When simplified, the expression (x ^1/8) (x^3/8) is 12. Which is a possible value of x?

Answers

Answer 1

(x ^1/8) (x^3/8) = x^4/8=x^1/2 = 12, x = 12^2 = 144

x=144

Answer 2

the possible value of x is 144

Related Questions

Video studying aboard and she's requested required to pay $3,500 in u.s. dollars per year to the university however she must pay in Euros how many euros can be there except to pay per month to the university round to the nearest Point 7306equals one u.s. dollar

Answers

We know that:
$1 = .7306 Euros
She has to pay $3,500 per year to the University.
$3,500 * .7306 = 2,557.10 Euros
And since we have to find how many Euros can be except to pay per month:
2,557.10 : 12 = 213.09 ≈ 213 Euros
Answer:
She would pay 213 Euros per month.

The quadratic function y = –10x2 + 160x – 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. What equation do you need to solve to find the selling price or prices that would generate $50 in daily profit? What method would you use to solve the equation? Justify your choice.

Answers

Daily profit, y, as a function of T-shirts sold, x, is
y = -10x² + 160x - 430

In order to generate $50 in daily profits, the number of T-shirts sold is determined by solving the equation
-10x² + 160x - 430 = 50

Divide through by -10.
x² - 16x + 43 = -5
x² - 16x + 48 = 0

Answer:
This quadratic equation can be solved by factorization.

Explanation:
Note that
48 = 4 x 12, and
4 + 12 = 16
Therefore
x² - 16x + 48 = (x - 4 )(x - 12 ) = 0
The solutions are
x - 4 = 0 => x = 4, and
x - 12 = 0 => x = 12

a. The required equation is x² - 16x + 48 = 0

b. I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.

The required equation is x² - 16x + 48 = 0

The required equation

Since the quadratic function y = -10x² + 160x - 430 models a store’s daily profit (y) for selling a T-shirt priced at x dollars. Since we require a profit of $50, then y = 50.

So, y = -10x² + 160x - 430

-10x² + 160x - 430 = 50

-10x² + 160x - 430 - 50 = 0

-10x² + 160x - 480 = 0

Dividing through by -10, we have

x² - 16x + 48 = 0

So, the required equation is x² - 16x + 48 = 0

I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.

The method

To determine the method you would use to solve the equation, you would need to determine the value of the discriminant.

Discriminant

For a quadratic equation ax² + bx + c = 0, the discriminant is D = b² - 4ac

Since x² - 16x + 48 = 0 and its discriminant D = (-16)² - 4 × 48

= 256 - 192

= 48

= 64 > 0 and is a perfect square, so it is factorizable. The equation would have real and distinct roots,

So, x² - 16x + 48 = 0

x² - 4x - 12x + 48 = 0

x(x - 4) - 12(x - 4) = 0

(x - 4)(x - 12) = 0

x - 4 = 0 or x - 12 = 0

x = 4 or x = 12

I would use factorisation to solve it and the selling prices that would generate a daily profit of $50 are $4 and $12 respectively.

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Tamara earns $8 an hour at her job working 25 hours per week. If 25% of her paycheck goes to taxes, what is Tamaras monthly cash flow? (Asssume this is her only source of income and that there are 4 pays per month)

Answers

i believe the answer is 600

8* 25* 0.75 = 150
so, she gets $150 a week.

A district manager rewards sales teams based on overall sales generated in a month. The data for earnings are shown in the table, where Low represents the lowest sales and High represents the highest sales generated by a single sales team member.Team Low High Range Mean Median IQR σTeam X 1970 2970 1200 2571.9 2684 426.3 313.8Team Y 250 375 125 315.8 311 59 37.8Team Z 950 1900 950 1529.9 1473 276 180.7Part A: If the manager wants to award the sales team that has the most consistent earnings among its team members, which team should it choose and why? Justify your answer mathematically. (5 points)Part B: If the manager wants to award the sales team with the highest average earnings, which team should it choose and why? Justify your answer mathematically. (5 points)

Answers

PART A:

The most consistent team is the team who has the lowest range, IQR and standard deviation (σ). From the table, the team who has the lowest range, IQR and the standard deviation is team Y.

