domain of f(x).
8. The functions fand g on the set of real
numbers are defined by f(x) = 3x - 1
and g(x)=5x+2 respectively. Find:
(a) f(g(x)]
(b) g[f(x)]
(c) f'(x)
(d) g ¹ (x)
(e) f'(g(x))
(f) g¹[f(x)]

The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C:  [130.10, 143.90]

Suppose that we have:

Then the confidence interval is obtained as

\(\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}\)

\(\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\)

For this case, we're given that:

At this level of significance, the critical value of Z is: \(Z_{0.1/2}\) = ±1.645

Thus, we get:

\(CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90]\)

Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C:  [130.10, 143.90]

Learn more about confidence interval for population mean from large samples here:

https://brainly.com/question/13770164

The ratio of y to x is 5 to 1. That means every time y increases by 5, x increases by 1

Answer:

The Answer is gonna be B.

You will get better rates on a home loan

This is the Answer for your question :3

I hope you are having a great day ❤️❤️❤️

Answer:

78

Step-by-step explanation:

Answer:

i need a photo

Step-by-step explanation:

Step-by-step explanation:

\( = \lim \limits_{x \to - 4} \frac{ \sqrt{x + 20} - \sqrt{12 - x} }{ {x}^{2} + 3x - 4 } \)

\( = \lim \limits_{x \to - 4} \frac{ \sqrt{x + 20} - \sqrt{12 - x} }{(x + 4)(x - 1)} \times \frac{ \sqrt{x + 20} + \sqrt{12 - x} }{ \sqrt{x + 20} + \sqrt{12 - x } } \)

\( = \lim \limits_{x \to - 4} \frac{ {( \sqrt{x + 20} )}^{2} - {( \sqrt{12 - x} )}^{2} }{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )} \)

\( = \lim \limits_{x \to - 4} \frac{x + 20 - 12 + x }{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )} \)

\( = \lim \limits_{x \to - 4} \frac{2x + 8}{(x + 4)(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )} \)

\( = \lim \limits_{x \to - 4} \frac{2 \cancel{(x + 4)}}{ \cancel{(x + 4)}(x - 1)( \sqrt{x + 20} + \sqrt{12 - x} )} \)

\( = \lim \limits_{x \to - 4} \frac{2}{(x + 1)( \sqrt{x + 20} + \sqrt{12 - x} )} \)

\( = \frac{2}{( - 4 + 1)( \sqrt{ - 4 + 20} + \sqrt{12 + 4} ) } \)

\( = \frac{2}{( - 3)( \sqrt{16} + \sqrt{16}) } \)

\( = \frac{2}{( - 3)(4 + 4)} \)

\( = \frac{2}{( - 3)(16)} \)

\( = \frac{1}{( - 3)(8)} \)

\( = - \frac{1}{24} \)

i) Based on exponential growth, Xavier's salary in 2015 is £44,274.

ii) The year that Xavier's salary first became greater than £47,500 would be 2019.

Exponential functions show the relationship between two variables and a variable exponent with a periodic constant rate of growth or decay in the value of something

Annual increase in Xavier's salary = 2% or 0.02

Xavier's salary in 2010 = £40,100

The number of years between 2015 and 2010 = 5 years

i) y = £40,100(1.02)^5

= £44,273.64

= £44,274

ii) £47,500 = £40,100(1.02)^t

t = 9 years

= 2019 (2010 + 9)

Learn more about exponential functions at https://brainly.com/question/30241796.

#SPJ1

The box should have base 52 cm by 52 cm and height 26 cm.

What is volume?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

The Volume of a box with a square base x by x cm and height h cm is

\(V = x^2h\)

Since the surface area directly affects the amount of material used, we can reduce the amount of material by reducing the surface area.

The surface area of the box described is  \(A = x^2 + 4xh\)

We need A as a function of x alone, so we'll use the fact that

\(V = x^2h= 70304 cm^3\)

⇒ \(h = \frac{70304}{x^2}\)

So, the area becomes,

\(A = x^2+4x(\frac{70304}{x^2})\\ A = x^2 + \frac{281216}{x}\)

We want to minimize A, so

\(A' = 2x - \frac{281216}{x^2} =0\\\frac{2x^3-281216}{x^2}=0\\ {2x^3-281216} = 0\\x^3 - 140608=0\\x^3 = 140608\\x = 52\)

The second derivative test verifies that A has a minimum at this critical number:

\(A'' = 2+\frac{562432}{x^3}\)  which is positive at x = 52.

