identify the horizontal aysmptote of each graph. t(x)=6^x

Answer:

applying one way ANOVA:

R² = SSR / SST

    = 0.133/1.807

     =0.0734

Source of Variation SS     df       MS       F   P-value    F0.05(2.27)

treatments               0.133      2      0.066      1.069   0.3574      3.354

error                       1.675     27     0.062    

Total                        1.807     29    

as p value is not significantly low:

Do the ANOVA results indicate that the null hypothesis (H0) can be rejected in favor of the alternative hypothesis (HA)? -No

Step-by-step explanation:

Answer:

The dimensions of the page are

3.46 ft by 5.20 ft

Step-by-step explanation:

Let

x---> the length of the sheet of paper in feet

y ---> the width of the sheet of paper in feet

[tex]A=xy[/tex]

[tex]A=18\ ft^2[/tex]

so

[tex]18=xy[/tex]

[tex]y=\frac{18}{x}[/tex] -----> equation A

Remember that

[tex]1\ ft=12\ in[/tex]

Convert the margins into feet

[tex]9\ in=9\12=0.75\ ft[/tex]

[tex]6\ in=6\12=0.50\ ft[/tex]

so

we know that

The area of the largest printed area is given by

[tex]A=(y-0.75-0.75)(x-0.50-0.50)[/tex]

[tex]A=(y-1.50)(x-1)[/tex]

[tex]A=xy-y-1.50x+1.50[/tex]

substitute equation A in the above expression

[tex]A=x(\frac{18}{x})-\frac{18}{x}-1.50x+1.50\\[/tex]

[tex]A=18-\frac{18}{x}-1.50x+1.50[/tex]

[tex]A=19.50-\frac{18}{x}-1.50x[/tex]

Now we have an output (A) in terms of only one variable (x),

so

we differentiate:

[tex]\frac{dA}{dx}=\frac{18}{x^2}-1.50[/tex]

equate to zero

[tex]\frac{18}{x^2}=1.50[/tex]

[tex]x^2=12\\x=3.46\ ft[/tex]

Find the value of y

[tex]18=(3.46)y\\y=5.20\ ft[/tex]

therefore

The dimensions of the page are

3.46 ft by 5.20 ft

The required dimensions are,

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

The formula of the area of the rectangle is [tex]A=l \times b[/tex]

Let [tex]A[/tex] be the area of the paper then,

[tex]A=(x+18)(y+12)...(1)[/tex]

And the printed area is [tex]xy=18...(2)[/tex]

Now, from the equation (1) and (2) we get,

[tex]A=(x+18)(\frac{18}{x}+12)\\ A=234+12x+\frac{324}{x} ..(3)[/tex]

Now, differentiating equation (3)

[tex]\frac{dA}{dx}=12-\frac{324}{x^2} \\\frac{dA}{dx}=0\\12-\frac{324}{x^2} =0\\x=3\sqrt{3}[/tex]

Substituting the obtained value of [tex]x[/tex] into the equation (2)

[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]

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Answer:

y=1

Step-by-step explanation:

6=2(y+2)

Divide each side by 2

6/2=2/2(y+2)

3 = y+2

Subtract 2 from each side

3-2 = y+2-2

1 = y

Answer:

y = 1

Step-by-step explanation:

6 = 2 ( y + 2 )

6 = 2y + 4

subtract four from both sides

2 = 2y

divide by 2 on both sides

y = 1

Answer:

Required average rate of change over the interval [1.9, 2] is 5.9, [1.99, 2] is 5.99, [2, 2.1] is 6.1, [2, 2.01] is 6.01 and the instantaneous change at x=2 is 6.

Step-by-step explanation:

Given function is,

[tex]f(x)=x^2+2x+9[/tex]

To find the avarage rate of change over given intervals. We know from Lagranges Mean value theorem, the average rate of change of a function F(x) over a interval [tex]a\leq x\leq b[/tex] is, [tex]\frac{f(b)-f(a)}{b-a}[/tex].