Lower range indicates a small range of data interval, meaning that there is no extremely low or high value on a set. It also means that most of the data values are repeated and therefore is more consistent.

PART B:

Average of a data can be shown by the value of the mean or median. From the table, we can see that team A has the highest mean and median. These values indicate the earning by sales each team member would have made.

Use newton's method to find the absolute minimum value of the function f(x)=x2+sinx correct to six decimal places.

Answers

The solution would be like this for this specific problem:

f(x) = x^2 + sin(x)

f '(x) = 2x + cos(x)

The minimum value is at f '(x) = 0,

So, let g(x) = 2x + cos(x)

Thus, g '(x) = 2 - sin(x)

x(new) = x - g(x) / g '(x)
or
x(new) = x - [2x + cos(x)] / [2 - sin(x)]

Calculation

x1 = -0.5 - [2 * -0.5 + cos(-0.5)] / [2 - sin(-0.5)]
= -0.4506266931
x2 = -0.4501836476
x3 = -0.4501836113
x4 = -0.4501836113

This value for x, f(x) = -0.2324655752.

After converting to 6 decimal places: the minimum point is (-0.450184, -0.232466).

Final answer:

To find the absolute minimum value of f(x)=x^2+sin(x), use Newton's method with Newton-Raphson iteration x_{n+1} = x_n - f(x_n)/f'(x_n). Start with an initial guess and iterate until the result converges to six decimal places, ensuring the second derivative at the critical point is positive.

Explanation:

To find the absolute minimum value of the function f(x)=x^2+sin(x) correct to six decimal places, we can use Newton's method. Newton's method helps to find successively better approximations to the roots (or zeroes) of a real-valued function. First, we need to find the derivative of the function, which gives us f'(x) = 2x + cos(x). We are looking for a critical point where the derivative is zero because this could indicate a potential minimum (or maximum).

Starting with an initial guess, we can apply the Newton iteration formula x_{n+1} = x_n - f(x_n)/f'(x_n) to find a better approximation. In this case, let's choose an initial guess close to the root of f'(x). Since we do not have the specific initial guess, we would theoretically pick a value near the expected minimum and iterate until the difference between consecutive approximations is less than the desired tolerance, which is the change in six decimal places.

The Newton-Raphson iteration would be applied repeatedly until convergence is seen at six decimal places. Note that in practice, one must also check the second derivative f''(x) at the found critical point to confirm it is a minimum (it should be positive).

Donna the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 7 clients who did Plan A and 9 who did Plan B. On Saturday there were 5 clients who did Plan A and 3 who did Plan B. Donna trained her Friday clients for a total of 12 hours and her Saturday clients for a total of 6 hours.
How long does each of the workout plans last?

Answers

x = plan A and y = plan B
7x + 9y = 720
5x + 3y = 360.....multiply by -3
---------------
7x + 9y = 720
-15x - 9y = -1080 (result of multiplying by -3)
---------------add
-8x = - 360
x = -360/-8
x = 45 minutes <== plan A

5x + 3y = 360
5(45) + 3y = 360
225 + 3y = 360
3y = 360 - 225
3y = 135
y = 135/3
y = 45 minutes <== plan B

so both plans last 45 minutes <==

what is the domain and range for the following function and its inverse f(x) = x2 – 2

Answers

When a function is graphed, the domain refers to the points along the x-axis that is covered by the graph. On the other hand, the range refers to the points along the y-axis that is covered by the graph. The inverse of the function can be determined when you substitute the negative value of x. The function and its inverse have the identical graphs.This is because of the term x^2. Whether x is negative or positive, it will yield the same positive the answer. The graph is shown in the picture.

