evalute a/b for a= -6 and b=-2

(1) p value is 0.234. So the 4th option is correct.

(2) p value grater that any alpha values so we fail to reject the null. So the 4th option is correct.

(3) The outcome is significant if the null hypothesis is rejected. So the third option is the correct choice.

4) We lack sufficient data to claim that UF students who are Florida residents differ from non-Florida residents in the average number of cities they have lived in since we are unable to reject the null hypothesis.

We consider the following hypothesis-

H0: µ1 = µ2 vs H1: µ1 ≠ µ2

Where µ1 is the population mean of the non FL res

µ2 is the population mean of the FL res

1) p value = 0.234

(Obtained by p value calculator corresponding to the test statistic at 0.05 significance level with degrees of freedom 232+1224-2 = 1454)

Hence the 4th option is correct.

2) We know if p value ≤ α we reject the null.

Here since p value grater that any alpha values so we fail to reject the null.

Hence the 4th option is correct i.e, t none of the usual α.

(3) The outcome is significant if the null hypothesis is rejected. This conclusion is neither statistically nor practically significant because we are unable to reject the null hypothesis. The third option is the correct choice.

(4) We lack sufficient data to claim that UF students who are Florida residents differ from non-Florida residents in the average number of cities they have lived in since we are unable to reject the null hypothesis.

To learn more about population mean link is here

brainly.com/question/19538277

#SPJ4

The right question is given below:

a) Composite function fog(x) = 3/(x+3)

b) Domain of fog(x) in interval notation = (-∞,-3)∪(-3,∞)

A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.

Given functions,

f(x) = x/(x+2)

g(x) = 6/x

a) (fog)(x) = f(g(x))

= f(6/x)

= (6/x)/((6/x) + 2)

= 6/x((6/x) + 2)

= 6/(6 + 2x)

= 3/(x+3)

fog(x) = 3/(x+3)

b) Domain of (fog)(x)

y = 3/(x+3)

For domain y = 0

⇒ x+3  = 0

⇒ x  = -3

But the function gets undefined for x = -3

So, Domain x ≠ -3

⇒ x > -3 or x < -3

Domain set Interval Notation : (-∞,-3)∪(-3,∞)

Hence, value of composite function

fog(x) = 3/(x + 3)

Domain of fog(x) : (-∞,-3)∪(-3,∞)

Learn more about function here:

https://brainly.com/question/12431044

#SPJ1

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer:

Step-by-step explanation:

Given GP with:

We can find the common ratio:

Using the nth term formula we can work out the first term:

So the explicit rule is:

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

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

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

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

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

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

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

For more such questions on remainder visit:

https://brainly.com/question/29347810

#SPJ8

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

Know more about the domain here:
https://brainly.com/question/30096754

#SPJ8

Answer:

Step-by-step explanation:

y=mx+b

m=(y2-y1)/((x2-x1)

m=(12-7.5)/(120-30)

m=0.05

y=0.05x+b, using point (30,7.5)

7.5=0.05(30)+b

7.5=1.5+b

b=6

y=0.05x+6

Answer:

0.0017784 m2

Step-by-step explanation:

Answer:

17,784 cm²

Step-by-step explanation:

\(3.42 \times 5.2 = \frac{342}{100} \times \frac{52}{10} = \frac{17784}{1000} = 17.784\)

The difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years is $1.32.

Simple interest is when only the amount deposited increases in value.

Simple interest = deposit x interest rate x time

1750 x 0.0275 x 2 = $96.25

Interest earned with compounding = future value - amount deposited.

The formula for calculating future value:

FV = P (1 + r) nm

1750 x (1/0275)^2 = $1847.57

$1847.57 - $1750 = $97.57

Difference in interest; $97.57 - $96.25 = $1.32

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

answer: the student made an error. The first factor, 9, was distributed to only one of the terms inside the parentheses

Answer:

\(8x + 152 = 224 \\ 8x = 72 \\ x = 9\)

Answer:

Slope: m = 0

Equation: y = -3

Step-by-step explanation:

A line perpendicular to the y-axis always has a slope of 0. Slope is calculated by (y2-y1)/(x2-x1) or rise/run or delta y/delta x (they're all the same thing, delta means difference and is notated with a triangle). When there is no change in y (perpendicular to the y-axis), no matter what the change in x is, the slope will be 0.

Since it is given that one of the points has a y-value of -3, the equation for this line would be y = -3. The formula for a linear equation is y=mx+b. Since the slope is 0, the value of mx is 0, and therefore not needed in the equation. b represents the y-intercept and in this case would be -3.

The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is \((\infty,-1] \cup [1,\infty)\).

The Domain of a function f(x) is the set of all values for which the function is defined.

The Range of a function is the set of all values that f takes.

As, \(sec x=\frac{1}{cos x}\) , so sec x is defined where \(cos x \neq 0\).

It implies, sec(3.14t/4) is defined where \(cos(3.14t/4)\neq 0\).

The cosine is 0 at \((2n+1)\frac{\pi }{2}\) , where n is any integer.

Now, \(\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}\)

         \(\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}\)

       \(t=2(2n+1)\\t=2+4n\)

Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.

Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is \((\infty,-1] \cup [1,\infty)\).