Now,

\(h = \frac{70304}{x^2}= \frac{70304}{(52)^2}=26\)

Hence, The box should have base 52 cm by 52 cm and height 26 cm.

To know more about volume, click on the link

https://brainly.com/question/463363

#SPJ4

The time which takes the call is $5.00 with the given ratio is 50 minutes.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Given that,

$0.10 for 1 minute

The ratio of time to cost = 1/0.10 = 10

Let's say the time taken in $5 is x minutes

The ratio of time to cost = x/5

x/5=10

x = 50 minutes

Hence "The time which takes the call is $5.00 with the given ratio is 50 minutes".

For more information about ratios and proportions,

brainly.com/question/26974513

#SPJ2

This statement is true, and if \(x^3\)  is irrational then x is also irrational. N: 2, 7, 8, 9.The proof that if \(x^3\)is irrational, then x is also irrational can be demonstrated by contradiction.

Suppose that x is a rational number, meaning that there exist integers a and b not equal to 0 such that x = a/b. Then,\(x^3 = a^3/b^3\), and since the cube of a fraction is a fraction, \(x^3\) is rational. Thus, by definition of rational, there exist real numbers c, f not equal to 0 such that\(x^3\) = c/f. Therefore, if x is rational then \(x^3\) is rational, or equivalently if\(x^3\) is irrational then x is irrational. Thus, this statement is true, and if \(x^3\) is irrational then x is also irrational. N: 2, 7, 8, 9.The proof that if \(x^3\) is irrational, then x is also irrational can be demonstrated by contradiction.

Learn more about irrational here:

https://brainly.com/question/15837135

#SPJ4

Answer:

110/24 feet

Step-by-step explanation:

Step one:

Given data

A basketball hoop is 10 1/24 feet high

Mark is 5 11/24 feet tall

Required

The distance from Mark's head to the top of the hoop

Step two:

the solution is the difference between the two heights

=10 1/24 - 5 11/24

let us convert the mixed fraction to simple fraction

=241/24- 131/24

LCM = 24

= 241-131/24

=110/24 feet

Answer:

180 g oats

0.9 L milk

45 g sugar

Step-by-step explanation:

those are all divided by 3/4 making just 3 portions :D

Answer:38.4 times 3 divided by 2

Step-by-step explanation:

Answer:

there would be 21 cents

Answer:

they would be 21 cents coins

HOPE IT WILL HELP U!

The total amount Ofelia had was $ 15.

The equations are mathematical statements with two algebraic expressions flanking the equal to the sign on either side.

It can demonstrate the equality of the relationship between the expressions printed on the left and right sides.

There are some components of an equation, that are:

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign.

The "=" sign determines on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is equal to the original amount of money

The amount Ofelia spends = $ 12

The remaining amount of money Ofelia had=(1/5)A

So, the equation will be

subtract the original amount of money A - amount Ofelia spends = remaining amount of money Ofelia had

By substituting the values in the equation, we get

A - 12 = ( 1/5 )A

Add 12 on both sides of the equation, and we get

A = (1/5)A + 12

Subtract (1/5 )A on both sides of the equation, and we get

A - ( 1/5 )A = 12

On simplifying the equation, we get

(5A - A)/5 = 12

4A/5 = 12

Multiplying by 5 on both sides of the equation, we get

4A = 60

Divide by 4 into both sides of the equation, and we get

A = $ 15

The value of A is $ 15

Hence, the original amount is $ 15

To learn more about equations:

https://brainly.com/question/229500

#SPJ4

The appropriate sample size formula on the TI-84 calculator, you can determine the sample size needed to achieve your desired margin of error for estimating population parameters.

To find the sample size with a desired margin of error on a TI-84 calculator, you can use the following steps:

1. Determine the desired margin of error: Decide on the maximum allowable difference between the sample estimate and the true population parameter. For example, if you want a margin of error of ±2%, your desired margin of error would be 0.02.

2. Determine the confidence level: Choose the desired level of confidence for your interval estimate. Common choices include 90%, 95%, or 99%.

Convert the confidence level to a corresponding z-score. For instance, a 95% confidence level corresponds to a z-score of approximately 1.96.