The domain is from -∞ to +∞, while the range is from -2 to +∞.

Answer:

x2-2 domain an range are 0, -2

Step-by-step explanation:

A simple random sample of 1350 registered voters shows that 58% favor Candidate A over Candidate B. Which is the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B.

Answers

Final answer:

The 99% confidence interval for the percentage of registered voters who prefer Candidate A is between 54.6% and 61.4%.

Explanation:

To calculate the 99% confidence interval for the percentage of the population of registered voters who prefer Candidate A over Candidate B, you can use the formula for the confidence interval of a proportion:

The sample proportion (p') is given as 58%, which is 0.58 in decimal form. The size of the sample (n) is 1350.

To calculate the confidence interval, we also need the z-value for the 99% confidence level. The z-value for a 99% confidence level is approximately 2.576 (you can find this value in a standard z-table).

The formula for the margin of error (EBP) is:

EBP = z * sqrt((p'*(1-p'))/n)

Plugging the values into the formula:

EBP = 2.576 * sqrt((0.58*(1-0.58))/1350)

EBP ≈ 0.034

The confidence interval for the true binomial population proportion is given by:

(p' - EBP, p' + EBP)

Therefore, the 99% confidence interval is:

(0.58 - 0.034, 0.58 + 0.034)

(0.546, 0.614)

Interpreting this, we can say with 99% confidence that the true percentage of all registered voters who prefer Candidate A over Candidate B is between 54.6% and 61.4%.

Final answer:

To calculate the 99% confidence interval for the percent of registered voters who prefer Candidate A, we can use the formula CI = p ± Z * √(p*(1-p)/n). Plugging in the values, we find the 99% confidence interval is between 54.6% and 61.4%.

Explanation:

To calculate the 99% confidence interval for the percent of the population of all registered voters who prefer Candidate A over Candidate B, we can use the formula:

CI = p ± Z * √(p*(1-p)/n)

Where:

p = sample proportion

Z = Z-value for the desired confidence level

n = sample size

In this case, the sample proportion is 0.58, the sample size is 1350, and the Z-value for a 99% confidence level is approximately 2.58.

Plugging in these values, we get:

CI = 0.58 ± 2.58 * √(0.58*(1-0.58)/1350)

Simplifying the equation gives us the 99% confidence interval for the percent of registered voters who prefer Candidate A: between 0.546 and 0.614, or 54.6% and 61.4%.

HELP
There are 20 alligators in the swamp. Each year, the number of alligators increases by 25%. There are 25 crocodiles in the swamp. Each year, 10 new crocodiles join the swamp.

Part A: Write functions to represent the number of alligators and crocodiles in the swamp throughout the years. (4 points)

Answers

alligators:

x = total number of alligators

n = number of years

x=20x1.25^n

crocodiles:

y = total number of crocodiles

n = number of years

y=25+10n

HELP ROUND 1.75170179212 TO 6 DECIMAL PLACES

Answers

1.75170179212

There are 11 decimal places here. We only need 7 to complete.

1.751701(7)xxxx
^
We need to round the 7th place to round to 6 decimals

If the 7th decimal place < 5, round to 1.
If the 7th decimal place > or = 5, round to 2.

Because 7 > 5, It rounds to 1.751702.

Answer:

The answer is 1.751702

Step-by-step explanation:

In this number there are 11 decimal places which can be found after the decimal point.

1.75170179212

As we want 6 decimal places, we need to look at the digit to the right of sixth decimal place. Therefore:

1.75170179212

So, in this case, the digit in the seventh place is a '7'.

If we want to round a number, there are two ways:

If the digit is less than 5, you leave the sixth decimal as it is.If the digit is equal or greater than 5, you add 1 up to the sixth decimal.

As the seventh decimal is a '7' which is greater than '5'.

We add a 1 to the Sixth decimal place.