(a) On the interval,

[tex]\frac{f(2)-f(1.9)}{2-1.9}= \frac{17-16.41}{0.1}=5.9[/tex]

[tex]\frac{f(2)-f(1.99)}{2-1.99}= \frac{17-16.9401}{0.1}=5.99[/tex]

(b) On the interval,

[tex]\frac{f(2.1)-f(2)}{2.1-2}= \frac{17.61-17}{0.1}=6.1[/tex]

[tex]\frac{f(2.01)-f(2)}{2.01-2}= \frac{17.0601-17}{0.01}=6.01[/tex]

(c) Instantaneous rate of change at x=2 is,

[tex]\lim_{x\to 2}\frac{\Delta y}{\Delta x}=\lim_{x\to 2}\frac{f(2)-f(x)}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{17-x^2-2x-9}{2-x}[/tex]

[tex]=\lim_{x\to 2}\frac{-(x+4)(x-2)}{-(x-2)}[/tex]

[tex]=\lim_{x\to 2}(x-4)[/tex]

[tex]=6[/tex]

Hence the results.

Answer:

The two integers the square root of 62 falls between are 7, and 8.

Step-by-step explanation:

the square root of 62 is 7.874.... so the numbers that it is between are 7 and 8 because its more than 7 but less than 8

The 62 will be in between of square root of 7 and 8.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

The square root of relevant numbers are given below,

2² = 4 , 3² = 9 , 4² = 16 ,5² = 25 , 6² = 36, 7² = 49,8² = 64 ,9² = 81

Now the number 61 is lying in between 49 and 64

So,

"The 62 will be in between of square root of 7 and 8".

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Answer:

The final approximation integral answer is 1.8975

Answer:

(See explanation)

Step-by-step explanation:

The expression is simplified as follows:

[tex]63 + 81[/tex]

[tex]9 \times (7+9)[/tex]

[tex]9\times 16[/tex]

[tex]144[/tex]

This answer can be checked by summing the previous formula:

[tex]63 + 81[/tex]

[tex]144[/tex]

Answer:

1500%

Step-by-step explanation:

From March 2004 - March 2006, this is 2 years. The number of "6-month" period there are in 2 years is:

2* 12 = 24 months

24/6 = 4  "6 month periods"

So, it doubles "4" times in that time frame.

Let Initial population be 100 (In March 2004).

1 times double = 100 * 2 = 200

2 times double = 200 * 2 = 400

3 times double = 400 * 2 = 800

4 times double = 800 * 2 = 1600

So, population goes from 100 to 1600. How much percentage increase is that?

To get percentage increase, we find the increase and divide by original (initial amount). Then multiply by 100 to get percentage. So,

1600 - 100 = 1500 increase

1500/100 = 15

15 * 100 = 1500%

        Percentage increase in the number of blogs from March'04 to March'06 will be 1500%.

          [tex]P(t)=P_0(1+r)^t[/tex]

          Here, [tex]P(t)=[/tex] Final value

          [tex]P_0=[/tex] Initial value

          [tex]r=[/tex] Growth rate

          [tex]t=[/tex] Period of 6 months

Given in the question,

"Number of blogs are doubled in every six months"

[tex]P(t)=2P_0[/tex]

[tex]2P_0=P_0(1+r)^1[/tex]

2 = (1 + r)

r = 1 Or 100%

Therefore exponential function will be,

[tex]P(t)=P_0(2)^t[/tex]

To find the increase in blogs from March 2004 to March 2006,

Number of six monthly periods in 2 years = 4

[tex]P(4)=P_0(2)^4[/tex]

P(4) = 16(P₀)

Percentage increase in blogs = [tex]\frac{P(4)-P_0}{P_0}\times 100[/tex]

                                                  [tex]=\frac{16P_0-P_0}{P_0}\times 100[/tex]

                                                  = 1500%

     Therefore, percentage increase in the number of blogs will be 1500%.

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Answer: sides across from each other are parallel

- Diagonals bisect each other

- opposite sides are congruent

- opposite angles are congruent

Answer:

Answer: A = (x + 20)(x + 10) − 12 is the correct answer

Step-by-step explanation:

We would take the length and width of the patio and subtract it by the area that does not need to be painted.

I got this right on the test!

