A one to one function is given. Write an equation for the inverse function
M(x)=4x^3-3

The correct answer is Option 4.

The factorized expression of 8^3 + 12x is 4(128+ 3x)

The expression is given as:

8^3 + 12x

Evaluate 8^3

8^3 + 12x = 512 + 12x

Factor out 2 from the expression

8^3 + 12x = 2(256+ 6x)

Factor out 2 from the expression

8^3 + 12x = 2 * 2(128+ 3x)

Evaluate the product

8^3 + 12x = 4(128+ 3x)

Hence, the factorized expression of 8^3 + 12x is 4(128+ 3x)

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Answer:

1 and 4

Step-by-step explanation:

x-1 = 0

x = 1

x^2 - 5x + 4

(x-4)(x-1) = 0

x can't be 1 or 4

Answer:  1 and 4

Step-by-step explanation:

1. To find excluded values, we need to make the denominator equal to zero.

x² - 5x + 4 = 0

2. Then we need to find the x the product of them was 4, but they add up to -5, which are -4 and -1. We get:

(x - 4)(x - 1) = 0

x - 4 = 0          x - 1 = 0

    x = 4               x = 1

These two numbers will make the denominator equal to 0, the denominator cannot be equal to 0, so they are excluded numbers.

The solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

A quadratic equations can be split to several equations and it can be solved as a whole

In this case, the quadratic equation is given as

-x^2 + 14x + 61 = 0

Using the form of the quadratic equation y = ax^2 + bx + c, we have

a = -1, b = 14 and c = 61

The quadratic equation can be solved using the following formula

x = (-b ± √(b^2 - 4ac))/2a

Substitute the known values of a, b and c in the above equation

x = (-14 ± √(14^2 - 4*-1*61))/2*-1

Evaluate the exponent

x = (-14 ± √(196 - 4*-1*61))/2*-1

Evaluate the products

x = (-14 ± √(196 + 244))/-2

Evaluate the sum

x = (-14 ± √(440))/-2

Express 440 as 4 * 110

x = (-14 ± √(4 * 110))/-2

Take the square root of 4

x = (-14 ± 2√110)/-2

Evaluate the quotient

x = 7 ± 2√110

Split the equation

x = 7 + 2√110 and x = 7 - 2√110

Hence, the solutions to the quadratic equation of the sprinkler in the exact form are x = 7 + 2√110 and x = 7 - 2√110

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Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

Assuming an uniform distribution, the standard deviation is given by:

[tex]S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size is found solving for n when the margin of error is of M = 0.006, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.006 = 1.96\frac{1.1547}{\sqrt{n}}[/tex]

[tex]0.006\sqrt{n} = 1.96 \times 1.1547[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 1.1547}{0.006}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 1.1547}{0.006}\right)^2[/tex]

n =  142,282.

A sample of 142,282 should be taken, which is not practical as it is too large of a sample.

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The value of the base b in the isosceles triangle is 3.1 inches.

According to the statement

we have given that the

equation is 2a + b = 15.7 and if one longer sides is 6.3 centimeter.

And we have to find the length of the base. Then

2a + b = 15.7

Here a is 6.3 cm then

Substitute the values in it then

2a + b = 15.7

2(6.3) + b = 15.7

After solving the equation

12.6 + b = 15.7

b = 15.7 - 12.6

Now we get the value of base b which is 3.1.

So, b = 3.1

So, The value of the base b in the isosceles triangle is 3.1 inches.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths.

If one of the longer sides is 6.3 centimeters, what is the length of the base?

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Answer:

45%

Step-by-step explanation:

Simply, 25/55 which gives you 0.454545.

Convert that to a percentage and you get 45%

Kayla made two errors which are as follows :-

How to Graph a Linear Inequality

First, graph the "equals" line, then shade in the correct area.

There are three steps:

Rearrange the equation so "y" is on the left and everything else on the right. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)Shade above the line for a "greater than" (y> or y≥)

       or below the line for a "less than" (y< or y≤).