As the sixth decimal place was a '1'. When we round it, it will be a 2

1.751702

write the expression in factored form: m²-n²

Answers

This expression is a difference of squares: [tex]x^2 - y^2 = (x + y)(x - y)[/tex]

[tex]m^2 - n^2 = (m + n)(m - n)[/tex]

difference of 2 squares

m^2 - n^2 = (m - n)(m + n)

Eloise started to solve a radical equation in this way: Square root of negative 2x plus 1 − 3 = x Square root of negative 2x plus 1 − 3 + 3 = x + 3 Square root of negative 2x plus 1 = x + 3 Square root of negative 2x plus 1 − 1 = x + 3 − 1 Square root of negative 2 x = x + 2 (Square root of negative 2 x)2 = (x − 4)2 −2x = x2 − 8x + 16 −2x + 2x = x2 + 8x + 16 + 2x 0 = x2 + 10x + 16 0 = (x + 2)(x + 8) x + 2 = 0 x + 8 = 0 x + 2 − 2 = 0 − 2 x + 8 − 8 = 0 − 8 x = −2 x = −8 Both solutions are extraneous because they don't satisfy the original equation. What error did Eloise make?

Answers

Please see attached image for the choices and proper formatting of the problem.

What she did:

[tex] \sqrt{-2x + 1 } - 1 = x + 3 - 1 \sqrt{-2x} = x + 2[/tex]

What she should have done:

[tex]( \sqrt{-2x + 1} ^{2} = (x + 3)^2 -2x + 1 = (x + 3)^2 -2x + 1 - 1 = (x + 3)^2 - 1 -2x = (x +3)^2 - 1[/tex]

The error that Eloise made in solving the radical equation was that she subtracted 1 before squaring both sides.

To add, the equation where at least one variable expression is fixed inside a radical, usually a square root is called a radical equation.

Answer:

We need to subtract 1 after squaring both sides

Step-by-step explanation:

Step1: [tex]\sqrt{-2x+1} -3 = x \\[/tex]

adding 3 both sides

[tex]\sqrt{-2x+1} =3 + x \\[/tex]

we need to square here first and then we need to subtract

and this is the error which Eloise make in solving it .

The area of a square is 2500 cm .what is the side legth of the painting?

Answers

Let side length be s.

Area = 2500 sq. cm

s² = 2500

s = √(2500)

s = √(5² × 10²)

s = 5 × 10

s = 50 cm

The population of greenville is currently 50,000 and declines at a rate of 1.2% every year. This models:
Exponential growth.
Exponential logarithm
Exponential decay

Answers

Exponential decay. Decay is clear, less. Exponential logarithm is contradictory.

So. the answer is
Exponential decay

Formula: 50000/1.12^years, which could be rewritten as 50,000/e^(number*years), and so it is exponential.

declines means getting less in number

So its decay

Choice C

Find the 6th term of the sequence with t1 = -4 and tn = 5tn-1

Answers

All you have to do is subtitle the t1 in the equation

T2= 5(-4)= -20 don the same thing for all of them :

-100 t3

-500. T4

-2500 t5

-12500 is t6

write the number 32.56 corrrect to one decimal place

Answers

32.56...correct to 1 decimal place = 32.6

What is the surface area of the square pyramid?
(Figure is not drawn to scale.)

Answers

area of the base = 8^2 = 64

area of 1 traingle = 1/2 * 8 * 5.4 = 21.6

there are 4 triangular sides so their area = 4 * 21.6 = 86.4

Total surface area = 64 + 86.4 = 150.4 cm2

D

Identify the number that does not belong with the other three. Explain your reasoning.

Answers

√18
It is the only number in the set that cannot be expressed as a fraction (or ratio) meaning it is an irrational number

Susie divided a9-pound bag of apples into 5 equal piled. How many pounds of apples are in each piles?