3. Calculate the estimated standard deviation: If you have an estimate of the population standard deviation, use that value. Otherwise, you can use a conservative estimate or a pilot study's standard deviation as a substitute.

4. Use the formula: The sample size formula for estimating a population mean is n = (z^2 * s^2) / E^2, where n represents the sample size, z is the z-score, s is the estimated standard deviation, and E is the desired margin of error.

5. Plug in the values: Input the values of the z-score, estimated standard deviation, and desired margin of error into the formula. Use parentheses and proper order of operations to ensure accurate calculations.

6. Calculate the sample size: Perform the calculations using the calculator, making sure to include the appropriate multiplication and division symbols. The result will be the recommended sample size to achieve the desired margin of error.

To know more about parameters refer here:

https://brainly.com/question/29911057#

#SPJ11

The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference.

Mathematicians use the term "radius" to label any line segment from the center of a circle to any point on the circle  is likely due to the historical development of geometry and the influence of Latin and Greek languages. and it helps to describe the size and properties of the circle.

The concept of the radius helps us understand the distance between the center of the circle and any point on its circumference. It is a fundamental measurement in geometry and is used in various mathematical formulas and equations involving circles.

In geometry, the study of circles and their properties has a long history that dates back to ancient times. The ancient Greek mathematicians, including Euclid, made significant contributions to the development of geometry. The Greek language was widely used in mathematics during that period.

The term "radius" itself originates from Latin and means "spoke of a wheel." It refers to the line segment from the center of a circle to any point on the circle, which resembles the spoke of a wheel radiating outwards. The concept of the radius played a fundamental role in understanding the properties of circles and their relationships with other geometric figures.

When mathematicians formalized the study of circles and developed a standard terminology, the term "radius" was adopted to describe this important line segment. Since mathematics often draws from historical and cultural influences in naming concepts, it is likely that the term "radius" was chosen to maintain consistency with its historical usage and to evoke the visual image of lines radiating from a center.

While the term "radius" may have originated from the analogy to a wheel spoke, its adoption and usage in mathematics have become established conventions that provide a concise and universally understood way to refer to this key element of a circle.

To know more about radius visit:

https://brainly.com/question/13449316

#SPJ11

The amount of the galleys or the number of galleys.

If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.

If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.

Learn more about Missing Ratio on:

https://brainly.com/question/16711686

#SPJ4

To prove that the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in a compact space x is compact, we need to show that any open cover of this sequence has a finite subcover. Here is the step-by-step explanation of the proof:

1. Let {Uα} be an open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x.
2. Since z1 is a closed subset of x, its complement, x - z1, is open.
3. Since {Uα} is an open cover of the sequence, there must exist an α1 such that z1 ⊆ Uα1.
4. Now, consider the set z2. It is a closed subset of x, so its complement, x - z2, is open.
5. Since {Uα} is an open cover of the sequence, there must exist an α2 such that z2 ⊆ Uα2.
6. By continuing this process, we can find α3, α4, and so on, such that z3 ⊆ Uα3, z4 ⊆ Uα4, and so on.
7. Since the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... is decreasing, we have z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN for any positive integer N.
8. Now, consider the subcover {Uα1, Uα2, ..., UαN} of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
9. Since {Uα} is an open cover of the sequence, each zN is covered by at least one Uα.
10. Therefore, the subcover {Uα1, Uα2, ..., UαN} is a finite subcover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... ⊇ zN.
11. Thus, we have shown that any open cover of the sequence z1 ⊇ z2 ⊇ z3 ⊇ ... has a finite subcover.
12. Therefore, the sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... in the compact space x is compact.
In summary, the proof demonstrates that in a compact space x, any sequence of nonempty closed subsets z1 ⊇ z2 ⊇ z3 ⊇ ... is also compact.

subsets : https://brainly.com/question/13458417

#SPJ11

To solve this we must be knowing each and every concept related to exponential decay and its calculations. Therefore, y=a.b(x) with o<b<1 is the equations that  best describes exponential decay. The correct option is option A.

Exponential decay is indeed a scalar many of the exponential function, which has a known expected value (i.e. the individual lifespan of each item is exponentially distributed).

It may be stated as y=a(1-b)x, where y seems to be the ultimate amount, an is indeed the initial amount, b is indeed the decay factor, as well as x seems to be the time elapsed. y=a.b(x) with o<b<1 is the equations that  best describes exponential decay.