To learn more about the Domain and Range of a function visit : brainly.com/question/28135761

#SPJ9

Answer:

The volume is  \(dV = 19.2 \pi \ cm^3\)

Step-by-step explanation:

From the question we are told that

    The height is  h =  20 cm

    The diameter is  d = 8 cm

    The thickness of both top and bottom is  dh  =  2 * 0.1  =  0.2 m

     The  thickness of one the side is dr =  0.1 cm

The  radius is mathematically represented as

            \(r = \frac{d}{2}\)

substituting values

            \(r = \frac{8}{2}\)

           \(r = 4 \ cm\)

Generally the volume of a cylinder is mathematically represented as      

       \(V_c = \pi r^2 h\)

Now the partial differentiation with respect to h is  

       \(\frac{\delta V_v}{\delta h} = \pi r^2\)

Now the partial differentiation with respect to r is  

      \(\frac{\delta V_v}{\delta r} = 2 \pi r h\)

Now the Total differential of \(V_c\) is mathematically represented as

       \(dV = \frac{\delta V_c }{\delta h} * dh + \frac{\delta V_c }{\delta r} * dr\)

       \(dV = \pi *r^2 * dh + 2\pi r h * dr\)

substituting values

      \(dV = \pi (4)^2 * (0.2) + (2 * \pi (4) * 20) * 0.1\)

     \(dV = 19.2 \pi \ cm^3\)

(I deleted my answer because it was incorrect)

When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.

When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.

The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.

Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.

To learn more about arithmetic growth and geometric growth link is here

brainly.com/question/3927222

#SPJ4

The solution to the inequality is -3 ≤ x ≤ -1/3

Given the inequality:

4|3x+5| ≤ 16

Let us simplify it by dividing both sides by 4 to get:

|3x+5| ≤ 4

Next, we can break the inequality into two cases, depending on whether 3x+5 is positive or negative:

First: 3x+5 ≥ 0

In this case, the inequality simplifies to:

3x+5 ≤ 4

Subtracting 5 from both sides, we get:

3x ≤ -1

Dividing by 3 (which is positive) gives:

x ≤ -1/3

Second: 3x+5 < 0

In this case, the inequality simplifies to:

-3x-5 ≤ 4

Adding 5 to both sides, we get:

-3x ≤ 9

Dividing by -3 (which is negative and requires us to flip the inequality), gives:

x ≥ -3

Therefore, the solution to the inequality is:

-3 ≤ x ≤ -1/3

The interval [-3,-1/3] is the solution set, and it includes all values of x between -3 and -1/3, including the endpoints.

Learn more about inequality here:

https://brainly.com/question/24372553

#SPJ1

Answer: A 15/100

Step-by-step explanation:

1. Convert 17/20 into percents

2. You get 85% Which is how much of her homework she has completed

3. To find what she has left subtract 85 from 100

4. You get 15 or 15/100 or 15% more of the test she hasn’t completed and needs to complete

Answer:

you have 10 cupcakes and give away 2 which is 20% of 10

Step-by-step explanation:

The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

learn more on sector here: https://brainly.com/question/22972014

#SPJ1

The distance you can see along the surface of the earth from the top of a tower of height h above the surface is approximately s = v(2hR), where R is the radius of the earth.

When you are at the top of a tower height h above the surface of the earth, you can see a certain distance along the surface. This distance can be approximated by the formula s = v(2hR), where R is the radius of the earth.

To understand why this formula works, imagine drawing a triangle with the tower, the point where you are looking, and the point on the surface of the earth directly below your line of sight. This forms a right triangle, where the height is h, the hypotenuse is the distance you can see (s), and the base is the radius of the earth (R).

Using the Pythagorean theorem, we can solve for s:

Taking the square root of both sides, we get:

Since R is much larger than h, we can approximate s as:

Expanding this expression using the binomial theorem and dropping the higher-order terms, we get:

Therefore, the distance you can see along the surface of the earth from the top of a tower of height h above the surface is approximately s = v(2hR), where R is the radius of the earth.

Learn more about the Radius of a Sphere:

https://brainly.com/question/1293273

#SPJ4

The domain of the function or relation is {6, 9, -4 and 2}

The function is represented by the set of relation or ordered pairs

The ordered pairs in the relation are:

(x, y)  = (6, -3), (9, -3), (-4, 1) and (2, 1)

Remove the y values in the above domain

x = 6, 9, -4 and 2

The x values represent the domain of the function

Hence, the domain of the function or relation is {6, 9, -4 and 2}

Read more about domain at:

https://brainly.com/question/1770447

#SPJ1

Answer:

96

Step-by-step explanation:

to be honest i just looked it up on google

Answer:

B

Step-by-step explanation:

Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Triangle LMN was dilated by a scale factor of 2 followed by a translation 1 unit right and 3 unit up to form triangle L'M'N'

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

The limit of the given function as x approaches 1 is 0.

To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:

1. Begin by substituting x = 1 into the numerator:

\(\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\]\)

2. Now, substitute x = 1 into the denominator:

(1³ + 5)(1 - 1) = 6(0) = 0

3. Finally, divide the numerator by the denominator:

0/0

The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:

4. Take the derivative of the numerator:

\(\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\]\)

5. Take the derivative of the denominator:

\(\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\]\)

6. Substitute x = 1 into the derivatives:

Numerator: \(\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\]\)

Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6

7. Now, reevaluate the limit using the derivatives:

lim as x approaches 1 of \(\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\]\)

= 0 / 6

= 0

Therefore, the limit of the given function as x approaches 1 is 0.

For more such questions on L'Hôpital's rule

https://brainly.com/question/24116045

#SPJ8