories of data within a table. Moreover, relative frequency is often used for the probability calculations.