Answers

divide the total weight by the number of piles

9/5 = 1.8 pounds per pile

what is 17pi/4 in decimal form nearest the thousandth

Answers

17 x PI = 53.40707511

divided by 4 = 13.35176878

rounded to nearest thousandth = 13.352

Which of the following statements are true? I. -(-6) = 6 and -(-4) > -4 III. 5 + 6 = 11 or 9 - 2 = 11 II. -(-4) < 4 or -10 > 10 - 10 IV. 17 > 2 or 6 < 9

Answers

IV : 17 > 2 or 6 < 9......these are true....17 is greater then 2 and 6 is less then 9

The answer would be an option (D) 17 > 2 or 6 < 9 because 17 is greater than 2 and 6 is less than 9 is always true.

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

I. -(-6) = 6 and -(-4) > -4

Here -(-4) > -4 is incorrect

-(-4) = 4 is correct

These statements are not true

III. 5 + 6 = 11 or 9 - 2 = 11

Here 9 - 2 = 11 is incorrect

So 9 - 2 = 7 is correct

These statements are not true

II. -(-4) < 4 or -10 > 10 - 10

Here -(-4) < 4 is incorrect

So -(-4) = 4 is correct

These statements are not true

IV. 17 > 2 or 6 < 9

Here 17 is greater than 2 and 6 is less than 9 is always true.

Hence, the correct answer would be an option (D)

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If the mean of a symmetric distribution is 82, which of these values is most likely to be the median of the distribution? A.92 B. 85 C.78 D.82

Answers

As the distribution is symmetrical the the mean is likely to be equal to the median

So its 82

The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to

Answers

Final answer:

The expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.

Explanation:

The expression sin 50 cos 40 + cos 50 sin 40 can be simplified using the trigonometric identity:

sin(a + b) = sin a cos b + cos a sin b

By applying this identity, we can rewrite the expression as:

sin(50 + 40) = sin 90 = 1

Therefore, the expression sin 50 cos 40 + cos 50 sin 40 is equivalent to 1.

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PLEASE HELP.

Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

The company also discovered that it cost $23 to produce 2 widgets, $103 to produce 4 widgets, and $631 to produce 10 widgets.

Find the total cost of producing 6 widgets.

Answers

quadratic
y = ax^2 + bx + d
c (x) = ax^2 + bx + d
c (3) = a (3^2) + b (3) + d
c (3) = 9a + 3b + d = 15.50

c (7) = a (7^2 + b (7) + d

c (7) = 49a + 7b + d = 23.50

c (12) = a (12^2) + b (12) + d
c (12) = 144a + 12b + d = 56

solve using simultaneous equations... to get a b and d

use that to solve for x = 5

hope this helps?

Answer:

The total cost of producing 6 widgets is $231.

Step-by-step explanation:

Given : Widget wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.

To find : The total cost of producing 6 widgets.

Solution :

Cost is given by [tex]c (x) = ax^2 + bx + d[/tex]

Cost $23 to produce 2 widgets,

[tex]c(2) = a(2)^2 + b(2) + d[/tex]

[tex]23= 4a+2b+d[/tex] .........[1]

Cost $103 to produce 4 widgets,

[tex]c(4) = a(4)^2 + b(4) + d[/tex]

[tex]103= 16a+4b+d[/tex] ............[2]

Cost $631 to produce 10 widgets.,

[tex]c(10) = a(10)^2 + b(10) + d[/tex]

[tex]631= 100a+10b+d[/tex] ...........[3]

Now, we solve equation [1], [2] and [3]

Subtract equation [2]-[1] and [3]-[2]

[2]-[1] → [tex]12a+2b=80[/tex] ........[4]

[3]-[2] → [tex]84a+6b=528[/tex] .......[5]

Solving equation [4] and [5] by elimination method,

Multiply equation [4] by 3 and subtract from [5]

[tex]84a+6b-3(12a+2b)=528-3(80)[/tex]

[tex]84a+6b-36a-6b=528-240[/tex]

[tex]48a=288[/tex]