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Answer:

12 walls

Step-by-step explanation:

Let's take everyone paints a different wall and there are no overlaps.

Given information from the question:

1.5 hours = 1 wall

1 hour =

[tex] \frac{1}{1.5} \\ = \frac{2}{3} walls[/tex]

per person.

From the information above, we can deduce:

6 people =

[tex] \frac{2}{3} \times 6 \\ = \frac{12}{3} \\ = 4 \: walls[/tex]

Since we know 6 people can paint 4 walls in an hour,

3 hours =

[tex]3 \times 4 \\ = 12 \: walls[/tex]

The value of x from the given circle is 4

The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

According to the theorem;

x * 3 = 2 * (4 + 2)

3x = 2(6)

3x = 12

Divide both sides by 3

3x/3 = 12/3

x =4

Hence the value of x from the given circle is 4

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The number 0.22 represents the population proportion and the correct way to represent it is p = 0.22.

Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.

It is given that:

It is given that:

The Department of Motor Vehicles reports that the proportion of all vehicles registered in California that are imported is 0.22.

The number 0.22 represent the population proportion.

The population proportion can be represented by the letter p:

p = 0.22

Thus, the number 0.22 represents the population proportion, and the correct way to represent it is p = 0.22.

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Answer:

Step-by-step explanation:

[tex]2x > 30+\frac{5}{4x} \\2x-\frac{5}{4x} > 30\\\frac{8x^2-5}{4x} > 30\\case~1\\if~x > 0\\8x^2-5 > 120x\\8x^2-120x > 5\\x^2-15x > \frac{5}{8} \\adding~(-\frac{15}{2} )^2~to~both~sides\\(x-\frac{15}{2} )^2 > \frac{5}{8}+\frac{225}{4} \\(x-\frac{15}{2} )^2 > \frac{455}{8} \\x-\frac{15}{2} < -\sqrt{\frac{455}{8} } \\x < \frac{15}{2}-\sqrt{\frac{455}{8} } \\or~x < 0\\rejected~as~x > 0[/tex]

[tex]x-\frac{15}{2} > \sqrt{\frac{455}{8} } \\x > \frac{15}{2} +\sqrt{\frac{455}{8} }[/tex]

case~2

[tex]if~x < 0\\8x^2-5 < 120x\\8x^2-120x < 5\\x^2-15x < \frac{5}{8} \\adding~(-\frac{15}{2} )^2\\(x-\frac{15}{2} )^2 < \frac{5}{8} +(-\frac{15}{2} )^2\\|x-\frac{15}{2} | < \frac{5+450}{8} \\-\sqrt{\frac{455}{8} } < x-\frac{15}{2} < \sqrt{\frac{455}{8} } \\\frac{15}{2} -\sqrt{\frac{455}{8} } < x < \frac{15}{2} +\sqrt{\frac{455}{8} } \\but~x < 0\\7.5-\sqrt{\frac{455}{8} } < x < 0[/tex]

The function f(x) = x² then the required function exists g(x) = -x²- 4.

The function exists described as y = f(x).

In mathematics, a function from a set X to a set Y allocates to each element of X exactly one element of Y. The set X exists named the domain of the function and the set Y exists named the codomain of the function. Functions stood originally for the idealization of how a variable quantity relies on another quantity.

For every x there exists a certain value of y.

From the graph g(x) exists reflection of f(x) at y = -4.

So g(x) = -f(x) - 4, the negative sign for reflection.

g(x) = -x² - 4

The required function exists g(x) = -x² - 4.

Therefore, the correct answer is option D. g(x) = -x² - 4.

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The complete question is:

F(x) = x². What is g(x)?

A. g(x) = x² - 4

B. g(x) = x² + 4

C. g(x) = -4x²

D. g(x) = -x² - 4

Answer: Neither

Step-by-step explanation:

It is not an angle of the quadrilateral, so it is not an interior angle.

It does not form a linear pair with any interior angle of the quadrilateral, so it is not an exterior angle.