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Step-by-step explanation:

Answer: the interest owed is $21

Step-by-step explanation:

The question is incomplete. The complete question is:

Sari Tagore obtains a $1000 loan to purchase a laser printer. Her interest rate is 7% ordinary interest for 108 days. What is the interest owed?

Solution:

When calculating ordinary interest, we assume that a year has 360 days. We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I represents interest paid on the loan

P represents principal or amount borrowed.

R represents interest rate

T represents duration in years

From the information given,

P = 1000

R = 7%

T = 108 days. Converting to years, it becomes 108/360

Therefore

I = (1000 × 7 × 108/360)/100

I = $21

Answer:

add middle numbers and divide by two.

Step-by-step explanation:

When you need to find the median with an odd set of numbers, you arrange the numbers in order from least to greatest and find the number in the middle of the set:

1 2 3

median is 2.

But, when you have an even set of numbers, you take the two middle numbers, add them together, then divide them by two (it's like finding the mean of those two middle numbers):

1 2 3 4

2 3

2+3=5

5÷2=2.5

median is 2.5

Answer: take the middle two numbers and divide them

Step-by-step explanation: when you line them up orderly from lowest to highest you need to cross out the numbers until you reach the final 2 or 1. If you have one number left that number is the answer. If you are left with 2 numbers you add them together and divide them by 2 and you will get your answer.

Answer:

D

Step-by-step explanation:

65% × 78 =

(65 ÷ 100) × 78 =

(65 × 78) ÷ 100 =

5,070 ÷ 100 =

50.7;

Answer:

A 120

Step-by-step explanation:

you divide 120 by 0.65 to find 78

Answer: a) 15, b) 1.

Step-by-step explanation:

A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?

(a)    10% of all adult Americans support the changes

Here, [tex]np>5\ and\ n(1-p)>5[/tex]

And , [tex]p=0.10[/tex]

So, consider the equality, to find the value of 'n'.

[tex]np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50[/tex]

So, there are [tex]50-35=15[/tex] more adult Americans needed.

(b)   15% of all adult Americans supports the changes

Here, [tex]p=0.15[/tex]

So, again we get that

[tex]np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34[/tex]

So, there are [tex]35-34=1[/tex] more adult Americans needed.

Hence, a) 15, b) 1.

Final answer:

To find the extrema of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4, one must apply the method of Lagrange multipliers and solve for the critical points that satisfy both the original function and the constraint.

Explanation:

To find the maximum and minimum values of the function f(x, y, z) = x²y²z² subject to the constraint x² + y² + z² = 4 using Lagrange multipliers, we need to set up the Lagrange function, also known as the Lagrangian, which incorporates the original function and the constraint. The Lagrangian for this problem is L(x, y, z, λ) = x²y²z² + λ(4 - x² - y² - z²), where λ is the Lagrange multiplier.

We then take the partial derivatives of L with respect to x, y, z, and λ and set them equal to zero:

∂L/∂x = 2xyz² - 2xλ = 0

∂L/∂y = 2xy²z - 2yλ = 0

∂L/∂z = 2xyz² - 2zλ = 0

∂L/∂λ = 4 - x² - y² - z² = 0

By solving this system of equations, we can find the values of x, y, z, and λ that maximize or minimize the function f under the given constraint.

Answer:

It is 0.578

Step-by-step explanation:

0.00578

to 2 significant figures

0.00578

0.578

Final answer:

0.00578 rounded to two significant figures is 0.0058, as you only count the first two non-zero digits and apply the standard rules of rounding off.

Explanation:

To correct the number 0.00578 to two significant figures, we need to identify the first two non-zero digits as those are the ones considered significant. Here, the non-zero digits are 5 and 7. Therefore, to maintain two significant figures, we need to round the third digit (8), keeping in mind the rules of rounding: if the third digit is 5 or more, we round up the second digit by 1.

In this case, since the third digit is 8, which is more than 5, we round up the second digit by 1. Hence, the number becomes 0.0058. Since we must retain only two significant figures, we do not count the zeros before the '5' as they are merely placeholders. Finally, to two significant figures, 0.00578 is correctly rounded to 0.0058.