[tex]a=6[/tex]

Put in equation [4]

[tex]12(6)+2b=80[/tex]

[tex]72+2b=80[/tex]

[tex]2b=8[/tex]

[tex]b=4[/tex]

Substitute the value of a and b in [1] to get d

[tex]23= 4a+2b+d[/tex]

[tex]23= 4(6)+2(4)+d[/tex]

[tex]23= 24+8+d[/tex]

[tex]23= 32+d[/tex]

[tex]d=-9[/tex]

Substitute a=6,b=4,d=-9 in the cost equation,

The required equation form is [tex]c(x) = 6x^2 + 4x-9[/tex]

The total cost of producing 6 widgets.

Put x=6

[tex]c(6) = 6(6)^2 + 4(6)-9[/tex]

[tex]c(6) = 216+15[/tex]

[tex]c(6) =231[/tex]

Therefore, The total cost of producing 6 widgets is $231.

A ______ is an expression that can be written in the form of p/q where p and q are polynomials and q

Answers

A rational number .... where q is not zero.

How high is a 40-foot ramp if it is propped at a 30 degree angle?

Answers

This is the concept of trigonometry, the height of the ramp will be given by:
sin theta=[opposite]/[hypotenuse]
theta=30
opposite=x
hypotenuse=40 ft
hence;
sin 30=x/40
thus;
x=40sin30
x=20 ft
the ramp is 20 ft high

How many cubic feet of dirt are there in a hole that is 3’ deep x 3’ wide x 3’ long? 0?

Answers

the volume of the hole would be 3*3*3 = 27 cubic feet.

however since it is a hole, there is nothing in it.

The product of a positive number and 14 more than seven times the number is 105. Find the two numbers. first number =______ and second number =_________

Answers

Let the positive number be [tex]x[/tex]

The expression is
[tex]x(14+7x)=105[/tex]⇒ expanding the bracket gives,
[tex]14x+7 x^{2} =105[/tex] ⇒ rearranging to equate one side to zero
[tex] 7x^{2} +14x-105=0[/tex] ⇒ Dividing each term by 7 to simplify
[tex] x^{2} +2x-15[/tex] ⇒ Factorising gives
[tex](x+5)(x-3)=0[/tex]
[tex]x=-5[/tex] and [tex]x=3[/tex]

Hence, the first number is -5 and the second number is 3

Answer:

can you explain it in more depth please

Step-by-step explanation:

The function h(x) = x2 + 6x + 7 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)

Part C: Determine the axis of symmetry for h(x). (2 points)

Answers

Part A.

The given equation is:

y = x^2 + 6x + 7

By completing the square:

y = (x^2 + 6x + 9) + 7 – 9

y = (x + 3)^2 – 2

y + 2 = (x + 3)^2

Part B.

The vertex form of a parabola is in the form:

y – k = 4p (x – h)^2

Where (h, k) is the vertex (x, y) of the parabola.

Therefore the vertex: (-3, -2)

Since 4p = 1, a positive number, therefore the parabola opens up which makes the vertex (-3, -2) the minima of the graph.

Part C.

The Axis of Symmetry is the x - coordinate of the vertex which is x = - 3

The graph and table shows the relationship between y, the number of words Jean has typed for her essay and x, the number of minutes she has been typing on the computer.

According to the line of best fit, about how many words will Jean have typed when she completes 60 minutes of typing?

2,500

2,750

3,000

3,250

Answers

Just follow the vertical line up from x = 60 and read off the number of words on vertical y axis.

You will find its 3,000.

The number of words Jean will type when she completes 60 minutes of typing is 3,000, This is further explained below Option C is correct

What is correlation?

Correlation is simply a relationship that exists between events or objects, A relationship between mathematical variables that are subject to variation.

In conclusion, The graph and table show the relationship between y and x

And the graph shows 3000 at "the number of words Jean has typed for her essay" axis denoted by y, for what she completes 60 minutes.