The solutions to the exponential growth problem are:

A. [tex]P(t) = 260e^0.3662t[/tex]

B.[tex]P(3) = 260e^0.3662(3) = 779[/tex]

C.3.367 hours

The  exponential growth problem obeys the equation:

P(t) = P0ekt

P0=population

time t

We can find the value of k At t=3 hours as,

780 = 260e^k(3)

k = (1/3) ln(780/260) hours-1 ≅ 0.3662 hours-1

A. [tex]P(t) = 260e^0.3662t[/tex]

B. [tex]P(3) = 260e^0.3662(3) = 779[/tex]

C.  1870 = 260e^0.3662t

To Solve for t, w2e make t the subject of the formula

t = ln(1870/260) / 0.3662 hours = 3.367 hours

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The given number is :

[tex]\qquad❖ \: \sf \: \cfrac{ - 20}{ \sqrt{10} } [/tex]

since 10 isn't a perfect square, root 10 is an irrational number, and therefore the whole number is irrational as well, and we already know that irrational numbers are also part of real numbers.

[tex] \qquad \large \sf {Conclusion} : [/tex]

So the Correct choices are :

Answer:

Step-by-step explanation:

deleted

Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

According to thermodynamics, heat is a type of energy that crosses a thermodynamic system's border due to a temperature differential across the barrier. In a thermodynamic system, heat is not present.

But the phrase is also frequently used when referring to the thermal energy that makes up a system's internal energy and is reflected in the system's temperature. Heat is a type of energy in both senses of the word. Heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

Therefore, heat Factors are determined by the location-specific average daily high and low temperatures during the warmest month of the year.

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Based on the given graph relating to the company's profit f(x), the x-intercepts are (0, 0) and (0, 8) and the maximum value is 270.

The x-intercepts are the points where the graph crosses the x axis. It does so at first at (0,0) and then after going up and coming down, it again intersects at (0, 8).

The maximum value the graph reaches is 270 on the y-axis.

The function is increasing at the interval, (0, 4) and decreasing from (4, 8).

What this shows is that an increase in price between 0 and 4 would lead to an increase in profit but between 4 and 8 results in profits dropping.

In part B, the average rate of change from x=1 to x =4 is:

= (270 - 120) / (4 - 1)

= 50

In part c, the constraints are:

x ≥ 0

f(x) x ≤ 8

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Answer:

  20

Step-by-step explanation:

The sides of the 4-sided figure are the same length, so we can find the perimeter (sum of side lengths) by multiplying one side length by 4.

Points F(-2, -2) and G(-2, 3) lie on the same vertical line: x = -2. The distance between them is the difference of their y-coordinates:

  FG = (3 -(-2)) = 5

Each side is 5 units long.

The length of the four sides is ...

  P = 4s = 4(5) = 20

The perimeter of the rhombus is 20 units.

Answer:

Step-by-step explanation:

find the prime factors of given numbers:

126= 2*3*3*7- this side can be cut into any number here or combination of numbers as per factors

108= 2*2*3*3*3 - same as above

As per prime factors, the squares can be of  sizes:

2×2, 3×3, 6×6, 9×9 and 18×18

The least number can be obtained with the biggest size option 18×18, this will give 7*6=42 square

The most suitable measurements for a box with a square base are 5cm (width) x 5cm (length) x 640cm (height). This box would be worth $4875

To find the minimum value of a box that must have a square base and 16000 cm³, we must try different measurements to find the variable that represents the least value.

In this case, the variable that represents less value is a base of 5cm x 5cm and a height of 640cm. This means that the box would be worth $4875 as shown below.

Base

Sides

Additionally, we can check that the volume of the box is the required 16000cm³, as shown below:

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The answers to the question are given as x²y + 24x +16y and 87

(2xy + 24, x² + 16)

We have to check in order to be sure that the vector that we have here is a gradient field

we have fx = 2xy + 24 and fy = x² + 16

Such that we would have x²y + 24x +g(y)

for f(y) g' = 16 = 16 + c

Given that there is no lose of generality, we are going to have the following where

x²y + 24x +16y

b. We have to solve this oart by making use of the fundamental theory of integrals

f2,4 = 4*4 + 24*2 + 16*4

= 16 + 48 + 64

= 128

f1,1 = 1*1  + 24*1  + 16*1

= 1 + 24 + 16

= 41

128 - 41 = 87

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Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we consider:

Hence the amounts Gilberta and Maria have left after t hours are given by:

Gilberta has more papers when:

G(t) > M(t).