Answer: Please see answer in explanatory column

Step-by-step explanation:

STEP 1 - Since the survey is not an experimental one which occurs in a laboratory with a control and interference with sample.

Then the professor will use an observational study is in which he will observe the  behavior of the students  in a systematic manner without interfering with the students behavior so as to know how satisfied the students are with the course.   After getting to know how satisfied the students are for his course he would record the behavior that he or she observes and rate accordingly

STEP 2:The sampling strategy the Professor can use in carrying out the research is a Stratified sampling which occurs when the population to be observed is divided into groups known as strata which contains similar cases grouped together, then a second sampling, mostly a random sampling where the professor will randomly sample few students from the different strata to get his observations. for example, the students divided in 4 groups of 40 students represents each strata placed in common according to the different teaching assistant, then the professor can then randomly sample few students from each strata from a class of the 120 students.

This study is an observational study. A possible sampling strategy for this study could be stratified sampling.

(a) This study is an observational study since the researcher is not manipulating any variables or assigning participants to groups. The researcher is simply observing and collecting data on the students' satisfaction with the course.

(b) A possible sampling strategy for this study could be stratified sampling. The researcher could divide the 160 students into four strata based on their lab sections and then randomly select a certain number of students from each stratum to participate in the survey. This ensures that each lab section is represented in the sample.

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Answer:

The median is 102

Step-by-step explanation:

Median = a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.

Therefore, the answer 102 is correct.

(I need to be granted one more brainliest to level up so if my answer helped, it would be very much appreciated to award that to me, no obligations though!)

Answer: 9 and -4

Step-by-step explanation:

9 and 4 are both factors of 36, however we want to multiply to -36 so one of them must be a negative.

The two must also add up to 5, so that means -9 and 4 would not work as those would add to -5, leaving 9 and -4 left as the answer.

The value of two numbers multiply by -36 and added to 5 would be - 36 and 5.

Used the concept of the equation that states,

Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that,

The multiplication of two numbers = - 36

The addition of two numbers = 5

Let us assume that the two numbers are x and y.

Hence the equations become,

x + y = 5   .. (i)

And, xy = - 36  .. (ii)

From (i);

x = 5 - y

Substitute the above value in (ii);

(5 - y)y = - 36

5y - y² = - 36

y² - 5y - 36 = 0

y² - (9 - 4)y - 36 = 0

y² - 9y + 4y - 36 = 0

y (y - 9) + 4 (y - 9) = 0

(y + 4) (y - 9) = 0

This gives,

y = - 4

y = 9

Substitute both the values in (i);

Put x = - 4

x - 4 = 5

x = 9

Put x = 9;

x + 9 = 5

x = - 4

Therefore, the two numbers are 9 and - 4.

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Answer:

Step-by-step explanation:

Hello!

The variable of the study is

X: taxi fare from Logan Airport to downtown Boston.

This variable has a normal distribution

Suppose a sample of 7 taxi fares was taken and a 95%CI for the population mean was calculated obtaining:

$[20.51; 24.21]

The confidence level is a way of estimating the value of a population parameter of interest just like the point estimation. The difference is that instead of obtaining one value that may or may not be close to the true value of the parameter you obtain the range of values the parameter may take with a certain level of confidence.

The confidence level of an interval is the probability under which it is built. This probability indicates that if they build 100 confidence intervals, we expect 95 to contain the value of the parameter of interest we are trying to estimate.

As mentioned before in this case the parameter of interest is:

μ: population mean of taxi fares from Logan Airport to downtown Boston

And the 95% CI can be interpreted as:

We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.

I hope this helps!

Answer:

-1/2

Step-by-step explanation:

Use Rise over run

Rise 8 - 10 = -2

Run 2 - (-2) = 4

The slope is - 1/2

Answer:

The distribution of symmetrical to asymmetrical will change so that close to 100% of birds will have symmetrical wingspans.

Answer:

Refer below.

Step-by-step explanation:

The appropriation of symmetrical to asymmetrical will change so near 100% of flying creatures will have symmetrical wingspans.

Answer:Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.