Therefore, y=a.b(x) with o<b<1 is the equations that  best describes exponential decay. The correct option is option A.

To know more about  exponential decay, here:

https://brainly.com/question/2193799

#SPJ1

The worth of the car after it is paid off 5 years later given the rate of exponential depreciation is $32,842.34.

When the car declines in value, it means that the car is depreciating. The formula that can be used to determine the value of the car with the depreciationn rate is:

FV = P (1 - r)^n

$42,000 x (1 - 0.048)^5 = $32,842.34

To learn more about future value, please check: https://brainly.com/question/18760477

Answer: The equation to solve is:

(x3y3+x2y2+xy+1)ydx+(x3y3−x2y2−xy+1)xdy=0

t3−t2−t+1t3+t2+t+1dt=dxx

any more help just ask :)

The required lengths of side of triangle are 15 in, 16 in and 17 in.

Given :

The sum of the angles of a triangle is always 180°

Given that :

Sides of a triangle are consecutive integers.

Also given that,

Perimeter of triangle is 48.

Let the sides of triangle are x, x + 1 and x + 2.

x + x + 1 + x + 2 = 48

3x = 48 - 3

3x = 45

divide by 3 on both sides

x = 15

The length of the triangles  

x + 1 = 15 + 1 = 16

x + 2 = 15 + 4 = 17

The side lengths of the triangle are 15, 16 and 17.

Learn more about the triangle here:

https://brainly.com/question/2773823

#SPJ4

Answer:

A. It increased both her intensity and her workout time.

Step-by-step explanation:

A. It increased both her intensity and her workout time.

B. It decreased her intensity but increased her workout time.

C. It increased her intensity but decreased her workout time.

D. It decreased both her intensity and work out time

Last week = 4 miles per day

This week = 5 miles per day

Intensity refers to how hard one exercises.

Workout time refers to how long one exercises the body.

By adding a mile, she has increased how hard she exercises her body (intensity))

And also increased how long she exercises the body (workout time) because the time she spent on 5 miles per day is more than time spent on 4 miles per day

Answer:

47.7

Step-by-step explanation:

length x width x height

6 x 3 x 2.65

Answer:

x = - 3 , y = - 4

Step-by-step explanation:

Given

- \(\frac{5}{7}\) - \(\frac{11}{7}\) x = - y ( multiply through by 7 to clear the fractions )

- 5 - 11x = - 7y ( rearrange )

- 11x + 7y = 5 → (1)

2y = 7 + 5x ( rearrange )

- 5x + 2y = 7 → (2)

Multiplying (1) by - 2 and (2) by 7 and adding will eliminate y

22x - 14y = - 10 → (3)

- 35x + 14y = 49 → (4)

Add (3) and (4) term by term to eliminate y

- 13x = 39 ( divide both sides by - 13 )

x = - 3

Substitute x = - 3 into (2) and solve for y

- 5(- 3) + 2y = 7

15 + 2y = 7 ( subtract 15 from both sides )

2y = - 8 ( divide both sides by 2 )

y = - 4

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

Learn more about holding period

brainly.com/question/32568151

#SPJ11

if the tangent line to y = f ( x ) at ( 6 , 2 ) passes through the point ( 0 , 1 ) , then f(6) = 2 and f'(6) = 1/6.

To find f(6), we can use the fact that the tangent line to y = f(x) at (6, 2) passes through the point (0, 1). The equation of a line can be written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

Since the line passes through (6, 2) and (0, 1), we can substitute these values into the equation to get:

2 - 1 = m(6 - 0)

1 = 6m

Solving for m, we find m = 1/6.

Since the slope of the tangent line is equal to the derivative of f(x) at x = 6, we have f'(6) = 1/6.

Now, to find f(6), we can integrate f'(x) with respect to x:

f(x) = ∫(f'(x))dx = ∫(1/6)dx = (1/6)x + C

To find the value of C, we can substitute the point (6, 2) into the equation:

2 = (1/6)(6) + C

2 = 1 + C

C = 1

Therefore, f(x) = (1/6)x + 1.

Substituting x = 6 into the equation, we get:

f(6) = (1/6)(6) + 1 = 2.

So, f(6) = 2 and f'(6) = 1/6.

You can learn more about tangent line  at

https://brainly.com/question/30162650

#SPJ11