Hence:

35 - 4.3t > 30.5 - 3.4t

-0.9t < -4.5

Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

Hence the inequality is:

t < 5.

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Answer:

t < 5

Step-by-step explanation:

Other dude is right but here's the version without explanation

Using the probability concept, the likelihood of landing on 2 or 3 is given by:

[tex]p = \frac{3}{8}[/tex]

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, considering the areas of 2 and 5 counting twice, the spinner has 8 areas, out of which 3 are 2 or 3, hence the probability is given as follows:

[tex]p = \frac{3}{8}[/tex]

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The answers to the question are:

This is the number of calls for the help desk

160000/3200 = 50per call

network center

735000/9800

= 75 per device that was monitored

Electronic mail

100000/10000 =

10 for the mail account

For smart phone support

124600/8900

= 14 per phone extension

for helpdesk

5200 * 0.25 * 0.96 *1.5 calls * $50

= 93600

For network center

(5200 * 0.25 * 0.96) + 600] x 75

= 138600

For Electronic mail

5200 * 0.25 * 0.96 * 10 per email account

= 12480

Smart support charge

5200 * 0.25 * 14 = 18200

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Answer:

87 adults

174 children

70 students

Step-by-step explanation:

Answer:

15.25 given using both

Step-by-step explanation:

Slow com= 60 all mail

Fast clm= 15 all mail

Given both bejng used

60 min ÷ 15 min = intervall of 4 unbroken min

and

15min÷60min= 0.25

0.25mjn×60sec= 15sec

Sret =15min anfd 15 seconds/ 15.25min

The solution to the question is mathematically given as

1)

H0: M [tex]\geqslant[/tex] 300

H0: M [tex]\geqslant[/tex] 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]

(1):

H0: M [tex]\geqslant[/tex] 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M [tex]\geqslant[/tex] 300 dollars:

(This is a left-tailed test)

(2):

when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.

(3):

[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]

(4):

[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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Answer:

  459

Step-by-step explanation:

The "long division method" algorithm for square root makes use of the relation described by the square of a binomial.

  (a +b)² = a² +2ab +b² = a² +b(2a +b)

The value for which the root is desired is written with digits marked off in pairs either side of the decimal point.

The initial digit of the root is the integer part of the square root of the most-significant pair. Here that is floor(√21) = 4. This is shown in the "quotient" spot above the leftmost pair. The square of this value is subtracted, and the next pair brought down for consideration. Here, that means the next "dividend" is 506.

The next "divisor" will be 2 times the "quotient" so far, with space left for a least-significant digit. Here, that means 506 will be divided by 80 + some digits. As in regular long division, determining the missing digit involves a certain amount of "guess and check." We find that the greatest value 'b' that will give b(80+b) ≤ 506 is b=5. This is the next "quotient" digit and is placed above the "dividend" pair 06. The product 5(85) = 425 is subtracted from 506, and the next "dividend" pair is appended to the result. This makes the next "dividend" equal to 8181.

As in the previous step, the next "divisor is 2 times the quotient so far: 2×45 = 90, with space left for the least significant digit. 8181 will be divided by 900-something with a "quotient" of 9. So, we subtract the product 9(909) = 8181 from the "dividend" 8181 to get the next "dividend." That result is zero, so we're finished.

The root found here is 459.

__

Additional comment

In practice, roots are often computed using iterative methods, with some function providing a "starter value" for the iteration. Some iterative methods can nearly double the number of good significant digits in the root at each iteration.

Using this "long division method," each "iteration" adds a single significant digit to the root. Its advantage is that it always works, and is generally suitable for finding roots by hand. Once the number of root digits begins to get large, the "divisor" starts to be unwieldy.