Step-by-step explanation:

Answer:

1 + 2y + y²

Step-by-step explanation:

Suppose,we want to expand a given binomial of the form;

( 1 + y)ⁿ we will have

1 + ny + n(n - 1)y²/2! + n(n - 1)(n - 2)y³/3! + ....

hence:

( 1+y)² = 1 + 2y + 2(2-1)y²/2!

= 1 + 2y + y²

Answer:

it's 20

Step-by-step explanation:

I just had the same question and I got it right it's 20.

There are 20 flowers in the garden and there are 4 flowers that have a height that is 7 1/4 inches or greater

From the complete question, there are 20 points in the line plot.

Each point represents a flower

Hence, there are 20 flowers in the garden

Using the same line plot in (a), there are 4 points in the line plot where the flower height is either 7 1/4 or more

Hence, there are 4 flowers that have a height that is 7 1/4 inches or greater

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Answer:

[tex]\bar{x}= 200[/tex]

Step-by-step explanation:

We are given the following in the question:

Population mean = 200

Population standard deviation = 50

Sample size, n = 100

We have to estimate the expected value of the sample mean.

The best point estimate for the sample mean is the population mean.

Thus, we can write:

[tex]\bar{x}= \mu = 200[/tex]

Thus, the expected value of the sample mean is 200.

Answer:

A and B

Step-by-step explanation:

We are given that

[tex]g(x)=x^2-4x+3[/tex]

[tex]g(x)=(x^2-2\times x\times 2+4)-4+3=(x-2)^2-1[/tex]

Compare with it

[tex]y=(x-h)^2+k[/tex]

Where vertex=(h,k)

We get

Vertex of g=(2,-1)

[tex]f(x)=x^2-4x=(x^2-2\times x\times 2+4)-4=(x-2)^2-4[/tex]

Vertex of f=(2,-4)

Equation of axis of symmetry=x-coordinate of vertex

Axis of symmetry of g

x=2

Axis of symmetry of f

x=2

Differentiate w.r.t x

[tex]g'(x)=2x-4=0[/tex]

[tex]2x-4=0\implies 2x=4[/tex]

[tex]x=\frac{4}{2}=2[/tex]

[tex]f'(x)=2x-4[/tex]

[tex]2x-4=0\implies 2x=4[/tex]

[tex]x=\frac{4}{2}=2[/tex]

[tex]g''(x)=2>0[/tex]

[tex]f''(x)=2>0[/tex]

f and g have both minima at x=2

Hence, option A and B are true.

Answer:the sum of the remote interior angles is 95 degrees.

measure of a:85

measure of B:95

Step-by-step explanation:

i just took this

Answer: 95

Step-by-step explanation:

Answer: A ( the data in shelter A show more spread than the data in shelter B )

Step-by-step explanation:

Answer: A

Step-by-step explanation: shelter A

Answer:

a) Expected value = 6.406

Variance = 4.905

Standard deviation = 2.45

b) The probability is 0.08547

Step-by-step explanation:

a) Let's suppose that:

X₁ = number of 6´s

X₂ = number of Jack, Queen, King or Aces

The mean of X₁ is:

MeanX₁ = n * p = 20 * (1/6) = 3.33

The variance of X₁ is:

[tex]Var-X_{1} =np(1-p)=3.33(1-(1/6))=2.775[/tex]

The mean of X₂ is:

MeanX₂ = 10 * (16/52) = 3.076

The variance of X₂ is:

[tex]Var-X_{2} =3.076(1-(16/52))=2.13[/tex]

The expect value of X is:

Xexp = MeanX₁ + MeanX₂ = 3.33 + 3.076 = 6.406

The variance of X is:

VarX = VarX₁ + VarX₂ = 2.775 + 2.13 = 4.905

The standard deviation is:

Xdevi = 4.905/2 = 2.45

b) The probability of drawing at least five six out of 20 rolls is equal to:

∑(1/6)ˣ(5/6)²⁰⁻ˣ = 0.231 with x = 5

The probability of at least 4 Jack, Queen, Kings or Aces is:

∑(16/52)ˣ(1-(16/52))¹⁰⁻ˣ = 0.37 with x = 4

The probability of given event is equal to:

P = 0.231 * 0.37 = 0.08547